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<title>The Balanced-L Network</title>
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<h1><img src="../images/elect.gif" align="middle" width="145" height="75" border="2" vspace="5" hspace="9">The Balanced-L Network<img src="../images/w4rnlwwr.gif" align="middle" width="99" height="83" border="2" vspace="5" hspace="10"></h1>
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<h3>L. B. Cebik, W4RNL</h3>
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<p>The demise of the link-coupled antenna tuner has left a hole in the array of available antenna tuners. The link-coupled tuner had been the mainstay among tuners for handling antennas that present a wide range of impedance values to parallel transmission line and required--ideally--a balanced coupler to coincide with the transmission line balance. The multi-band doublet, the horizontal or vertical multi-band loop, and a host of phased arrays come to mind as antennas that achieve the greatest efficiency with a balanced antenna tuner. However, as of this writing (12-2002), despite some initial hope, no maker has come forward with a commercial link coupled tuner to replace the long-gone U.S. Johnson MatchBox or the German Annecke ATU.</p>
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<p>The single-ended network--including the PI, T, and L--is inherently unsuited to matching the impedances of such antennas, as presented to the ATU terminals, to the standard 50-Ohm unbalanced outputs of current transmitting and receiving equipment. Placing a 4:1 balun at the output terminals of such tuners has always been a source of concern, since the impedance at the terminals may be highly reactive, a condition unsuited to many balun designs. As well, the terminal impedance may also be low as the line transforms the impedance continuously along each half wavelength, and a 4:1 balun only succeeds in making it lower.</p>
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<img src="l-bal-1.gif" width="353" height="217" border="2" vspace="5" hspace="9">
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<p>A 1:1 choke balun has been used with some success. As <b>Fig. 1</b> shows, placing this choke-balun at the shack-entry point can serve two purposes. A. It converts the balanced line input to an unbalanced condition by essentially suppressing currents that would otherwise flow on the outside of the coax braid. B. It permits the installation of a good earth ground at the shack-entry point, which has some advantages for safety and for further isolation of equipment from common-mode currents.</p>
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<p>However, the advantages come at a price. The SWR on the coax inside the shack remains in many cases very high. The losses in this line due to SWR increase with both frequency and the length of the line and function as a multiplier on the basic loss per unit length of the coax line selected. The keys to minimal inside line loss are then to use as short as feasible a length of coax from the entry-point to the tuner and to use the lowest-loss coax that one can obtain. Even at QRP power levels, using a large diameter, low-loss length of coax for this run is extremely advisable.</p>
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<h4>The Balanced L-Network</h4>
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<img src="l-bal-2.gif" width="355" height="250" border="2" vspace="5" hspace="9">
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<p>Recent times have seen the development of balanced network tuners. <b>Fig. 2</b> shows a comparison between the single-ended L-network and its balanced counterpart, set up here for up conversion and in a low pass configuration. (A down conversion L-network would place the capacitor at the input side of the network. A high- pass configuration would use series capacitors and shunt or a parallel inductor.) The values required for converting a single-ended network to a balanced network are in the aggregate the same as those for the single-ended network. However, the inductors in the lower part of the figure are in series, so each has 1/2 the value of the required single-ended inductor.</p>
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<p>The capacitor, as shown, represents the total capacitance required across the network output to effect a match for a given impedance condition. With a single capacitor, we cannot place an earth ground at the line center as an aid to effecting balance between the two legs of the transmission line. In most, but not all, practical applications, this ground is not necessary. However, should we wish to implement such a line-centered ground, we may change the capacitor to a split-stator type and ground its common. Since the two halves of the capacitor must in series yield the required total capacitance for a match under given output terminal conditions, each half of the capacitor must have twice the capacitance of the single unit shown in the figure. This requirement result in large capacitors, especially where high power and high voltage across the plates might be anticipated. The vastly increased space requirements (or cost requirements for one who purchases such a component) generally has led designers to use single-section capacitors.</p>
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<p>The 1:1 balun in the balanced L-network appears at the input side of the network, between the balanced L and the line connector for the transceiving equipment. Except for brief periods during initial tune-up, the balun operates under ideal or close to ideal conditions, that is, with 50 Ohms resistive at its output terminals. Hence, most standard trifilar or bead-choke 1:1 balun designs operate at very high efficiency levels.</p>
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<img src="l-bal-3.gif" width="358" height="252" border="2" vspace="5" hspace="9">
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<p><b>Fig. 3</b> shows the balanced L-network--and its single-ended counterpart--set up as a down converter using a low-pass configuration. If we had used a high-pass configuration, with series capacitors and a parallel or shunt inductor, we would achieve a circuit identical to that of the beta or hairpin match. The hairpin match achieves its shunt inductive reactance with a shorted transmission line stub instead of a "lumped" inductor. Otherwise, all of the principles applicable to the up-converting L also apply to the down-converting L, whether single-ended or balanced.</p>
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<h4>Balanced L-Networks vs. 3-Component Networks</h4>Commercial implementations of the balanced L-network are beginning to appear. In general, they are offered in preference to balanced PI-networks and balanced T-networks. <b>Fig. 4</b> shows the general outlines of both of these 3-component networks in single-ended configurations. The PI is a low-pass configuration, while the T is a high-pass configuration.
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<img src="l-bal-4.gif" width="260" height="334" border="2" vspace="5" hspace="9">
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<p>The 3-component network offers a distinct advantage over the L-network. One may effect a match on a given frequency for any "in-range" impedance without switching a component from the output to the input side of the network (or vice versa). As well, one may even effect a match for a 50-Ohm resistive load at the antenna terminals of the tuner. In most cases, the user does not know what the load impedance is, and the ability to tune any load within the overall tuner range is a convenience.</p>
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<p>However, we pay a price for the convenience. For virtually any load impedance, the L-network has lower losses than the T or PI. We may define a factor for any of the networks and call it (following Terman) delta. In recent times, we have come to refer to the factor as the network Q or the working Q of the network. For the L-network,</p>
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<b>Delta = SQRT ((Ri/Ro)-1)</b>
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<p>where Ri is the network input impedance and Ro is the network output impedance.</p>
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<p>By itself, delta is simply a number. However, the network losses are directly related to the ratio of delta to the unloaded Q of the network components. In most--but not all-cases, the limiting component Q is that of the inductor. Maintaining a low loss network of any type requires that we uses network components with the highest possible unload values of Q.</p>
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<p>The calculations of delta for PI and T tuner networks are more complex. In the series "Antennas From the Ground Up, see the article <a href="../gup/gup14.html"><b>ATUs, Delta, and Tuner Losses</b></a> for further information on 3-component network losses, and the following item as well. The general outcome is this: for any matching conditions within the range of both an L-network and a PI or a T network, the L-network sill show lower losses (assuming that the components in all cases have the same unloaded Q values).</p>
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<p>However, the L-network, whether single-ended or balanced has a second inconvenience besides the requirement for switching the shunt component when going from up-conversion to down-conversion and back. The component values required to effect a match for impedances within a ratio of about 1.5:1 (or .67:1 for down conversion) relative to the input impedance tend to be impractical in a wide-band antenna tuner. Hence, for matching impedance above 35 Ohms but below about 75 Ohms, one must simply omit the L-network and feed the antenna directly (accounting for the shift from unbalanced coax to a balanced line, of course).</p>
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<p>Commercial implementations of the balanced network tuners tend to opt for the L- network because it achieves economy. Anyone who has priced high-voltage variable capacitors of either standard or vacuum design will easily note the saving accrued by eliminating one from the circuit. A patch panel, switch, or relay tends to be far less expensive. While this economy also affects ATU home- builders, the lower losses of the 2-component network may also be appealing, while the inconvenience of switching network ends with the shunt component may be accepted as the appropriate trade-off.</p>
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<h4>Balanced L-Network Component Values</h4>The next question concerning a balanced L-network concerns the components that we must use to effect a match with various loads. Using calculation methods developed by Brian Egan, ZL1LE, and available on recent version of <a href="../radio.html#HAMCALC">HAMCALC</a> from VE3ERP, we can survey those values from 160 to 10 meters. <b>Table 1</b> provides calculated data for some up- and down-conversion loads that are purely resistive.
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<pre> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Table 1. Calculated Values for L-Network matching to various Resistive loads
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from 15 to 2500 Ohms. All inductance values (L) in uH, all capacitance values
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(C) in pF. Loads are in Ohms.
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Up-Conversion Load = 100 Load = 250 Load = 500 Load = 1000 Load = 2500
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Freq. L C L C L C L C L C
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1.8 4.4 884 8.8 707 13.3 531 19.3 385 30.9 248
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3.75 2.1 424 4.2 340 6.4 255 9.3 185 14.9 119
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7.15 1.1 223 2.2 178 3.3 134 4.9 97 7.8 62
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10.125 .79 157 1.6 126 2.4 94 3.4 69 5.5 44
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14.175 .56 112 1.1 90 1.7 67 2.4 49 3.9 31
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18.118 .44 88 .88 70 1.3 53 1.9 38 3.1 25
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21.225 .38 75 .75 60 1.1 45 1.6 33 2.6 21
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24.94 .32 64 .64 51 .96 38 1.4 28 2.2 18
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29.0 .27 55 .55 44 .82 33 1.2 24 1.9 15
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Down-Conversion Load = 35 Load = 25 Load = 15
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Freq. L C L C L C
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1.8 2.0 1158 2.2 1768 2.0 2701
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3.75 .97 556 1.1 849 .97 1296
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7.15 .51 291 .56 445 .51 680
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10.125 .36 206 .39 314 .36 480
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14.175 .36 147 .28 225 .26 343
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18.118 .20 115 .22 176 .20 268
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21.225 .17 98 .19 150 .17 229
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24.94 .15 84 .16 128 .15 195
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29.0 .13 72 .14 110 .13 168
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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
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<p>The table uses amateur-band center frequencies for all but the limiting bands, where we use a low frequency for 160 meters and a high (but not the highest) frequency on 10 meters.</p>
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<h4>Maximum and Minimum Component Values</h4>For up-conversion, the maximum component values are all feasible, even on 160 meters. However, for down-conversion, the lower the impedance, the greater the chances for requiring a capacitance value that exceeds practical implementation as a standard-construction high-voltage air-variable capacitor. A 3000-pF, 5-kV or higher air-variable is a very large unit, indeed.
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<p>The inductor--with respect to maximum required component values--is not a problem. The table lists the total for the 2 series inductors, so each inductor requires only half the total. A pair of inductors, each with a 20 uH maximum value, would easily handle the required load.</p>
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<p>The troublesome part of the patterns of required component values concerns minimums. The values given are--in a practical circuit--the sum of the component values and any stray capacitances and inductances within the overall ATU unit. The minimum capacitance available is partly a consequence of capacitor construction. Many capacitors--especially military surplus units found at hamfests--use heavy frames with full size end plates and even bottom plates that cover most of the bottom of the capacitor. Such units may have a minimum capacitance of up to 30 pF for a maximum capacitance of 150-200 pF. In contrast stand the E. F.Johnson (later, Cardwell) high-voltage units that have small trapezoidal end plates and a bar running the length of the unit to connect the end plates and permit mounting. For the same maximum capacitance, the minim is only 12-15 pF. Even better are some current designs that use non-conductive end plates and front-to-rear bracing bars. Their minimum value may be as low as 8-9 pF. Some capacitors also use plate-shaving techniques to further lower the minimum capacitance.</p>
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<p>However, minimum capacitance is not solely a function of the capacitor structure. The plates and other components of the network may be at a different potential from each other, from nearby leads, and from the metal ATU case. In all of these instance, we have a level of capacitance that we cannot eliminate with redesign of the circuit and the overall unit. The simplest way to tell if a case is introducing stray capacitance is to remove it and check the ATU settings under very low power and otherwise controlled test conditions.</p>
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<p>As the basic table shows, minimum inductance can be a major limitation in down conversion. All is not lost in this regard, even if the minimum inductance that we can obtain is higher than the required component value. Down conversion tends to be very broad-band, and one can obtain usually a match to within less than 1.5:1 50-Ohm SWR, a useful if not perfect value.</p>
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<p>Adding to the series combination (additive) of the two inductors in a balanced L-network is the inductance of the leads. The more complicated the switching-- whether we are switching in a fixed capacitor to achieve a high value or switching the capacitor from the output to the input end of the network--the more likely we are to find stray inductance that raises the minimum value that we may obtain. A secondary problem associated with stray inductance within an ATU is the fact that is usually has a low unloaded Q. Hence, the loss level of the circuit rises.</p>
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<p>The appropriate countermeasures, of course, include a detailed inspection of the circuit to see if one can redesign component placement to keep leads as short as feasible. With large components designed for high power duty, we can do only so much in this arena. We can also try replacing the case with a non-conductive case. To a large measure, any radiation from an ATU is a function of linear leads that do nothing to confine the fields that surround them. Hence, it is a bit of a gamble to move to a non-conductive case. However, it is worth a try. If the radiation is too high and eludes efforts to reduce it, then one can simply use a larger case within which we try to center the network components, that is, we try to keep the network components well-spaced from the case walls.</p>
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<h4>Reactive Loads</h4>We have based our initial survey of the conditions under which a balanced L- network must operate on resistive loads. As a general guide, let's look at some sample cases of reactive loads. In <b>Table 2</b>, we shall examine some high- and low- impedance loads, each impedance having a 45-degree phase angle. Hence, we shall match 100 Ohms resistance with +j100 Ohms and with -j100 Ohms. In addition, we shall only look at 160, 80, and 10 meters, the HF frequencies likely to represent the limits of an ATU that we might construct.
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<pre> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Table 2. Calculated Values for L-Network matching to various Resistive +/-
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Reactive loads from 100 to 2500 Ohms. All inductance values (L) in uH, all
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capacitance values (C) in pF. Loads are in Ohms.
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Up-Conversion R = 100 R = 100 R = 2500 R = 2500
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X = j100 X = -j100 X = j2500 X = -j2500
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Freq. L C L C L C L C
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1.8 7.7 1208 7.7 324 44.0 194 44.0 158
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3.75 3.7 580 3.7 155 21.1 93 21.1 76
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29.0 .48 75 .48 20 2.7 12 2.7 10
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Down-Conversion R = 35 R = 35 R = 15 R = 15
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X = j35 X = -j35 X = j15 X = -j15
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Freq. L C L C L C
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1.8 2.8 2062* 5.1 1158 0.7 2701 3.4 2701
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3.75 1.3 990* 2.5 556 .34 1297 1.6 1297
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29.0 .17 128* .32 72 .04 168 .21 168
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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
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<p>The starred entries in the down-conversion portion of the table indicate that the required configuration of the balanced L-network is for up-conversion, that is, with a shunt output capacitor. Note the high values of capacitance required for both 160 and 80 meters. such values will likely fall outside the range of what we build into either a 160-10-meter or an 80-10-meter ATU.</p>
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<p>At the highest frequency for which I calculated values, down conversion requires the smallest inductance values. 0.2 uH will be difficult enough to attain with the best components; 0.04 uH is outside of practical reality in a multi-band tuner.</p>
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<p>For an interesting home-brew balanced-L tuner using tapped coils, see the website of Adam, N4EKV: <a href="http://www.n4ekv.com/tuners.asp" target="_blank"><b>www.n4ekv.com/tuners.asp</b></a>.</p>
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<h4>Why 160 or 80 Meters Through 10 Meters?</h4>I once designed an SPC single-ended network tuner for 20-10 meters due to the relatively poor performance on my C-L-C single-ended T-network tune on the highest bands (12, 10). No single cause attended the weakness in the 80-10-meter ATU, but the component minimum values and a tight-fitting metal case all contributed to 10-meter problems with a 100' doublet. The SPC unit used Johnson 4.5 kV air variables (a 50 pg single unit and a 50-50 pF split stator), and the rotary inductor had a maximum inductance of 6 uH. The case was no deeper than the original, although the components were considerably shorter. My case was both wider and higher than the commercial case. These measures doubled--at least--the range of matchable impedances, and the component Q was sustained at least through 30 MHz.
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<p>Similar thinking is applicable to a balanced L-network. Although we tend to think of an 80-10-meter ATU as some sort of standard, only our demand for convenience has created that standard. Neither commercial nor handbook designs covering those bands tend to address either the range of matchable impedances as it changes with frequency or the loss of component Q with increasing frequency due to strays.</p>
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<p>Consequently, it is up to the individual ATU builder to design a unit to meet his or her needs and having the highest component Q available. If attaining a wide tuning range on the upper HF bands requires one to reduce the coverage to 20-10 meters to achieve this goal, then perhaps this is the route to go. In many cases, we shall have to suffer with the shortcomings of a wide-band unit, since it is difficult to carry individual ATUs for each band to a DXpedition on a remote island. Nevertheless, we are not under such restrictions at the home station. As well, it is often easier to find rotary coils with low values at good prices, since they are in far less demand then units with a maximum inductance ranging from 10 to 30 uH.</p>
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<p>These notes certainly do not cover every aspect of balanced L-networks. However, they may serve to alert you to both the potentials and the limitations of these substitutes for the link-coupled tuner.</p>
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<br>
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<p><i>Updated 12-13-2002. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.</i></p>
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<img src="../images/colorbar.gif" align="middle" width="540" height="4">
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<p><a href="../radio.html"><img src="../images/return.gif" align="bottom" width="40" height="40"> Go to Amateur Radio Page</a></p>
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<p class="topics-footer">Topics: <a href='../topics.html#matching'>Matching</a></p><br>
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<title>Link-Coupled Antenna Tuners</title>
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<h1><img src="../images/elect.gif" align="middle" width="145" height="75" border="2" vspace="5" hspace="9">Link-Coupled Antenna Tuners<img src="../images/w4rnlwwr.gif" align="middle" width="99" height="83" border="2" vspace="5" hspace="10"></h1>
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<center>
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<h3>L. B. Cebik, W4RNL</h3>
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<p>We have gone to great lengths to adapt unbalanced antenna tuners (ATUs or transmatches) to service with balanced lines. Among the schemes used are the following most common ones:</p>
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<p>1. Float the tuner from ground and install a balun at the input end;</p>
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<p>2. Install a balun, usually 4:1, at the antenna side of the tuner, to convert the balanced line to an unbalanced line;</p>
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<p>Either system is subject to limitations. Floating the tuner does not guarantee freedom from common-mode currents that defeat balance. A 4:1 balun often reduces the already low impedance at the antenna terminals to a still lower one, and high reactances are normally unfriendly to the cores used in such baluns.</p>
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<p>It is possible to build perfectly usable balanced network tuners. However, the parts count goes up, and ganging the components often presents further building and size difficulties. However, in the search for an ATU design that will handle balanced lines naturally, balanced PIs and Tees should not be overlooked by adventuresome home builders. A simple 1:1 balun on the transmitter side converts the resistive balanced input load to the unbalanced line for which the transceiver is designed.</p>
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<p>To make a balanced network, chose a good unbalanced network as a model. Look at the series elements. Put one in each line in corresponding positions, but use half the reactance. For a coil, that is half the inductance; for a capacitor, that is twice the capacitance. Now look at the shunt component(s), those from the series line to ground in the unbalanced network. Use the same value across the two lines of the balanced network. This simple conversion leaves the system center floating, but that is rarely a problem. Do not forget to add the balun (1:1, 50 ohms) at the input. And remember that there is no safe place to put your finger when the system is hot.</p>
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<p>A more classic alternative is the link-coupled or inductively coupled ATU. The figure shows the basic circuitry. The unbalanced input is inductively coupled to the main inductor. Since the mutual inductance between the coils is critical for maximum efficiency, the coupling is varied either by a movable link or by a series input capacitor.</p>
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<img src="link1.gif" width="369" height="432" border="2" vspace="5" hspace="9">
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</center>
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<p>The output is shown in a typical parallel configuration. To effect the best match, clips are provided to connect the line to the proper turns on the main inductor, as determined by maximum feedline currents. The split- stator capacitor or dual ganged capacitors can be connected to ground so that the system is balance with respect to system ground, as shown at *. However, the tuner will remain balanced if the ground is lifted.</p>
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<p>The ** point indicates that the rotators of the capacitors may be separated and lifted from ground. In this case, they can be connected to the output terminals instead of using a coil tap. For further flexibility, the stators can be connected to various taps on the coil for maximum output. This configuration, often called the series connection, permits efficient matching to low impedances presented at the output terminals of the ATU.</p>
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<p>To the best of my knowledge, no one in the U.S.A. is currently producing such a tuner commercially. Chapter 25 of recent <i>ARRL Antenna Books</i> has a simple tuner with some limitations in link-main coil coupling efficiency, but not a bad start. The only commercial unit I know of was made in Germany until a few years ago.</p>
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<p>Despite their relative scarcity, link-coupled tuners have certain advantages over all other tuners. First, they are inherently designed for use with balanced feedlines. Second, they exhibit very low losses, even at high power levels with reasonable care of construction. Third, they can be configured to almost any balanced line condition that might face the operator.</p>
|
||||
<p>However, they also have certain disadvantages. First, they do not lend themselves to automated or rapid changes in setting and configurations as one changes bands. Second, they work best when equipped with plug-in coil sets that permit the most optimal coil-link size ratios.</p>
|
||||
<p>A network tuner provides the most efficient match when its variable components are truly variable rather than switched. This principle applies especially to the inductor. A switched inductor may provide a 1:1 match at one or more settings, but it does not necessarily permit the use of the most efficient (lowest loss) setting of the coil. Likewise, a single coil and link for all HF bands does not provide the best coupling ratios for all possible conditions. Without provision for coil tapping and series connections, the most efficient operating mode may be inaccessible, despite a 1:1 match.</p>
|
||||
<p>For a "hurry-up" operator, these inconveniences may be worse than the losses inherent in current systems pressed into balanced-line duty. However, for operators seeking the most efficient transfer of power to balanced lines, nothing beats a properly designed and constructed link- coupled ATU.</p>
|
||||
<p>Will we ever see link-coupled tuners on the market--or even the components necessary for us to roll our own? These include reasonably priced capacitors or capacitor sets, along with plug-in coil systems similar in concept to some of the old Millen sets. (I doubt that, even under the best of conditions, that we shall see reasonably priced swinging link sets.)</p>
|
||||
<p>Here is a wide-open field for the entrepreneur who understands both the concepts of link coupled tuners and has the know-how to develop well constructed plug-in coil assemblies and allied components. If parts and designs were available, I'll bet there is a customer base that would make the venture mildly profitable at the 100-200 watt level and at least break- even at the 1500 watt level. (For QRP work, I would use nothing less than a 100-200 watt ATU to minimize losses associated with tiny layouts and components. I would reserve the super-tiny--for example, compact Z- matches--for field work, where size and weight reductions may overshadow potential losses.)</p>
|
||||
<p>To this moment, I have received no direct word of a return of the Annecke tuner to the marketplace or of a modern replacement for the Johnson Matchbox. Parts, especially coil stock for the inductor and link, may have become prohibitively expensive. As well, there is a fiercely competitive market for single-ended network tuners equipped with various types of toroidal baluns (transmission-line transformers) to handle balanced lines. However, interest in inherently balanced tuner designs, such as the link coupled tuner and some balanced network tuners with 1:1 choke baluns on the 50-Ohm side of the system remains quite high. Interestingly, the latest and most competent of the single-ended network tuners seem to be priced in the range one might expect for a link tuner of the same power-handling capability. Balanced network tuners are even more costly. Indeed, the manufacturing economies inherent in network tuners may likely have removed the possibility of any return to commercially-made link-coupled tuners.</p>
|
||||
<center>
|
||||
<h3>The Johnson Matchbox and the Annecke Parallel-Line Tuners</h3>
|
||||
</center>I have heard the Johnson Matchbox described as a modified Z match, which is not quite right. Having obtained one, I thought I might describe the circuit, which appears to be very similar to the link coupler offered by Annecke in Germany.
|
||||
<p>The circuit is a straightforward link-coupled circuit. The input with the relay and associated circuitry includes taps for a 50-ohm transmitter connection and a 300-ohm receiver connection, since receivers continued to used balanced input strips long after transmitters had gone to shielding, pi networks, and 50-ohm outputs.</p>
|
||||
<center>
|
||||
<img src="link2.gif" width="615" height="326" border="2" vspace="5" hspace="9">
|
||||
</center>
|
||||
<p>The Johnson Matchbox uses a single link for all bands with no variability. The Annecke design does away with the relay, receiver tap, and other pre-50-ohm transceiver features. Instead, it uses a larger (overcoupled) link with taps for the various bands (80, 40, 30-20, 17-15, and 12-10) mechanically linked to the secondary coil tap switches. In addition, it employs a series variable capacitor to adjust coupling (or input impedance, which amounts to the same thing). The Annecke design is superior in this regard.</p>
|
||||
<p>The secondary systems of both the Matchbox and the Annecke are almost identical, differing only in output connection options. The secondary coil is tapped at reasonable positions for 80/40/20/15/10 meters, shorting out the unused turns toward the outer ends. Although the Annecke is marked with the preferred settings for the WARC bands, Matchbox users will have to experiment on these bands. Across the outer limits of the coil is a split stator capacitor, center grounded, which is used to set the tank at resonance. The required value of capacitance will vary somewhat as the reactance and resistance at the antenna terminals is varied.</p>
|
||||
<p>The terminals are not connected directly to the outer limits of the tank. Each side of ground passes to a differential capacitor. The center of each differential goes to the antenna terminal. A differential capacitor is a split stator variable arranged so that as capacitance on one side goes up, it decreases on the other. The antenna terminal on each side of ground is thus set at a certain reactance from ground and certain series reactance from the tank. This arrangement is said to form a voltage divider. It also forms a means of compensating for reactance at the antenna terminal of the tuner, allowing it to match a wide range of R+/-jX combinations that might be present at the antenna terminals and still present the requisite high impedance to the tank circuit ends. Because the entire series combination of capacitance (and capacitive reactance) appears across the tank circuit and the load, the function of the differential capacitors is not so simple as this brief note might lead one to believe.</p>
|
||||
<p>The design goes back to AM days, so the 275 watt rating is likely not only conservative, but conservative to the power of the carrier plus side bands of a 100% modulated AM signal. Capacitors appear to be spaced for at least 3 kV or better. The KW matchbox uses the same circuit with beefed up components and only some slight connection changes. The Annecke unit is rated at 200 watts and appears (from the photo of the case and the control arrangement) to use slightly lighter components than the Johnson, even though the 200 watt rating is also conservative.</p>
|
||||
<p>Perhaps the only thing I would do to improve the design is not mechanically feasible: to have a rotary coil with contra-rotating sections (in line) to permit the full span of taps in order to eliminate the switch. The goal is to make available the most efficient coil settings for every possible set of R+/-jX presented, but I have no idea of how to make that work mechanically and preserve the center link and main coil center efficiency.</p>
|
||||
<p>I thought those who have never seen a Matchbox might be interested in the basic design. (Love those elegant Johnson panel colors used after about 1960, similar to the colors on my own QSL, but not intended that way.) I have come across two photos, one of the 275 watt unit without meter for SWR through the external directional coupler, and the other with the available couplers on top and the meter in place. The difference in the panel lettering is a clue as to which is older and which is younger.</p>
|
||||
<center>
|
||||
<img src="mb1.jpg" border="2" vspace="5" hspace="9" width="422" height="301">
|
||||
</center>
|
||||
<center>
|
||||
<img src="mb2.jpg" border="2" vspace="5" hspace="9" width="482" height="403">
|
||||
</center>
|
||||
<p>The rearside detail is also interesting for those who might wish to home brew a link tuner or for those wishing to know what to expect from the unit. Jan Axing, SM5GNN, provided photos of the rear of his unit, which does not have the coupler. My thanks for his thoughtfulness. The 275-watt Match Box is about 10" wide, 10" deep, and 7.5" high.</p>
|
||||
<center>
|
||||
<img src="nye%20matchbox%20back.jpg" border="2" vspace="5" hspace="9" width="640" height="480">
|
||||
</center>
|
||||
<center>
|
||||
<img src="nye%20matchbox4.jpg" border="2" vspace="5" hspace="9" width="640" height="480">
|
||||
</center>Phil Grill, KA2IWR, sent me photos of the Nye-Viking version of the Matchbox. Nye obtained rights to the Matchbox when Johnson ceased production. The Nye version omits the relays from the start, since the transceiver had already become the main type of amateur rig. However, Nye either used surplus Johnson cases or the dies for punching cases, since the relay terminal strip cut-out is evident. Due either to increased difficulties in obtaining parts or the prevalent hype about single-ended network tuners, Nye ceased making the Matchbox clone and turned to a single-ended design. So Nye Viking Matchboxes are not common.
|
||||
<center>
|
||||
<img src="mbrear.jpg" border="2" vspace="5" hspace="9" width="600" height="438">
|
||||
</center>
|
||||
<center>
|
||||
<img src="mbins.jpg" border="2" vspace="5" hspace="9" width="380" height="227">
|
||||
</center>
|
||||
<p>The circuitry of the KW version of the Match Box is virtually identical to that of the smaller 275 watt version, although considerably beefier. Instead of a ceramic terminal for single-ended antennas, there is a coax connector. For identificatioin purposes, here are photos, front and back, of the KW Match Box, but they appear to be of different units. The front shows the later paint scheme, while the back shows the earlier logo without the "J" behind the Viking. You can gauge the relative size difference between the 275 watt and KW versions from the directional couplers on top of the respective units. My thanks to Peter, SM5HUA, for the photos.</p>
|
||||
<center>
|
||||
<img src="mbkw.jpg" border="2" vspace="5" hspace="9" width="600" height="451">
|
||||
</center>
|
||||
<center>
|
||||
<img src="mbkwb.jpg" border="2" vspace="5" hspace="9" width="600" height="373">
|
||||
</center>
|
||||
<p>A copy of the Johnson Manual--used for both sizes of the Match Box--can be obtained from <a href="ftp://bama.sbc.edu/downloads/johnson/matchbox/">K4XL's BoatAnchor Manual Archive</a>. Incidentally, the 1963 prices for the Johnson Matchbox were $64.95 for the 275 W unit less the indicator, $94.94 for the same unit with the SWR indicator, and $154.50 for the 1 KW Matchbox.</p>
|
||||
<p>At some point in the production of Matchboxes, Johnson added an extended range tuner covering about 2 to 30 MHz, with obvious applications to the 160-meter amateur band. Harry MacLean, VE3GRO, sent me the following panel close-up of the extended range version that he has. It is a 275-watt model, and I do not know if there was an extended-range KW version of this design.</p>
|
||||
<center>
|
||||
<img src="mb-ext.jpg" border="2" vspace="5" hspace="9" width="800" height="600">
|
||||
</center>Note the "auxiliary" control at the top left corner of the main panel. As Harry describes the interior, "The coils--both main and link--are the same as in the 5-band ham matchbox, but the variable capacitors all have double the number of plates. The auxilary capacitors are switched in on only the three lower ranges. Ranges are 2-3.5, 3.5-5, 5-7 7-9, 9-14, 14-21.6, and 21.6-30 Mhz." Harry has used the unit on 160 meters be adding a couple of turns to the ends of the main coil.
|
||||
<p>My photocopies of the Annecke case are black and white, so I do not know the color scheme (although it appears to be black and white). The outer case thickness gives the impression of battleship construction. Catalog price (now out of date) was 495 DM. I have since learned (Jan. 4, 1999) that the Annecke company is no longer in business due to the severe illness of its owner. So far as I know, the designs have not been bought or otherwise picked up by any other company. It is indeed regretable that the only surviving major commercially-made link-coupled antenna tuner is no longer available. Now European hams can feel the loss of these units as keenly as we U.S. hams feel the loss of the old faithful Match Box. However, any entrepreneur will tell me that now the market is clear for the first manufacturer who presents us with a new match box. (Late note: Annecke may have been purchased by a Dutch ham. Will post more as it is learned.)</p>
|
||||
<p>Courtesy of Jan Anker, ON4CAF/PA0LBN, I can show something of the inside of the Annecke unit. The first photo is of the inside from the bottom rear, showing the split-stator tuning capacitor to the left. The input tuning capacitor is to the right.</p>
|
||||
<center>
|
||||
<img src="annecke1.jpg" border="2" vspace="5" hspace="9" width="305" height="220">
|
||||
</center>
|
||||
<p>The second photo is of the interior from the top rear, showing the differential capacitor to the right (with the input capacitor nbow to the left). Since the two large capacitors are vertically aligned, a single photo cannot show both.</p>
|
||||
<center>
|
||||
<img src="annecke2.jpg" border="2" vspace="5" hspace="9" width="320" height="240">
|
||||
</center>
|
||||
<p>The last photo is of the coil assembly, which is remarkably similar to the scheme used in the Johnson Match Box. For maintenance of circuit balance, symmetry is essential.</p>
|
||||
<center>
|
||||
<img src="annecke3.jpg" border="2" vspace="5" hspace="9" width="320" height="240">
|
||||
</center>
|
||||
<p>The 200-watt Annecke unit is about 5" high, 10" deep, and 12" wide. Personally, I would have left a bit more room in the cabinet to reduce stray capacitance, but I certainly would not refuse to use the Annecke unit.</p>
|
||||
<p>Again, courtesy of ON4CAF/PA0LBN, here is a photo of the schematic on the back of the Annecke unit. In case the cvalues are hard to read, the split stator os 155 pF per section, the differential is 100 pF per section, and the input capacitor is 270 pF.</p>
|
||||
<center>
|
||||
<img src="annesch1.jpg" border="2" vspace="5" hspace="9" width="479" height="359">
|
||||
</center>
|
||||
<p>One bad habit of all antenna tuner makers is to list a simple impedance range for the antenna matching capabilities, for example, 50-3000 ohms for the Annecke. Actually, the ability of any tuner to effect a match is determined by the combination of R and jX at the antenna terminals. Whatever the reactance-compensating scheme, it will have some limitations, usually being more effective with large values of either jX or -jX, but not both. Moreover, the range of impedances for which any given tuner design can achieve maximum efficiency is ordinarily quite a bit narrower than for achieving a mere 1:1 SWR on the transmitter side. However, bringing the impedance presented to the antenna terminals within the range of the tuner's maximum efficiency potential is usually only a transmission-line length change away.</p>
|
||||
<p>In early 2004, Anthony (Tony) Brent, WD7G, sent me some useful notes on the availability of components for anyone wishing to replicate either of the classic link tuner designs. With his permission, I shall simply quote what he wrote.</p>
|
||||
<blockquote>
|
||||
<p>I thought I would pass along some information to you that I have found that will be of interest to anyone who wants to build such a tuner.</p>
|
||||
<p>I recently ordered new manufacture Johnson variable capacitors which are duplicates of those used in the Johnson Matchbox. Cardwell Condensers in New Jersey is manufacturing these units, and also Hammarlund variable capacitors under the original Johnson and Hammarlund part numbers, so these nice variables are indeed available again brand new in the box.</p>
|
||||
<p><a href="https://cardwellcondenser.com/" target="_blank">www.cardwellcondenser.com</a></p>
|
||||
<p>I spoke with Paul Meyer, who was very helpful. He informed me that Cardwell can also manufacture custom variable capacitors to customer's specifications.</p>
|
||||
<p>I ordered two Johnson 154 series capacitors, a single section 450 pF 2000 volt for $75, and a dual section 330pF 2000 volt for $150. See the attached photo. Not exactly ham fest prices, but not that outrageous either. A builder ought to be able to come up with a finished Matchbox for somewhere in the neighborhood of $250 to $300, I would think, and that isn't bad given the price of most of the mid- to high-power T-network tuners on the market today.</p>
|
||||
<p>Cardwell also has various fixed and variable inductors, and the old stand-by Velvet Vernier drives.</p>
|
||||
<p>Jackson Brothers in England also have variable capacitors available at their web site: <a href="https://web.archive.org/web/20080324130535/http://www.mainlinegroup.co.uk/jacksonbrothers/" target="_blank">www.mainlinegroup.co.uk/jacksonbrothers/</a> (web.archive.org)</p>
|
||||
<p>They also have the nice Jackson Brothers vernier drives and other parts that may be useful.</p>
|
||||
<p>The remaining hurdle is the coils. B and W are still in the coil stock business, but they are quite expensive, and some times out of stock. I have experimented with a method of coil winding that the British and Australian amateurs have been using that works very well, and is quite easy to do.</p>
|
||||
<p>Their trick is to use an acrylic or polycarbonate sheet laid out and drilled for the proper coil diameter and spacing. One set of holes is offset by half the coil spacing from the other so the coil will advance at the proper pitch when wound through the holes. One extra hole is added at each end of one line of holes for the start and finish of the winding. The other row has the same number of holes as the number of turns in the coil.</p>
|
||||
<p>The wire is wound on a former a little smaller than the finished diameter, and then is threaded through the holes in the acrylic, which hold the coil to its proper dimensions and keeps everything in place while only touching the wire at two points along the coil. It also provides a secure means of mounting the coil by using brackets fastened to the acrylic. It works very well.</p>
|
||||
<p>I imagine other materials could also be used. I happened to have some acrylic on hand so I gave it a try. I was very pleased with how well it worked.</p>
|
||||
<center>
|
||||
<img src="wd7g.jpg" border="2" vspace="5" hspace="9" width="800" height="600">
|
||||
</center>
|
||||
<p>See the attached photo, which is my attempt at a single coil Z match tuner following the design work of Lloyd Butler, VK5BR (<a href="https://www.qsl.net/vk5br/" target="_blank">www.qsl.net/vk5br</a>) Interesting circuit that I am still playing with, but I think I still prefer the Matchbox circuit.</p>
|
||||
<p>The same type of coil former ought to work well for winding a Matchbox style coil and link, and perhaps with some extra holes to hold the wires for the coil taps, so they don't depend only on the solder joint.</p>
|
||||
</blockquote>
|
||||
<center>
|
||||
<img src="../images/colorbar.gif" align="middle" width="540" height="4">
|
||||
</center><br>
|
||||
<br>
|
||||
<p><i>Updated 5-23-1999, 12-30-2000, 08-16-2002, 09-01-2003, 03-01-2004, 09-12-2004, 08-04-2006. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.</i></p>
|
||||
<center>
|
||||
<img src="../images/colorbar.gif" align="middle" width="540" height="4">
|
||||
</center>
|
||||
<p><a href="../radio.html"><img src="../images/return.gif" align="bottom" width="40" height="40"> Go to Amateur Radio Page</a></p>
|
||||
<p class="topics-footer">Topics: <a href='../topics.html#matching'>Matching</a></p><br>
|
||||
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||||
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||||
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||||
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||||
<head>
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||||
<meta charset="UTF-8">
|
||||
<meta name="keywords" content="Matching">
|
||||
<title>Link-Coupled Antenna Tuners Index</title>
|
||||
<link rel="stylesheet" href="../styles.css">
|
||||
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|
||||
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|
||||
<center>
|
||||
<h1><img src="../images/elect.gif" align="middle" width="145" height="75" border="2" vspace="5" hspace="9">Link-Coupled Antenna Tuners: A Tutorial<img src="../images/w4rnlwwr.gif" align="middle" width="99" height="83" border="2" vspace="5" hspace="10"></h1>
|
||||
</center>
|
||||
<center>
|
||||
<h3>L. B. Cebik, W4RNL</h3>
|
||||
</center><br>
|
||||
<br>
|
||||
<center>
|
||||
<img src="../images/colorbar.gif" align="middle" width="540" height="4">
|
||||
</center><br>
|
||||
<br>
|
||||
In recent editions of various amateur radio handbooks in English, information on inductively coupled (link-coupled) antenna tuners has decreased just to the degree that data on unbalanced network tuners has increased. We may be passing a certain critical threshold below which the information is insufficient for a good understanding of inductively coupled circuits. In response to a number of requests, I have pulled together materials from some older sources (from the 1940s through the 1970s) to make available a more complete and hopefully more cohesive account of link- coupling. The account might be made even more complete, but at the risk of making it excessively obscure. As with every tutorial, one draws a line and takes a risk that enough has been shown to aid understanding without breeding misunderstanding from what has not been said.
|
||||
<ul>
|
||||
<li><b><a href="link1.html">Part I: Inductive Coupling</a></b></li>
|
||||
<li><b><a href="link2.html">Part II: The Input Story</a></b></li>
|
||||
<li><b><a href="link3.html">Part III: The Output Story</a></b></li>
|
||||
<li><b><a href="link4.html">Part IV: Series Circuits and Reactance</a></b></li>
|
||||
<li><b><a href="link5.html">Part V: Components, Construction, and Measurement</a></b></li>
|
||||
</ul><br>
|
||||
<br>
|
||||
<center>
|
||||
<img src="../images/colorbar.gif" align="middle" width="540" height="4">
|
||||
</center><br>
|
||||
<br>
|
||||
<p><i>Updated 11-25-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.</i><br>
|
||||
<br></p>
|
||||
<center>
|
||||
<img src="../images/colorbar.gif" align="middle" width="540" height="4">
|
||||
</center><br>
|
||||
<br>
|
||||
<a href="../radio.html"><img src="../images/return.gif" align="bottom" width="40" height="40"> Go to Amateur Radio Page</a><br>
|
||||
<br>
|
||||
<br>
|
||||
<p class="topics-footer">Topics: <a href='../topics.html#matching'>Matching</a></p><br>
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<title>Link-Coupled Antenna Tuners Part I: Inductive Coupling</title>
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||||
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||||
<h1><img src="../images/elect.gif" align="middle" width="145" height="75" border="2" vspace="5" hspace="9">Part I: Inductive Coupling<img src="../images/w4rnlwwr.gif" align="middle" width="99" height="83" border="2" vspace="5" hspace="10"></h1>
|
||||
</center>
|
||||
<center>
|
||||
<h3>L. B. Cebik, W4RNL</h3>
|
||||
</center><br>
|
||||
<br>
|
||||
<center>
|
||||
<img src="../images/colorbar.gif" align="middle" width="540" height="4">
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||||
</center><br>
|
||||
<br>
|
||||
Link-coupled--or inductively-coupled--antenna tuners virtually disappeared from the amateur market almost a quarter century ago. In their place came network tuners, most notably the C-L-C Tee network and its variants: the Universal Transmatch of Lew McCoy, and the SPC brought to our attention by Doug DeMaw. Although these networks perform admirably with unbalanced (coaxial) cables, they require special accommodations for balanced (parallel) transmission lines. As a result, there is a growing new interest in link-coupled tuners, along with a continuing interest on the part of many wire antenna users.
|
||||
<p>Just as interest grows, the number of available link-coupled tuners continues to dwindle. Moreover, parts for such tuners grow scarcer. Along with the depletion in tuners and parts, there is also a scarcity in available information on the operating and construction principles underlying the link-coupled tuner. This series of articles is designed at least to correct the information part of the problem. Restoration of the parts supply and the inventory of complete units is another problem entirely.</p>
|
||||
<center>
|
||||
<h3>The Need</h3>
|
||||
</center>Although numerous hams have found ways of adapting single ended antenna tuners to service with balanced lines, perfectionists see many remaining problems. Some tuners use baluns at their outputs, and these units may be (depending upon design) subject to losses when faced with highly reactive loads. Many of these baluns use a 4:1 ratio, which can give the tuner added problems when it is presented with very low load impedances. A few operators have gone so far as to carefully measure their parallel transmission lines so as to present a 200-ohm load with a mild capacitive reactance that is tuned out with an external capacitor across the line.
|
||||
<p>Some hams have attempted to avoid balun losses by placing a 1:1 balun at the source side of the tuner and floating the unit to provide a nearly balanced output to the load. Common- mode currents continue to be a problem in many installations.</p>
|
||||
<p>Rarely have hams attempted to build balanced networks for their tuners. Balanced Ls, Tees, and PIs are certainly feasible, but at a cost. In some schemes, component values double; in others, mechanical linkages present construction complexities. Such units remain rare.</p>
|
||||
<p>For many hams, the tuner of choice for parallel transmission line systems is the inductively-coupled tuner. It yieldss efficient power transfer to a naturally balanced output. Moreover, it provides a degree of isolation from the line due to the inductive or magnetic coupling. This latter feature often suffices to attenuate out-of-band RF from strong local sources.</p>
|
||||
<p>However, not just any old tank and link will make a satisfactory tuner. We have largely forgotten the fundamental principles behind good tuners of this type. Perhaps the high point of available information was in the 1960s. In my own collection of old <i>ARRL Antenna Books</i>, the 9th Edition of 1960 contains an account that is both mathematically and practically superior to the account of my next older edition, the 7th of 1955. By the 13th edition of 1974, much of the material had been digested to make room for the single ended network and baluns and has remained essentially unchanged since that time. The link coupled transmatch still in the 18th edition of the <i>ARRL Antenna Book</i> of 1997 is the same as that in my 1982 <i>ARRL Handbook</i> (although few have noticed that the front panel photo has changed appearance over the years, while the top view shows the original unit).</p>
|
||||
<p>These notes on the evolutionary ups and downs in available link tuner information are not at all a criticism of ARRL publications. Quite to the contrary, other handbooks in English present considerably less information on these tuners and their principles. Yet the information is available from a combination of sources. The 1960 <i>ARRL Antenna Book</i> account is, of course, crucial. One source especially useful on inductive coupling is George Grammer's <i>A Course in Radio Fundamentals</i> which ARRL published as a full text in 1972. The source behind this treatment--as it is for so many other matters relating to radio fundamentals--is Terman's <i>Radio Engineers' Handbook</i>. They all make good reading for those interested in going beyond the treatment presented here.</p>
|
||||
<p>So perhaps it is time to go back to the beginning and reintroduce the link coupler from the ground up. Nothing in these notes will be new, but only a restatement of principles and practices gleaned from the sources. At most, I shall be adding some tables and examples to the account in order to give the applicable equations some real meaning. The tables may also allow those who do their math intuitively a chance to see the trends of values to permit more accurate ballpark extrapolations. Moreover, I shall not try to give a fully integrated mathematical account, but simply present certain of the most useful equations that either explain tuner operation or permit calculations useful to constructing such tuners. Since most will be practical simplifications, there will be gaps in mathematical progressions of derivation. But then, our aim is to provide--so far as possible--a practical grounding in inductive tuner principles.</p>
|
||||
<center>
|
||||
<h3>What's in a Name</h3>
|
||||
</center>
|
||||
<center>
|
||||
<img src="link1-1.gif" width="395" height="385" border="2" vspace="5" hspace="9">
|
||||
</center>We call the line-to-transmitter matching device a link-coupled tuner, which it is and isn't. The name arose in the days before PI network outputs. As shown in Figure 1A, older transmitters used a parallel-tuned output circuit, with energy coupled to a low-impedance secondary. Often, the secondary coil was connected to another such coil, which in turn was coupled to a high-impedance parallel-tuned circuit used to match the high impedance of the antenna. The link, as such low-impedance-to-low-impedance coils were called, might be something as simple as a twisted line. Such circuits were equivalent (assuming zero losses in the link) to a direct coupling between the two tank coils, as shown in Figure 1B, with theoretically calculable adjustments of values. Few hams made the calculations because it was simply easier to adjust the number of turns in the link coils to achieve maximum power transfer.
|
||||
<center>
|
||||
<img src="link1-2.gif" width="524" height="280" border="2" vspace="5" hspace="9">
|
||||
</center>
|
||||
<p>In isolation, the antenna tuning unit (ATU) shown in Figure 2, is an inductively coupled impedance matching network. Even though networks dominate the output circuits of modern transmitters, the concept of coefficient of coupling may still be applied to the inductively coupled circuit, and to that degree it is still correct to call these ATUs link-coupled tuners.</p>
|
||||
<p>However, the old name often carries with it an attitude: the small coil is merely the link and as such is not of great importance. Calling the unit an inductively coupled impedance matching network gives equal importance to both the primary and secondary inductors. That is crucial for understanding this class of ATUs.</p>
|
||||
<p>We shall keep the old name, since that is only a war of words, but we shall lose the old attitude. That way, the link coupler and the inductively coupled impedance matching network will become one and the same. Now if we only knew what is going on with inductive coupling, we would be in good shape to understand the link coupler.</p>
|
||||
<center>
|
||||
<h3>Inductive Coupling: Back to Basics</h3>
|
||||
</center>When any two coils are positioned such that the magnetic lines of force of the one which is connected to a source of RF energy cut across the turns of the other coil (assumed to be connected to a load), energy is coupled to the second coil. The expanding and collapsing field of the first coil provides the changing magnetic field necessary to induce a voltage across the second coil, with a consequential current flow through the load.
|
||||
<p>Two key concepts arise in this connection. The first is mutual inductance (M), that is, the voltage induced in the second coil by the rate of current change in the first. M is measured in Henrys, just as is the inductance of the coils. Often neglected is the fact that mutual inductance can be measured. First measure the inductance of the two coils individually and well apart from each other. Second, fix the positions of the coils with respect to each other, connect the coils in series, and measure the total inductance. Finally, reverse the series connections and remeasure the inductance. Note that inductance-measuring devices ordinarily use an internal alternating current signal source to make their measurements.</p>
|
||||
<center>
|
||||
<img src="link1-3.gif" width="324" height="271" border="2" vspace="5" hspace="9">
|
||||
</center>
|
||||
<p>If the two coils as positioned have any mutual inductance, as illustrated in Figure 3, then the two readings will differ, one being larger than the sum of the inductances of the coils as measured independently, the second smaller than that sum. The larger reading (LTA) records the coils connected so that the fields are said to aid each other; the smaller (LTO) records the connections that oppose each other. In fact, the readings express some precise relationships:</p>
|
||||
<center>
|
||||
<img src="link1e1.gif" width="256" height="58" border="2" vspace="5" hspace="9">
|
||||
</center>and
|
||||
<center>
|
||||
<img src="link1e2.gif" width="252" height="61" border="2" vspace="5" hspace="9">
|
||||
</center>where all values are in Henrys or in fractions thereof. By some easy combination of the equations, we get
|
||||
<center>
|
||||
<img src="link1e3.gif" width="230" height="72" border="2" vspace="5" hspace="9">
|
||||
</center>again, in Henrys.
|
||||
<p>The importance of reviewing this very basic idea is to establish the significance of mutual inductance in the coupling of energy in a magnetic circuit. Because M is a real inductance, it also has a reactance (XM) associated with it for any given frequency, which we calculate in the ordinary way:</p>
|
||||
<center>
|
||||
<img src="link1e4.gif" width="222" height="59" border="2" vspace="5" hspace="9">
|
||||
</center>where XM is in ohms, M in Henrys, and f is the frequency in Hertz.
|
||||
<p>Mutual coupling increases as the coils are brought closer together or positioned so that more lines of force from the source or primary coil cut across the turns of the load or secondary coil. If we use magnetic materials, such as iron cores as power line frequencies, the value of M can reach close to the square root of the product of the two individual inductors. In fact, the square root of the product of the inductances of the two coils defines the highest possible value for M. Under these ideal conditions, the coupling is as high as it can possible go and is said to be 1. All other situations will have a coefficient of coupling (k) of less than 1.</p>
|
||||
<center>
|
||||
<img src="link1e5.gif" width="223" height="85" border="2" vspace="5" hspace="9">
|
||||
</center>Air wound coils, no matter how closely coupled, will have a coefficient of coupling well below 1. For most cases, values of k from 0.3 to 0.6 are common with air wound coils. Table 1 provides a sampling of some variations in k and M with different values for L1 and L2.
|
||||
<pre> Sample Values of M and k With Sundry Values of L1 and L2
|
||||
|
||||
L1 L2 LTA LTB M k
|
||||
Values yielding k = 1
|
||||
5 5 20 0 5 1.0
|
||||
8 4 23.32 0.68 5.66 1.0
|
||||
10 1 17.32 4.68 3.16 1.0
|
||||
Values yielding M = 2.5
|
||||
5 5 15 5 2.5 0.5
|
||||
8 4 17 7 2.5 0.44
|
||||
10 1 16 6 2.5 0.79
|
||||
Values yielding M = 1.0
|
||||
5 5 12 8 1.0 0.2
|
||||
8 4 14 10 1.0 0.18
|
||||
10 1 13 9 1.0 0.32
|
||||
|
||||
Note: Values of L1, L2, and M are inductances and may be read as Henrys,
|
||||
milli-Henrys, or micro-Henrys, so long as the unit of measure is the same
|
||||
for L1, L2, and M.
|
||||
|
||||
Table 1. Sample values of M and k with sundry values of L1 and L2.</pre>
|
||||
<p>One misconception is that a lower coefficient of coupling implies that less than full power is being coupled from the primary to the secondary circuit. This is incorrect. The value of k is simply a very convenient way of helping to calculate various factors involved in the transfer of energy or in impedance matching. What is correct is this: the rules we learn to use with power and other transformers with high coefficients of coupling do not apply to air wound coil pairs with lower coefficients of coupling. Hence, the technique of using the turns ratio to calculate voltage, current, and impedance ratios must be set aside for inductive coupling with air wound coils.</p>
|
||||
<p>Transformers with strong magnetic core materials not only achieve high coefficients of coupling, but tend also to be frequency insensitive within the working range of the core material. Thus, we can build wide-band transformers for radio work by employing either ferrite or powdered iron materials in a toroidal core. Like the laminated iron cores of power transformers, these cores concentrate the magnetic lines of force within a very tight area surrounding all the turns of the primary and secondary coils. Air-wound coils have more widely spread magnetic fields. They tend to retain their energy transfer characteristics over a much narrower frequency range in ways related to the reactance of the coils.</p>
|
||||
<center>
|
||||
<h3>Simple (Untuned) Inductive Circuits</h3>
|
||||
</center>
|
||||
<center>
|
||||
<img src="link1-4.gif" width="353" height="434" border="2" vspace="5" hspace="9">
|
||||
</center>Figure 4A shows the simplest inductively coupled circuit, with a resistive source and a resistive load. The inductors are designated LP and LS, as primary and secondary coils for the circuit. Because the circuits are coupled, the coupled impedance from the secondary appears in the primary in the form of series components. The values for the series resistance (RA) and reactance (XA) can be approximated from the following equations:
|
||||
<center>
|
||||
<img src="link1e6.gif" width="250" height="87" border="2" vspace="5" hspace="9">
|
||||
</center>and
|
||||
<center>
|
||||
<img src="link1e7.gif" width="256" height="82" border="2" vspace="5" hspace="9">
|
||||
</center>where XM is the reactance of the mutual inductance, RS is the secondary circuit resistance, and XS is the secondary circuit reactance. Figure 4B shows the coupled impedance factors in place.
|
||||
<p>For example, suppose we use an inductor pair (taken from a table of recommended values) where LP is 1.2 micro-H and LS is 12 micro-H. XS will be 528 ohms at 7 MHz. Add a load resistance of 1500 ohms. We shall assume a coefficient of coupling (k) of 0.6. From equation (5) transformed, M = 2.3 micro-H, and the value of XM is 100 ohms. Under these conditions, using the equations above, the coupled values in the primary will be RA = 5.9 ohms and XA = 2.1 ohms.</p>
|
||||
<p>Note that the reactance of the secondary which is coupled back to the primary is numerically equal to the transformed secondary reactance, but of the opposite sign or type. Hence, the reactances cancel in part. Ideally, selection of the right values for the two inductors and the right coefficient of coupling would provide a resistive load for the source.</p>
|
||||
<p>In order to effect a match between the load and the source, both the mutual inductance and the reactance of one of the inductors must be varied, a highly impractical situation. I have passed along these equations only to demonstrate the reversal of reactance sign in the mutually coupled reactance, a factor that will be of importance in practical link-coupled circuits of only slightly more complex design.</p>
|
||||
<center>
|
||||
<h3>Coupling With a Tuned Secondary</h3>
|
||||
</center>
|
||||
<center>
|
||||
<img src="link1-5.gif" width="357" height="436" border="2" vspace="5" hspace="9">
|
||||
</center>Figure 5A shows the more commonly used inductively coupled circuit: an untuned primary circuit with a resonated secondary circuit. For resonate circuits, the Q is determined almost wholly by the load resistance relative to the reactance of either the coil or the capacitor (which are equal) at resonance. The resistive impedance of a resonant parallel tuned circuit is very high, and the lower load resistance in parallel with the tuned circuit largely determines the coupled resistance into the primary.
|
||||
<p>The loaded Q (QL) of the secondary of Figure 5A is given by</p>
|
||||
<center>
|
||||
<img src="link1e8.gif" width="214" height="78" border="2" vspace="5" hspace="9">
|
||||
</center>where X is the reactance of either the coil or the capacitor at resonance. For example, if the resistive load is 2500 ohms and the reactance of the coil and capacitor are each 250 ohms at resonance (a common value), the loaded Q is 10.
|
||||
<p>For loaded Qs of 10 and better, simplified equations are possible with little error. With lower values of QL, some error will results, but not outside the range of the variable components. One way to show the resistance coupled back to the primary (RA)--shown as a series resistance in Figure 5B--is with this expression:</p>
|
||||
<center>
|
||||
<img src="link1e9.gif" width="222" height="81" border="2" vspace="5" hspace="9">
|
||||
</center>where XM is the reactance of the mutual inductance, RL is the resistive load on the secondary, and XL is the reactance of the coil at resonance.
|
||||
<p>If we use the same coil values as earlier, 1.2 micro-H and 12 micro-H, for the primary and secondary coils, along with the presumed coefficient of coupling, 0.6, we may obtain values of 100 ohms for XM and 528 ohms for XL at 7 MHz. The requisite capacitor to resonate the circuit at this frequency is 43 pF. With a load resistance of RL = 1500 ohms, QL = 2.8. Since the loaded Q of the circuit is well under 10, the calculations from this point onward will provide ballpark guidance, not accuracy, since the equations employed are intended for use with circuits with loaded Qs of 10 or more. However, employing equation (9), we derive a value for RA of about 54 ohms.</p>
|
||||
<p>Notice that in figure 5B we have a primary impedance consisting of a resistance (desired) and a reactance (not desired in matching circuits). The reactance of the primary inductance remains uncompensated because the tuned secondary is wholly resistive. To make the primary impedance wholly resistive, we must alter the component values of the tuned circuit to permit it to show a small inductive reactance. From equation 7, we know that the transformed and coupled value of this inductive reactance will be capacitive, thus cancelling the inductive reactance. What is left will be a pure resistance.</p>
|
||||
<p>The procedure employed is normally derived empirically rather than calculated. We tune the secondary circuit to a higher frequency than the operating frequency, normally by reducing the value of capacitance and thereby increasing the value of capacitive reactance to the increased value of the fixed inductor at this higher frequency. The parallel resonant secondary circuit at the original (slightly lower) frequency will show inductive reactance, just what we need to couple back to the primary, where it appears as a capacitive reactance in series with the reactance of the primary inductor. With the correct selection of secondary values, the primary reactances will cancel, leaving a purely resistive impedance for the primary circuit. In the process, the value of the resistance coupled back to the primary will not change by very much at all.</p>
|
||||
<p>Because we are now using ballpark equations at low operating or loaded Qs, any calculation of this phenomenon will not be precise. However, if we walk through the process a couple of times, we can get a view of the trends and understand how things work. The standard equation for determining the reactance of a parallel combination of L and C, when transformed into reactances XL and XC for the frequency in question, is</p>
|
||||
<center>
|
||||
<img src="link1e10.gif" width="234" height="68" border="2" vspace="5" hspace="9">
|
||||
</center>where XP is the resultant reactance that is in parallel with the load resistance, RL.
|
||||
<p>Using the same example we have been tracking, we can plug simplified series transforms of these parallel values into equations (6) and (7) and obtain something like the values in Table 2. Although these values are not precise by any means, they do show that as we increase the resonant frequency of the parallel resonant secondary circuit, the capacitive reactance coupled back to the primary increases steadily, while the resistance decreases very slowly. The right combination of values will eventually yield a purely resistive input impedance, although the coefficient of coupling might have to be altered to keep the value of RA close to 50 ohms. Remember that in equations (6) and (7), the numerator is XM2, and raising its value will raise the values of both the RA and XA. However, the example employs a value of k of 0.6, already close to the limit of what is feasible with air-wound inductors.</p>
|
||||
<pre>Sample Values of RA and XA as the Secondary is Resonated at Higher Frequencies
|
||||
|
||||
Resonant Parallel Parallel Series Series Coupled Coupled
|
||||
Frequency Resistance Reactance Resistance Reactance Resistance Reactance
|
||||
FMHz RL (ohms) XP (ohms) RS (ohms) XS (ohms) RA (ohms) XA (ohms)
|
||||
|
||||
7.0 1500 -- 186 -- 54 --
|
||||
7.3 1500 6590 186 42 51 -12
|
||||
7.5 1500 4090 186 68 47 -18
|
||||
|
||||
Note 1. Resonant Frequency refers to the resonant frequency of the parallel tuned
|
||||
secondary circuit and is altered by reductions in the capacitance, while maintaining a
|
||||
fixed value for the inductor.
|
||||
|
||||
Note 2. Because simplified calculations have been used, the table is useful only for
|
||||
noting the trends in values. Actual values will vary considerably due both to the the
|
||||
low loaded Q of the circuit and the variables of actual coupler construction.
|
||||
|
||||
Table 2. Sample values of RA and XA as the secondary is resonated at higher frequencies.
|
||||
</pre>
|
||||
<p>The purpose of this exercise in equation-mongering is to provide you with an understanding of some of the basic principles of link-coupled tuners. More exacting forms of the equations applicable to the low values of loaded Q often encountered in ATUs are available. We have restricted ourselves to these convenient approximations because the evolution of practical coupler circuits has largely proceeded by workbench experience. If this brief account simply makes you a little more comfortable dealing with inductively coupled circuits and convinces you that they operate in accord with principles that do allow us to calculate necessary values, it will have served its purpose.</p>
|
||||
<p>The next step is to begin wending our way through typical inductively coupled circuits in order to see how some of the enhancements work. Unlike many other accounts of tuners, we shall start where the transmitted signal starts: on the input side of the tuner.<br>
|
||||
<br></p>
|
||||
<center>
|
||||
<img src="../images/colorbar.gif" align="middle" width="540" height="4">
|
||||
</center><br>
|
||||
<br>
|
||||
<p><i>Updated 11-28-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.</i><br>
|
||||
<br></p>
|
||||
<center>
|
||||
<img src="../images/colorbar.gif" align="middle" width="540" height="4">
|
||||
</center><br>
|
||||
<br>
|
||||
<a href="link2.html"><img src="../images/return.gif" align="bottom" width="40" height="40"> Go to Part 2: The Input Story</a><br>
|
||||
<br>
|
||||
<a href="link0.html"><img src="../images/rtnhome.gif" align="bottom" width="40" height="40"> Return to Index</a><br>
|
||||
<br>
|
||||
<br>
|
||||
<p class="topics-footer">Topics: <a href='../topics.html#matching'>Matching</a></p><br>
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||||
<meta name="keywords" content="Matching">
|
||||
<title>Link-Coupled Antenna Tuners Part II: The Input Story</title>
|
||||
<link rel="stylesheet" href="../styles.css">
|
||||
</head>
|
||||
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|
||||
<center>
|
||||
<h1><img src="../images/elect.gif" align="middle" width="145" height="75" border="2" vspace="5" hspace="9">Part II: The Input Story<img src="../images/w4rnlwwr.gif" align="middle" width="99" height="83" border="2" vspace="5" hspace="10"></h1>
|
||||
</center>
|
||||
<center>
|
||||
<h3>L. B. Cebik, W4RNL</h3>
|
||||
</center><br>
|
||||
<br>
|
||||
<center>
|
||||
<img src="../images/colorbar.gif" align="middle" width="540" height="4">
|
||||
</center><br>
|
||||
<br>
|
||||
Having digested the fundamentals of inductive coupling, we can next turn to a step-by- step investigation of inductively coupled antenna tuning units (ATUs). We already know that the tuner will consist of an input inductor (LP) plus any other refinements we eventually choose to add. It will also consist of an inductor (LS) and capacitor (CS) in the secondary, where the components for a parallel resonant or near resonant (tank) circuit, with the load (RL) connected in parallel to the tank. Figure 1 shows the most basic schematic once more.
|
||||
<center>
|
||||
<img src="link2-1.gif" width="430" height="396" border="2" vspace="5" hspace="9">
|
||||
</center>
|
||||
<p>The input resistance in series with LP is designated RA and is the resistive impedance coupled back to the primary. As we have noted, the secondary tuned circuit at resonance has no series-equivalent reactance and therefore does not couple a reactance back to the primary or input side of the circuit. To couple a compensating capacitive reactance back to the primary, one must resonate the secondary at a frequency somewhat higher than the operating frequency. In this case, there is both a resistive and reactive component to the secondary impedance, and hence, resistive and reactive components to the impedance coupled back to the primary.</p>
|
||||
<p>Since the offset adjustment has little effect on the value of the coupled resistive component, but chiefly provides the capacitive reactance needed to cancel the inductive reactance of the primary inductor, we shall normally not mention (except where necessary) this offset adjustment. However, tuner designers and users should remember that this offset is a normal part of most antenna tuner adjustments. When we use an SWR meter between the ATU and the transmitter, we are making this adjustment automatically in seeking a 1:1 SWR. If we leave the reactance of the primary inductor uncompensated, the SWR will be above 1:1 for the case where RA is 50 ohms.</p>
|
||||
<center>
|
||||
<h3>A Little Orientation</h3>
|
||||
</center>In the account of inductive coupling fundamentals, we gave the following equation as the most basic approximation of the input resistance to the remaining conditions in the coupling circuit:
|
||||
<center>
|
||||
<img src="link2e1.gif" width="223" height="87" border="2" vspace="5" hspace="9">
|
||||
</center>where RA is the resistive impedance coupled back to the primary, XM is the reactance of the mutual inductance between coils, and XLS is the reactance of the secondary inductor (or capacitor) at secondary resonance on the operating frequency.
|
||||
<p>In editions of the <i>ARRL Antenna Book</i> since at least 1960, a different equation is given, presenting the initial appearance that the account there may differ from this one. However, let's do a little work on equation (1) above.</p>
|
||||
<p>First, we know that the coefficient of coupling (k) and the mutual inductance (M) are related by the square root of the product of the two coupled inductances. Since converting an inductance to its reactance at any given frequency is a matter of multiply the inductance by 2pif, which cancel out in the relationship, we can also express how k relates to M this way:</p>
|
||||
<center>
|
||||
<img src="link2e2.gif" width="237" height="52" border="2" vspace="5" hspace="9">
|
||||
</center>where XM is the reactance of the mutual inductance, and XLP and XLS are the reactances of the primary and secondary inductances, respectively.
|
||||
<p>Squaring both sides of equation (2), we can replace the term XM2 in equation (1), cancel out an XLS above and below the line, and reach this step:</p>
|
||||
<center>
|
||||
<img src="link2e3.gif" width="235" height="82" border="2" vspace="5" hspace="9">
|
||||
</center>where all terms have the definitions given in the equations so far.
|
||||
<p>For a parallel loaded circuit where the load resistance is small compared to the resistive impedance of the resonant circuit, the loaded circuit Q is approximately the following:</p>
|
||||
<center>
|
||||
<img src="link2e4.gif" width="209" height="73" border="2" vspace="5" hspace="9">
|
||||
</center>If we replace RL over XLS with Q, we obtain the very equation shown in the <i>ARRL Antenna Book</i>:
|
||||
<center>
|
||||
<img src="link2e5.gif" width="232" height="49" border="2" vspace="5" hspace="9">
|
||||
</center>The only differences lie in the choice of subscripts, and I have selected mine to be consistent with those in Part I.
|
||||
<p>Equations (3) and (5) give us important information about the design of inductively coupled ATUs. First, the resonant secondary ATU is most efficient when the numerical values of RA and XLP are the same. (Note that we only approximate this condition when we detune the secondary in order to cancel the reactance in the primary.) Under these conditions, a relationship emerges between k and Q:</p>
|
||||
<center>
|
||||
<img src="link2e6.gif" width="241" height="92" border="2" vspace="5" hspace="9">
|
||||
</center>
|
||||
<p>The upshot is this: we can optimize our ATU design by varying the relationship between the load resistance and the reactance of the secondary inductor, or we can optimize our design by varying the coefficient of coupling--or we can do both. That gives us a good bit of flexibility in designing the ATU.</p>
|
||||
<p>We shall look at both sides of the circuit for ways to optimize our design. As we did in Part I, we shall stick to purely resistive loads and leave the question of reactance on the line for later consideration. Likewise, we shall retain the parallel configuration of the secondary circuit and devote some attention later on to low impedance loads and the series-counterpart of the circuit. Let's master one thing at a time.</p>
|
||||
<center>
|
||||
<h3>The Big Little k and XLP</h3>
|
||||
</center>Let's reset the parameters of our initial ongoing problem that we initiated in Part 1. We wanted a tuner for 7 MHz and chose a secondary inductor of 12 micro-H (with a reactance of 528 ohms at that frequency) along with a primary inductor of 1.2 micro-H (53 ohms reactance). The resonant capacitance was 43 pF. We chose as our load (RL) 1500 ohms (resistive).
|
||||
<p>With the chosen values and an assumed k of 0.6, the mutual reactance was 100 ohms. The secondary loaded Q was 2.8 or so (which tells us that everything we are doing here is an approximation, since the equations are truly accurate only for Qs above 10). Whichever equation we use to obtain the coupled resistance to the primary, we obtain about 54 ohms. However, this value of RA applies only to a load of 1500 ohms resistive.</p>
|
||||
<p>What happens if we have a different load to match with the same components? The following table tells us a story.</p>
|
||||
<pre> Some Values of RA for Various Loads
|
||||
RL (ohms) Loaded Q RA (ohms)
|
||||
500 0.95 18
|
||||
1000 1.89 36
|
||||
1500 2.84 54
|
||||
2000 3.79 72
|
||||
2500 4.73 90
|
||||
|
||||
Table 1. Some values of RA for various loads (RL) in the standardized circuit.</pre>
|
||||
<p>In order to effect a 50-ohms match, we might consider altering the value of XLP. This would entail altering the size of the primary inductor, which would inevitably alter the values of M and k. However, assuming we could retain a k of 0.6, the following table gives us the trend of value changes needed for the 50-ohms match.</p>
|
||||
<pre> Some Values of XLP for a 50-ohms Match
|
||||
RL (ohms) Loaded Q XLP (ohms)
|
||||
500 0.95 146
|
||||
1000 1.89 73
|
||||
1500 2.84 53
|
||||
2000 3.79 37
|
||||
2500 4.73 29
|
||||
|
||||
Table 2 Some values of XLP for various loads (RL) to achieve a 50-ohms match.</pre>
|
||||
<p>For most inductively coupled tuners, this is not a practical alternative. The primary inductor is normally fixed within or immediately over the secondary inductor. Tapping it precisely would require closely spaced taps. Mechanically, the switch leads or the manual tapping wires would introduce variations in the impedance seen at the input terminals of the tuner. But the exercise does give us a feel for what happens at the primary with changes in antenna feedline loads.</p>
|
||||
<center>
|
||||
<h3>Swinging Links</h3>
|
||||
</center>We mentioned that our changes in the reactance of the primary inductor would occasion changes in the coefficient of coupling. We can use that idea in another way. Suppose that we could change the coefficient of coupling without disturbing (too much) the reactance of the primary inductor. Figure 2 shows how this has been done traditionally.
|
||||
<center>
|
||||
<img src="link2-2.gif" width="354" height="503" border="2" vspace="5" hspace="9">
|
||||
</center>
|
||||
<p>The swinging or movable link or primary inductor, moving within a space at the center of the secondary coil, effectively changes the coefficient of coupling and hence the mutual impedance of the coupled inductors. The value of k increases as coupling is increased, that is, as the link is moved into the secondary field. Notice that the value of k changes continuously with changes in the primary inductor position, in effect giving us a variable k-control. We cannot say in the abstract what the value of k might be with each possible position. However, we can look at the values of k necessary to effect a 50-ohms match in our standard circuit.</p>
|
||||
<pre> Some Values of k for a 50-ohms Match
|
||||
RL (ohms) Loaded Q k
|
||||
500 0.95 0.99
|
||||
1000 1.89 0.71
|
||||
1500 2.84 0.57
|
||||
2000 3.79 0.50
|
||||
2500 4.73 0.45
|
||||
|
||||
Table 3 Some values of k for various loads (RL) to achieve a 50-ohms match.
|
||||
</pre>
|
||||
<p>Since values of above about 0.6 are normally not achievable with air-wound inductors, the standardized 7 MHz tuner circuit would not be able to match loads less than about 1500 ohms. However, we might select a larger primary inductor value, which would reduce the required values of k. Unfortunately, this move would also increase the value of XLP so that it no longer match the desired value of RA, thus setting a less than optimum ratio between the two figures.</p>
|
||||
<p>A second alternative results from equation (6), which suggests that we might redesign the coupler secondary, tailoring its Q to provide a more usable range of values for k. We shall retain a target values for RA and XLP of 50 ohms each. Let's also set a limit: at a load impedance (RL) of 300 ohms, the value of the coefficient of coupling (k) will be 0.6. From Table 3, we can see that at lower impedance values, k will need to reach values not likely to be achieved, but at load values above this value, required values of k will be lower. By swinging the link further out from the main inductor, these values of k can be achieved.</p>
|
||||
<p>Since k, XLS, and RL are related, we can rewrite equation (6) as</p>
|
||||
<center>
|
||||
<img src="link2e7.gif" width="228" height="51" border="2" vspace="5" hspace="9">
|
||||
</center>Having set the limits as k=0.6 and RL=300, we can calculate that XLS=108 ohms. At 7 MHz, this translates into an inductor of 2.45 micro-H and a capacitor of 210 pF for the tuned secondary. With these values, we obtain the following table of values of k vs. the various load resistances.
|
||||
<pre> Some Alternative Values of k for a 50-ohms Match
|
||||
RL (ohms) Loaded Q k
|
||||
500 4.63 0.46
|
||||
1000 9.26 0.32
|
||||
1500 13.89 0.27
|
||||
2000 18.52 0.23
|
||||
2500 23.15 0.21
|
||||
|
||||
Table 4 Some values of k for various loads (RL) to achieve a 50-ohms match
|
||||
with the revised swinging link coupler.</pre>
|
||||
<p>Although this redesign achieves the immediate goal of providing values of k within the range of a swinging link for a span of realistic load values, all is not well. When the Q exceeds a value of about 10, the tuning becomes very sharp, requiring one to reset the tuner variables more than once across a single amateur band.</p>
|
||||
<p>Although the swinging link might be combined with some techniques applied to the tuner secondary that we shall explore a bit further on, they are no longer the input circuit of choice. Swinging links were once popular, but have essentially gone out of style because they are mechanically large and complex. Moreover, there is a much simpler means of achieving the same goal.</p>
|
||||
<center>
|
||||
<h3>The Series Capacitor</h3>
|
||||
</center>
|
||||
<p>The most common way to adjust the input circuit of an inductively coupled ATU is with a series capacitor. See Figure 3 for a revision of our standard circuit to incorporate the unit.</p>
|
||||
<center>
|
||||
<img src="link2-3.gif" width="438" height="368" border="2" vspace="5" hspace="9">
|
||||
</center>
|
||||
<p>The first task that the new series capacitor, CP, can perform is to cancel the reactance of LP. This frees us from having to retune the secondary circuit to achieve this effect. Essentially, CP and LP form a resonant series circuit, leaving only RA as the input impedance of the overall impedance matching circuit.</p>
|
||||
<p>We choose the value of CP to resonate with LP at the lowest frequency in the band to be covered. In our running example, at 7 MHz the reactance XLP is 53 ohms; hence, the reactance of the capacitor must be the same at resonance. The corresponding capacitance is 430 pF. However, we show the capacitor as a variable for a set of good reasons.</p>
|
||||
<p>The values just calculated apply for the case where the overall circuit load is 1500 ohms resistive. However, not all loads faced by the ATU will be exactly 1500 ohms. Other load values will not be converted by the circuit constants to the values of RA and XA in the example (where XA has had a value of zero).</p>
|
||||
<p>In the first episode, we showed how to cancel the value of XLP by tuning the secondary circuit to a higher frequency, so that at the operating frequency, XLP and XCP did not have the same values at the operating frequency. As we increased the frequency at which XLP and XCP were equal, a value of XA was coupled back into the primary circuit, and the value was capacitive. At the same time, the value of RA slowly lowered.</p>
|
||||
<p>Had we begun with a secondary load, RL, that was higher than 1500 ohms, the value of RA would also have been initially higher. To a limited degree, we may use the same technique of making XLP and XCP equal at a higher frequency to produce something closer to 50 ohms for RA. However, when we do this, we also couple a capacitive reactance, XA, into the primary circuit. Since this coupled reactance provides part of the reactance needed to cancel the reactance of the primary inductor, the new series capacitor, CP, must now be set at a lower reactance--just enough lower so that the sum of its reactance and the coupled reactance together cancel the coil reactance. A lower reactance in CP means a higher capacitance. Therefore, the series capacitor used in the primary should have a value sufficiently greater than the target value to handle such cases.</p>
|
||||
<p>Lower values of RL would have yielded lower values of RA. To raise them, within limits, we may set XLP and XCP to be equal at a frequency below the operating frequency. This will simultaneously raise the value of RA coupled back to the primary and also introduce a value of inductive reactance XA. The series capacitor must now be set at a higher value of reactance (and a lower value of capacitance) to cancel the sum of the introduced and the primary inductor reactances.</p>
|
||||
<p>The series capacitor in the ATU primary circuit may be thought of as a "fine tuning" device, capable of allowing a given fixed secondary circuit inductor and its associated variable capacitor to handle a wider range of loads without directly altering the coefficient of coupling. Still, the range of variation that the primary capacitor, CP, can handle is limited. For wide ranges of RL, other means of coupling the load to the primary are necessary. The chief function of the series primary capacitor is always to cancel the primary inductor reactance, thus presenting the input source with a resistive load.</p>
|
||||
<center>
|
||||
<h3>A Note on Resonance</h3>
|
||||
</center>To this point, we have referred to resetting the value of the tank capacitor as an offset tuning. Relative to our ordinary understanding of resonance, where the values of XLS and XCS are equal, the retuning of the tank amounts to an offset. However, let's remember that we are dealing with circuits whose operating Q is often well under 10. And here the single definition of resonance breaks down into several definitions, each with a proper context of use.
|
||||
<center>
|
||||
<img src="link2-4.gif" width="379" height="429" border="2" vspace="5" hspace="9">
|
||||
</center>
|
||||
<p>Figure 4 shows a conventional parallel tuned circuit. Note that the series resistance in the coil leg (RS) is in addition to the load resistance (RL), but the two are not in either direct series or parallel with each other. When the operating Q of the circuit is above 10, the presence of RS makes little or no difference to the notion of resonance. When the operating Q is below 10, differences begin to appear.</p>
|
||||
<p>When a series or parallel tuned circuit is just off resonance, we expect several differences from performance at resonance. First, XL is not equal to XC. Second, the current through the parallel circuit (in contrast to current within the circuit load) is greater than minimum. Third, the current through the circuit is not in phase with the voltage. In a high loaded-Q circuit, XL and XC are equal, current though the circuit is minimum, and current is in phase with the voltage all at just about the same frequency. However, in low-QL circuits, these three phenomena occur at somewhat different frequencies.</p>
|
||||
<p>The goal in tuning a parallel resonant circuit in an impedance matching circuit is to achieve minimum current within the parallel circuit and maximum current to the load at the operating frequency. With respect to this goal, successful tuning of the circuit produces resonance. It is not the goal to have the current and voltage in perfect phase within the tank circuit or to have XL and XC be equal. These latter phenomena may occur at nearby frequencies, and they become resonant frequencies relative to each phenomenon. (In 1995, the ARRL Handbook expanded the coverage of low-Q parallel resonant circuits to cover these points more thoroughly: see pages 6.37-6.42 of any edition since then.)</p>
|
||||
<p>Hence, for the aims of the inductively coupled tuner, the definition of resonance that is relevant is to maximize current in the load of the secondary (equivalent to minimizing current through the paralleled inductor and capacitor). Hence, when we retune the secondary to achieve maximum power output from the tuner, we are resonating the circuit, no matter what values of XL and XC may be required to do this.</p>
|
||||
<p>We have also ignored the values of resistance and reactance coupled from the primary into the secondary. Given the disparity of coil sizes, the amounts are quite small in most matching situations and hardly call for any change of control settings to maximize current in the secondary. However, the effect is real and the control settings are not quite the same as they would be without the mutual coupling. In some cases, these further adjustment requirements add to those just mentioned; in other cases, they may partially cancel each other out. Nonetheless, the overall readjustment of the tank circuit to account of all factors affecting maximum current flow within the tank circuit are part of the effort to achieve resonance.</p>
|
||||
<p>The most certain way to assure that proper resonance has been achieved is some form of output power measurement.</p>
|
||||
<p>We have only begun to see the flexibility of the inductively coupled impedance matching circuit by surveying the most common variations we impose on the input side of the circuit. In the next installment, we shall look at some useful variations of the output side of the circuit.<br>
|
||||
<br></p>
|
||||
<center>
|
||||
<img src="../images/colorbar.gif" align="middle" width="540" height="4">
|
||||
</center><br>
|
||||
<br>
|
||||
<p><i>Updated 11-28-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.</i><br>
|
||||
<br></p>
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||||
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|
||||
<img src="../images/colorbar.gif" align="middle" width="540" height="4">
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</center><br>
|
||||
<br>
|
||||
<a href="link3.html"><img src="../images/return.gif" align="bottom" width="40" height="40"> Go to Part 3: The Output Story</a><br>
|
||||
<br>
|
||||
<a href="link0.html"><img src="../images/rtnhome.gif" align="bottom" width="40" height="40"> Return to Index</a><br>
|
||||
<br>
|
||||
<br>
|
||||
<p class="topics-footer">Topics: <a href='../topics.html#matching'>Matching</a></p><br>
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<title>Link-Coupled Antenna Tuners Part III: The Output Story</title>
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<h1><img src="../images/elect.gif" align="middle" width="145" height="75" border="2" vspace="5" hspace="9">Part III: The Output Story<img src="../images/w4rnlwwr.gif" align="middle" width="99" height="83" border="2" vspace="5" hspace="10"></h1>
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<center>
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<h3>L. B. Cebik, W4RNL</h3>
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<br>
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<img src="../images/colorbar.gif" align="middle" width="540" height="4">
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<br>
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In the preceding installment, we look closely at the most common circuit variations on the input side of the inductively coupled ATU. The adjustments available to the coefficient of coupling and the series L-C combination provide limited flexibility. However, in conjunction with some techniques we can apply to the output side of the coupler, they add the refinement needed for very precise tuning that provides a 50-ohm resistive load for the source and maximum power output to the feedline.
|
||||
<p>First, before we jump into these output side circuit variations, let's again reset the parameters of our initial ongoing problem that we initiated in Part 1 and continued in Part II. We wanted a tuner for 7 MHz and chose from a list of recommended values a secondary inductor of 12 micro-H (with a reactance of 528 ohms at that frequency) along with a primary inductor of 1.2 micro-H (53 ohms reactance). The resonant capacitance was 43 pF. We chose as our load (RL) 1500 ohms (resistive). As in the earlier sections, we shall continue to work with resistive loads and save reactance for later.</p>
|
||||
<p>With the chosen values and an assumed k of 0.6, the mutual reactance was 100 ohms. The secondary loaded Q was 2.8 or so (which tells us that everything we are doing here is an approximation, since the equations are accurate for Qs above 10). We obtain about 54 ohms for RA, given the resistive load of 1500 ohms.</p>
|
||||
<p>Second, let's take another look at the basic equation that will aid our overall understanding of inductively coupled tuners, expressed both in terms of working Q and in terms of the relationship in the secondary parallel tuned circuit of the load resistance and the reactance of the tank components.</p>
|
||||
<center>
|
||||
<img src="link3e1.gif" width="274" height="81" border="2" vspace="5" hspace="9">
|
||||
</center>where RA is the primary resistive impedance (coupled back from the secondary), k is the coefficient of coupling, XLP is the reactance of the primary inductor, RL is the load resistance, XLS is the reactance of the secondary inductor (and of the capacitor at resonance), and Q is the loaded or working Q of the circuit.
|
||||
<p>The ratio of the load resistance to the reactance of the inductor (or Q) is critical to obtaining a desired value of RA. If we alter that ratio, then we must alter one of the other components of the equation in order to obtain the same value of input impedance. For a fixed parallel-tuned secondary and a fixed value for the input inductor, if Q increases as the load resistance increases, then the coefficient of coupling must decrease. Under the same circumstances, if the load resistance decreases, thus decreasing Q, we must increase k. However, we are already close to or at a practical limit for coefficients of coupling for air-wound inductors.</p>
|
||||
<p>In addition, many of the coupled loads we shall face will be well below 1500 ohms. The range from 200 to 1000 ohms is perhaps the most common with parallel feedlines. Clearly, we need some flexibility in the secondary values.</p>
|
||||
<center>
|
||||
<h3>Changing the L-C Ratio</h3>
|
||||
</center>As the load resistance decreases, we can simply decrease the inductor reactance accordingly and preserve the original value of Q. This move would seem to allow us to retain the same input inductor and coefficient of coupling to arrive at the same desired value of RA. There is a catch in this plan which we shall take up shortly. However, let's begin with the assumption that we can maintain the coefficient of coupling and input inductor value. Then we might imagine a modification to our basic tuner as in Figure 1.
|
||||
<center>
|
||||
<img src="link3-1.gif" width="538" height="313" border="2" vspace="5" hspace="9">
|
||||
</center>
|
||||
<p>Figure 1 shows a series input capacitor, but for now, let us only use it to cancel out the reactance of the input inductor so that the source has a purely resistive load. The secondary shows a set of coil taps to which the capacitor is connected, so that the result is a tuned circuit of differing L-C ratio as one moves from one tap to another. Since each tap represents a different value of inductance, the inductive reactance also changes accordingly. This requires a new value of capacitive reactance for resonance, and hence a new value of capacitance. Since we are lowering the inductance and the inductive reactance of the secondary, new lower values of the load resistance will be needed to re-establish Q at its former value.</p>
|
||||
<p>For the exercise, here is a table of values we might derive from this situation, using our initial tuner design as a basic starting point:</p>
|
||||
<pre> Tuner Component Values for a Constant Q and Varying Loads
|
||||
|
||||
RL (ohms) XLS=XCS (ohms) L (micro-H) C (pF)
|
||||
1500 528 12.0 43
|
||||
1350 475 10.8 48
|
||||
750 265 6.0 86
|
||||
300 105 2.4 215
|
||||
|
||||
Table 1. Tuner component values for a constant Q and varying loads.</pre>
|
||||
<p>The table presents us with usable values down to at least a 750-ohms load. Below that point, the required value of capacitance to resonate with the tapped inductor increases to a much more difficult level. If we install a 250 pF capacitor, the rate of change of capacitance grows higher, while if we install only a 100 pF capacitor, the range is insufficient for lower values of RL. This is a limitation of changing the L-C ratio of the secondary tuned circuit, but it is not the catch we mentioned.</p>
|
||||
<p>The catch is simply this: in order to reduce the value of the secondary inductor reactance, we have to reduce the inductance of the coil. In practice, simply eliminating some turns in the secondary coil will alter the relationship of the primary to the secondary, changing the mutual inductance and hence the coefficient of coupling. Restoring the coefficient of coupling will therefore require some physical alteration of the coil positions.</p>
|
||||
<center>
|
||||
<img src="link3e2.gif" width="237" height="55" border="2" vspace="5" hspace="9">
|
||||
</center>The equation relating k to XM gives an indication of the required change. If k is to remain constant, then the mutual inductance must decrease as the square root of the decrease in secondary coil inductance and inductive reactance. Restoring or retaining the coefficient of coupling will therefore require some physical alteration of the coil positions.
|
||||
<p>Although this system of tailoring the inductor reactance to the load resistance for a constant Q is feasible for a single band of operation, it has additional drawbacks when applied to link couplers designed to cover most of the HF bands. First, the number of taps grows well beyond the range of a switching system, and manual tapping becomes necessary. Second, on the higher frequency bands, most of the coil is unused. Since inductors have inter-turn capacity, it is possible for the large unused portion of the coil to have a self-resonant frequency at the operating frequency or a harmonic of it.</p>
|
||||
<center>
|
||||
<h3>Load Impedance Transformation</h3>
|
||||
</center>A number of the potential problems associated with changing the L-C ratio of the secondary tuned circuit can be avoided by leaving the L-C ratio constant. To handle load resistances lower than the natural value of RL that--with the given size of LP and value of k-- transforms to a primary impedance of about 50 ohms, we first transform the load resistance to the natural value of RL. In the running example, this value is 1500 ohms.
|
||||
<center>
|
||||
<img src="link3-2.gif" width="537" height="318" border="2" vspace="5" hspace="9">
|
||||
</center>
|
||||
<p>Figure 2 shows one way of effecting the transformation. We simply create a second inductively coupled circuit between the original secondary and the load. We may call this new inductor LL, the load winding. We could even add optional series capacitors, CL, which would provide us with the ability to resonate LL at the operating frequency.</p>
|
||||
<p>The impedance transformation between LS and LL operates according to the same equations that govern the relationship between LS and LP. Since we are interested here in the ratio of primary to secondary impedance, let's rewrite equation (1) in general primary-secondary terms:</p>
|
||||
<center>
|
||||
<img src="link3e3.gif" width="239" height="85" border="2" vspace="5" hspace="9">
|
||||
</center>where RP is the primary resistive impedance, RS is the secondary resistive impedance, XLP is the primary inductor reactance, XLS is the secondary inductor reactance, and k is the coefficient of coupling. The value of k, of course, indicates the function of XM, the mutual inductance between the inductors. Unless k=1, the ratio of primary to secondary impedance will always be less than the ratio of the inductor reactances. Since the individual inductor reactances are directly proportional to coil size--or, for a given inductor diameter and turns per inch, the number of turns--the ratio of primary to secondary impedance will always be less than the ratio of primary to secondary coil turns.
|
||||
<p>Where the secondary of the coupled load circuit is not resonant, the ratio will vary further due to the presence of a coupled value dependent on XLL, the reactance of the load winding, and an additional reactance will be coupled to the tuned parallel circuit. The reactance is normally compensated for by a revised setting for the variable capacitor.</p>
|
||||
<p>The circuit of Figure 2 is not often used in amateur work, although it is an efficient way in which to transform lower load resistances to the higher value required by the parallel tuned inductive circuit. The use of a further inductor complicates mechanical arrangements, especially if the arrangements involve switch leads. However, the circuit is applicable to special situations that call for the matching of a single load value with small variations around the target value.</p>
|
||||
<center>
|
||||
<img src="link3-3.gif" width="532" height="297" border="2" vspace="5" hspace="9">
|
||||
</center>
|
||||
<p>Equivalent to the coupled circuit in figure 3 is the arrangement shown in Figure 3. Instead of a separate winding, we use coil taps on LS to create an autotransformer. Nothing changes relative to the principles of operation that we have just surveyed, except that we lose control over the value of k. However, normal practice is to tap the inductor LS every turn or two, depending upon its construction. The result is the ability to handle a wide range of specific values of RL lower than the value required by the full inductor for a given desired primary impedance.</p>
|
||||
<p>Although subject to variations by virtue of the value of k (or the mutual inductance) necessary to effect maximum power transfer between windings, the impedance transformation may be crudely estimated by taking the ratio of the squares of the individual inductor values (or the squares of the inductor reactances). In the following representative table, we have further simplified the calculation to one comparing numbers of turns, beginning with a coil of 20 turns. Since the coil is tapped inward one turn from each end with each step, the net reduction is 2 turns per step.</p>
|
||||
<pre> Values of RL vs. Approximate Turns Ratios
|
||||
|
||||
Number Ratio to Ratio Squared Approximate Ideal RL
|
||||
of Turns Full Coil
|
||||
20 1.0 1.00 1500 ohms
|
||||
18 0.9 0.81 1215
|
||||
16 0.8 0.64 960
|
||||
14 0.7 0.49 735
|
||||
12 0.6 0.36 540
|
||||
10 0.5 0.25 375
|
||||
|
||||
Table 2. Values of RL vs. approximate turns ratios.</pre>
|
||||
<p>The values in Table 2 are not be construed as accurate for any particular coil. Their function is to show the trend in values as an inductor is tapped further toward its center. Note that it is possible to obtain a good match with load resistances in the neighborhood of 300 ohms by this method. Indeed, loads as low as 25 to 50 ohms may be accommodated by this arrangement, although when loads are less than about 100 ohms, a series circuit is generally recommended for maximum efficiency and convenience. We shall discuss series secondary circuits in a future installment.</p>
|
||||
<p>The values of RL which transform to the higher value occur in step-fashion. However, the values of RL between those steps are ordinarily easily accommodated by the variable capacitors in the tuned circuit and in the primary. Therefore, the optional series capacitors in the output circuit, which we noted were optional, are usually not required in order to effect a match.</p>
|
||||
<p>One operating inconvenience of the tapping arrangement is that the effective Q of the circuit increases as the coil is tapped closer to its center. The lower the load resistance, the higher the Q. The result throws off the values in Table 2, but this is rarely a problem, given the number of available taps and the variable capacitors in the primary and in the tuned circuit. The inconvenience arises from the sharpness of the resultant tuning. The higher the load resistance and the lower the Q, the more easily a single setting of controls and taps may cover an entire amateur band. With lower load resistances, settings may have to be changed several times to cover the same band. For very low load resistances, a series tuned secondary circuit may provide a lower-Q alternative and more convenient operation.</p>
|
||||
<p>A second inconvenience associated with the tapped-secondary form of the inductive coupler is the need to change taps. On multi-band tuners, the number of available taps can easily outgrow the ability of good RF-rated switches to handle. Manual tapping with band changes is possible, but it is often inconvenient in high speed operations, such as contests. Therefore, the tapped-secondary type inductive coupler is often used mostly for casual operation or for single-band units, such as couplers for 160 meters, where a set of taps may suffice for a given antenna, with only capacitor adjustments required as the operator moves across the band.</p>
|
||||
<center>
|
||||
<h3>Capacitor-Divider Impedance Transformers</h3>
|
||||
</center>The inconvenience of tapped secondary inductors can be largely overcome by changing the method of transforming the load resistance to the desired higher value. Instead of changing the impedance by inductive methods, one can use a capacitor divider circuit, as illustrated in Figure 4.
|
||||
<center>
|
||||
<img src="link3-4.gif" width="598" height="329" border="2" vspace="5" hspace="9">
|
||||
</center>
|
||||
<p>Except for the input-side capacitor, the schematic is similar to the Johnson Match Box design. With the capacitor, it resembles the Annecke link coupler. To see how the capacitor diver system accomplishes the same goal as the tapped inductor, lets break the circuit down into useful chunks. First, we can note that the circuit is balanced around the ground point, so let's work with a single-ended (or unbalanced) circuit. It might make the principles somewhat clearer.</p>
|
||||
<center>
|
||||
<img src="link3-5.gif" width="467" height="491" border="2" vspace="5" hspace="9">
|
||||
</center>
|
||||
<p>In Figure 5, we take a single-ended tuned circuit through several stages of development. In 5B, we simply divide the tuning capacitor shown in 5A into two paralleled capacitors: CT, which will be the main tuning capacitor, and CD, the "divider" capacitor. Of course, no dividing is yet going on.</p>
|
||||
<p>In our running example, we needed 43 pF of capacitance. We might have selected a 75 pF capacitor to provide plenty of range on either side of the projected ideal setting. If we divide the capacitor into 2 sections, we might let CT be 65 pF and CD be 12 pF. (We are here working with some convenient hypothetical values that ignore the balanced nature of the full circuit. We shall restore that circuit and more nearly correct values at the end of this exercise.)</p>
|
||||
<p>In 5C, we replace the simple capacitor CD with a differential capacitor. A differential capacitor is a split stator capacitor with the plates arranged so that as one set meshes, the other set separates. If the plates are cut for straight-line capacitance, the sum of the two capacitances is approximately equal.</p>
|
||||
<p>However, the two capacitors are arranged in series, so that the net capacitance will range from a very low value (depending on the minimum capacitance of each unit) to a maximum when each unit is meshed 50%. We might select a capacitor with a maximum capacitance per section of 50 pF, which would yield a maximum total capacitance across the unit of 12.5 pF with the plates meshed half way. If the minimum capacitance is 10 pF, then the minimum capacitance for a 10 pF and a 50 pF capacitor in series is a little over 8 pF. The differential would require very little readjustment of the tuning capacitor, CT, across the range of our new CD.</p>
|
||||
<p>Of greater interest here is the fact that the differential capacitors form a capacitor-divider, with the load resistor connected at the center junction of the differential. Since capacitive reactance is inversely proportional to capacitance, the lower capacitance side of the differential has the greater reactance, and vice versa. The reactances that apply to 5C are XT (total reactance across the differential), XU (upper side reactance), and XL (lower side reactance). since the reactances are in series, XT = XU + XL.</p>
|
||||
<p>A load of 1500 ohms (our ideal load resistance that couples back to the primary as just about 50 ohms) would require that the XU be minimum and XL be maximum. Since the minimum value of reactance is set by the maximum value of the capacitor section, there may still be some division and the load may appear as a higher value across the tuned circuit than the actual 1500 ohms value.</p>
|
||||
<p>For load values less than 1500 ohms, the differential is set at an intermediate value such that the load appears across the tuned circuit as close to the ideal value as feasible. As a crude approximation that ignores some of the variables involved in the actual circuit, the load resistances to be matched vary as the ratio of the square of the reactance across the load to ground to square of the total reactance across the capacitor divider. The following table will illustrate the trend.</p>
|
||||
<pre> Values of RL vs. Approximate Capacitor Reactance Ratios
|
||||
|
||||
CU XCU CL XCL XT XCL/XT RL
|
||||
(ideal = 1500 ohms)
|
||||
10 2273 50 455 2728 .17 43
|
||||
25 909 25 909 1818 .50 375
|
||||
40 455 10 2273 2728 .83 1041
|
||||
|
||||
Table 2. Values of RL vs. approximate capacitor reactance ratios.</pre>
|
||||
<p>Once more, the values in the table are not meant to be accurate, but to indicate the trends. Obviously, some circuit adjustments to the secondary L-C ratio would have to be made to handle higher loads, since a load of a little over a thousand ohms appears as 1500 ohms across the tuned circuit. However, it is evident that the capacitor-divider system is capable of handling a very wide range of load resistances with components of limited range.</p>
|
||||
<p>There is no reason why the sections of the differential capacitor must have the same maximum capacitance. The capacitance per section can be tailored for a desired range of XCL to XT. However, in multi-band tuners, expected perhaps to cover 80 thorugh 10 meters, the component selection will be a compromise. Hence, the range of load resistances that the tuner can accommodate may differ from one part of the spectrum to the another.</p>
|
||||
<p>In order to restore our circuit to a fully balanced version, as shown in Figure 4, we need to use a split stator tuning capacitor. Since the total capacitance across the series connected capacitor sections is to be about 75 ohms, we need to choose a 150-150 pF unit (although a 100-100 pF unit will provide the basic 43 pF required by the running example). Likewise, for a 12.5 pF total series capacitance maximum for the dual differential unit (when it is set for 50% mesh of both differential units), we shall need a maximum capacitance of about 100 pF per section at full mesh.</p>
|
||||
<p>One final advantage attaches to the dual differential capacitance divider: tuning is continuous, with none of the stepping required by the tapped inductor. Thus, a precise setting is possible for any load resistance within the divider range. In principle, this ability within the secondary does away with the need for a series variable capacitor in the primary circuit, and the Johnson Match Box indeed omitted this component. However, Annecke has restored it in order to provide the operator with an added measure of flexibility. The flexibility does mean that more than one set of control positions will provide a 1:1 SWR for the input. The best set of control positions is the one providing maximum output to the line, which requires a measurement not usually provided in any ATU.</p>
|
||||
<center>
|
||||
<h3>A Final Note on Approximations</h3>
|
||||
</center>It is necessary to add to the running warnings a final warning that all of the tables shown in this episode are based on approximations that presumed that certain other variables remained constant. In practice, these other variables would change, thus giving figures different from those in the tables. Thus, the tables show trends in values, but not actual values.
|
||||
<p>Although it is possible for any particular case to calculate quite accurate values, doing so would require the specification of all applicable variables. Where those variables can be fully specified, one might adapt the full algebraic procedures spelled out in detail in an old Rider publication called <i>Impedance Matching</i>, one small volume in the "Electronic Technology Series" from the late 1950s (edited by Alexander Schure). The relevant section is called "Transformer as Impedance Matching Device."</p>
|
||||
<p>For our purposes in this brief tutorial, not only would the full specifications obscure the general principles being presented, they would also be of limited, if any, use in designing a working link-coupled ATU. Because real ATUs operate over a wide range of load resistances and Qs, their actual design is largely a combination of approximation and experimental experience. Later, we shall present some tables of recommended values based on experience, and hopefully, these principles will be evident in their selection.</p>
|
||||
<p>At the same time, a good link-coupled ATU must also provide maximum flexibility to achieve a good match and maximum output together. So far, the circuit in Figure 4 comes closest to that ideal.<br>
|
||||
<br></p>
|
||||
<center>
|
||||
<img src="../images/colorbar.gif" align="middle" width="540" height="4">
|
||||
</center><br>
|
||||
<br>
|
||||
<p><i>Updated 11-28-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.</i><br>
|
||||
<br></p>
|
||||
<center>
|
||||
<img src="../images/colorbar.gif" align="middle" width="540" height="4">
|
||||
</center><br>
|
||||
<br>
|
||||
<a href="link4.html"><img src="../images/return.gif" align="bottom" width="40" height="40"> Go to Part 4: Series Circuits and Reactance</a><br>
|
||||
<br>
|
||||
<a href="link0.html"><img src="../images/rtnhome.gif" align="bottom" width="40" height="40"> Return to Index</a><br>
|
||||
<br>
|
||||
<br>
|
||||
<p class="topics-footer">Topics: <a href='../topics.html#matching'>Matching</a></p><br>
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<title>Link-Coupled Antenna Tuners Part IV: Series Circuits and Reactance</title>
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<h1><img src="../images/elect.gif" align="middle" width="145" height="75" border="2" vspace="5" hspace="9">Part IV: Series Circuits and Reactance<img src="../images/w4rnlwwr.gif" align="middle" width="99" height="83" border="2" vspace="5" hspace="10"></h1>
|
||||
</center>
|
||||
<center>
|
||||
<h3>L. B. Cebik, W4RNL</h3>
|
||||
</center><br>
|
||||
<br>
|
||||
<center>
|
||||
<img src="../images/colorbar.gif" align="middle" width="540" height="4">
|
||||
</center><br>
|
||||
<br>
|
||||
Every ATU circuit--network or link-coupled--has limitations. No circuit can match every possible load to the typical 50-ohms transmitter line. Two of the limitations are reactance in the load and very low values of load resistance. In this episode, we shall look at both of these problems and typical routes of solution. There is a third limitation associated with trying to design a tuner to cover all of the amateur bands. We shall deal with that one in the next installment, when we pass along some notes on components, construction, and measurement.
|
||||
<center>
|
||||
<h3>The Effects of Reactance</h3>
|
||||
</center>So far, we have dealt exclusively with resistive loads. Our purpose has been to keep the calculations--however approximate they may be--within reason. But inevitably, one has to admit that typical loads have both resistive and reactive components.
|
||||
<p>Arithmetically, we have two ways of handling reactance as part of the load. For some purposes, it is better to treat the two components together as a complex number typically shown as R +/- jX, where both R and X are given in ohms. In other applications, we can separate the two. When it comes to ATUs, reactance can usually be treated separately at the load end of the design.</p>
|
||||
<center>
|
||||
<img src="link4-1.gif" width="584" height="328" border="2" vspace="5" hspace="9">
|
||||
</center>
|
||||
<p>Figure 1 shows once more out basic link-coupled tuner circuit. We have opted initially to use a simplified tapped inductor scheme for matching lower resistive loads to the full tuned circuit. As a first step, let's consider once more a 1500 ohms resistive load connected in parallel with the resonant parallel L-C circuit. At 7 MHz, with a secondary inductor of 12 micro-H (with a reactance of 528 ohms at that frequency) and a primary inductor of 1.2 micro-H (53 ohms reactance), the resonant capacitance in the secondary was 43 pF. We chose our 1500 ohms resistive load (RL) to go with an assumed k of 0.6 for a mutual reactance (XM) of 100 ohms. The secondary loaded Q was 2.8 or so to obtain about 54 ohms for RA.</p>
|
||||
<p>However, Figure 1 shows a complex load impedance with the series values RL +/- jXL. normally, complex antenna feedpoint impedances and impedances to be found along the length of a given feedline are specified in series terms. In order to evaluate the situation, we need to convert the complex load into parallel equivalents, using the standard conversion equations:</p>
|
||||
<center>
|
||||
<img src="link4e1.gif" width="236" height="77" border="2" vspace="5" hspace="9">
|
||||
</center>and
|
||||
<center>
|
||||
<img src="link4e2.gif" width="248" height="80" border="2" vspace="5" hspace="9">
|
||||
</center>where RP and XP are the parallel equivalents to the series values RS and XS, shown as RL and XL in Figure 1. Figure 2 shows the equivalent circuits, using for the moment only the secondary of the ATU circuit.
|
||||
<center>
|
||||
<img src="link4-2.gif" width="279" height="453" border="2" vspace="5" hspace="9">
|
||||
</center>
|
||||
<p>Note that XP is in parallel with XLS and XCS, the reactances of the secondary coil and capacitor, respectively. If the equivalent parallel load reactance, XP, is inductive, then the total inductive reactance is the parallel combination of XLS and XP. Likewise, if the equivalent parallel load reactance is capacitive, then the total capacitive reactance is the parallel combination of XCS and XP.</p>
|
||||
<p>Since calculators have a convenient inverse (1/X) key, it is normally much more convenient to convert parallel reactances to parallel susceptances, which simply add, in order to obtain the value of the parallel combination. In other words,</p>
|
||||
<center>
|
||||
<img src="link4e3.gif" width="244" height="77" border="2" vspace="5" hspace="9">
|
||||
</center>where XT is the total parallel reactance, XP is the parallel equivalent of the series load reactance, and XXS is either XLS or XCS, as is appropriate to the combination being evaluated.
|
||||
<p>The following table illustrates what happens to the parallel combinations for our standard 1500-ohms resistive load when there are various series reactive loads, XL, of moderate proportions.</p>
|
||||
<pre> Parallel Inductive and Capacitive Reactances with Load Reactances
|
||||
RL=RS XL=XS RP XP XLT XCT
|
||||
1500 -500 1667 - 5000 528 -477
|
||||
1500 -200 1527 -11450 528 -505
|
||||
1500 200 1527 11450 505 -528
|
||||
1500 500 1667 5000 477 -528
|
||||
|
||||
Note: all values in ohms.
|
||||
|
||||
Table 1. Total parallel inductive (XLT) and capacitive (XCT) reactances with load
|
||||
reactances.</pre>
|
||||
<p>With modest (XL < 1/3 RL) reactive components to the load, the parallel equivalent resistive load across the tuned circuit does not change very much. The values of reactance that now compose the tuned circuit are sufficiently different to require adjustment of the variable capacitor to restore resonance. Where the reactive load is capacitive, the capacitor must show less capacitance and more capacitive reactance to make up for the loss occasioned by the parallel equivalent capacitive load reactance.</p>
|
||||
<p>Where the reactive load is inductive, the capacitor must show more capacitance and less reactance to resonate with the reduced inductive reactance occasioned by the parallel equivalent inductive load reactance. However, these values are not the optimum to effect a transformation to 50 ohms in the primary. Hence, other adjustments of the tuner components may be needed to effect a good match, including moving to a different tap of the coil.</p>
|
||||
<p>When the load is transformed from a lower value to a higher value needed by the secondary tuned circuit to effect a transformation to a desired primary impedance, not only is the resistive component increased in value, but so too is the reactive component. For most cases, the chief effect of this transformation is to reduce the effects of the secondary variable capacitor in compensating for the changes in total parallel reactance. This effect is especially pronounced with inductively reactive loads which, when treated in parallel equivalent form, move the inductive reactance of the tuned circuit components well off their optimum values. The capacitor setting required may result in a considerable offset, resulting in a resonant frequency (in terms of XLS = XCS) significantly removed from the operating frequency. The result will often be higher circulating currents within the tuned secondary circuit and lower efficiency of power transfer to the load. However, these losses are ordinarily very small if a high Q coil is used and the loaded Q of the circuit is held low.</p>
|
||||
<p>The conditions of maximum efficiency cannot always be achieved, especially if the ratio of reactance to resistance in the load becomes great. Moreover, the higher the Q of the secondary circuit, the smaller the frequency range over which a single set of adjustments are usable. These conditions hold true whether one is using a tapped inductor or a capacitor divider as the means of effecting a match with a wide range of load values.</p>
|
||||
<center>
|
||||
<h3>Advanced Compensation for Reactance</h3>
|
||||
</center>As we earlier noted, we can separate the resistive and reactive components of the load impedance presented to the ATU terminals. In doing so, we can think about compensating for the reactance before it becomes part of the secondary tuned circuit values. Figure 3 shows several ways of handling the situation.
|
||||
<center>
|
||||
<img src="link4-3.gif" width="296" height="528" border="2" vspace="5" hspace="9">
|
||||
</center>
|
||||
<p>In 3A and 3B, we treat the reactance at the terminals in its series form. If the reactance is inductive, we insert a mechanically linked pair of capacitors--one in each side of the line--to provide an equal but opposite value of capacitive reactance. If the reactance at the terminals is capacitive, we insert a pair of series inductors in the line to provide equal but opposite reactance. The net reactance is zero, and the tuner sees a resistive load.</p>
|
||||
<p>Series compensation is normally mechanically difficult, especially with the use of variable components. First, each side of the line must be broken to insert the proper compensating component. Dual components are necessary to preserve line balance. Second, mechanically linked components are bulky--inductors even more so than capacitors. Series compensation is rarely used.</p>
|
||||
<p>In 3C and 3D, we treat the reactance in its parallel equivalent form. This conversion permits us to place either a coil or a capacitor across the line to provide an equal but opposite reactance value to cancel the parallel equivalent reactance presented by the load. Very usually, single ended components are employed in this function. Because of slight imbalances in the structure of such components, the line balance may be slightly disturbed, but ordinarily not enough to hinder circuit or transmission line operation. The switching or tapping methods should remove both sides of the compensating component when it is not in use.</p>
|
||||
<p>The use of advance reactance compensation is necessarily reserved for very high load reactances that challenge the ability of the variable capacitor in the secondary circuit to effect a match or which unduly raise the Q of line or the coupler circuit. Series reactances in this range normally convert to parallel-equivalent low to moderate reactance values which are within the range of reactance compensation by good quality everyday components. When series reactances are themselves low to moderate, most coupler designs can easily accommodate them. In addition, their parallel equivalent values may be beyond the range of compensating components.</p>
|
||||
<p>For example, in Table 1, a series reactance of 200 ohms, is easily handled by the coupler design used in our running example. However, compensation by parallel components is another matter. If the load reactance is capacitive, it would require a compensating inductance of 260 micro-H, and if the load reactance is inductive, it would require a compensating capacitor of 2 pF at the 7 MHz operating frequency. Needless to say, neither of these are practical values to find in variable components.</p>
|
||||
<center>
|
||||
<h3>Feedline Length</h3>
|
||||
</center>An alternative means of reducing the reactance at the terminals of any coupler is to change the length of feedline from the antenna to the coupler output terminals.
|
||||
<p>Every feedline is also an impedance transformer all along every 180 degrees of its length. If the antenna feedpoint impedance exactly matches the characteristic impedance (ZO) of the feedline, then the impedance along the line is constant at the value of line ZO. If the antenna feedpoint impedance differs from the ZO of the line, then the value of impedance, in terms of R +/- jX, varies all along each 180-degree length of line. This is true, whether the antenna feedpoint impedance is purely resistive or a combination of resistance and reactance.</p>
|
||||
<p>With a complex feedpoint impedance that does not match the ZO of the feedline, there may be some line lengths that present easy combinations of R +/- jX for a given coupler design to handle and other lengths that present values that may exceed the coupler design limits. Hence, selecting something close to an optimum line length may enhance the ability of the tuner to compensate for the reactance and maximize power transfer to the feedline.</p>
|
||||
<p>Let's use a challenging antenna case to see how this works. A certain antenna presents a feedpoint impedance at 7 MHz of 1828 + j1826 ohms. Assuming that we are using 450-ohms parallel feedline with a velocity factor of 0.95, we can obtain the following table of impedance values along a 180-degree length of line. (Similar tables at 5-degree intervals can be obtained from a program included with the VE3ERP <a href="../radio.html#HAMCALC">HAMCALC</a> collection. The values assume lossless line, but for planning use with antenna tuners, the accuracy will be more than adequate.)</p>
|
||||
<pre> Resistance and Reactance Along a 450-ohms Feedline
|
||||
|
||||
Line Length Impedance
|
||||
Degrees Feet Resistance (ohms) Reactance (ohms)
|
||||
0 0 1828 1826
|
||||
10 3.7 3173 -1291
|
||||
20 7.4 857 -1513
|
||||
30 11.1 334 - 970
|
||||
40 14.8 179 - 662
|
||||
50 18.5 116 - 469
|
||||
60 22.3 85 - 333
|
||||
70 26.0 69 - 226
|
||||
80 29.7 60 - 136
|
||||
90 33.4 55 - 55
|
||||
100 37.1 55 22
|
||||
110 40.8 57 101
|
||||
120 44.5 64 187
|
||||
130 48.2 77 285
|
||||
140 51.9 100 407
|
||||
150 55.6 146 571
|
||||
160 59.3 249 820
|
||||
170 63.0 545 1245
|
||||
180 66.7 1828 1826
|
||||
|
||||
Table 2. Resistance and reactance along a 450-ohms feedline for a typical antenna.</pre>
|
||||
<p>If the line length must be more than 1/2 wavelength, just add increments of 66.7' to the lengths listed to get just about the same values. But now that we have the table, what do we look for?</p>
|
||||
<p>We are seeking a length of line where the reactance values are low. Achieving a zero level of reactance is unnecessary, but values under 200 ohms would be well within the range of virtually any coupler. Notice that the reactance passes through zero in two places. However, reactance curves are not orderly sine waves. Between 0 and 10 degrees, the reactance rapidly changes from a high inductive value to a high capacitive value. Since this makes finding the right length difficult, we shall avoid this transition. Between 90 and 100 degrees, the reactance passes slowly through 0. Hence, the exact line length becomes far less critical. In feet at 7 MHz, the ideal length is close to 36 feet long, but plus or minus 7-10 feet either way would not challenge the coupler.</p>
|
||||
<p>Since almost any multi-band antenna can be modeled with reliable ballpark accuracy on all intended bands of use, it is possible to develop a full set of feedline charts plotting the excursions of resistance and reactance. Simply plug the modeled feedpoint impedance for each band into the impedance transformation program and print out a chart. By examining the reactance progressions for each band, it may be possible to find a minimal number of line lengths that will permit an easy match for the coupler.</p>
|
||||
<p>Under very fortunate circumstances, you may find a single line length that will physically work with the antenna in question and also provide reasonable reactance levels for the tuner. If two or more lengths are requires, then switching or manually adding in the required line lengths for the band or bands which need them becomes the next order of business. Of course, all of the rules for treating parallel line carefully apply to this system. Hence, the actual switching system becomes a challenge for the creativity of the individual station operator. Line switching is often very much cheaper and less complex than installing and switching pre-coupler compensating inductors and capacitors.</p>
|
||||
<center>
|
||||
<h3>Low Impedances and Series Connections</h3>
|
||||
</center>Because parallel-tuned secondary capacitor-divider load input ATUs are capable of matching loads from less than 50 ohms up to several thousands of ohms, we have focused primarily on parallel connection of the load to the secondary of the coupler. However, there are antennas which present loads in the 5 to 100 ohms range which can often benefit from a series secondary in the coupler. Figure 4 shows a typical arrangement.
|
||||
<center>
|
||||
<img src="link4-4.gif" width="547" height="320" border="2" vspace="5" hspace="9">
|
||||
</center>
|
||||
<p>Typical inductor and capacitor values are so similar to those for parallel tuners that we can retain our chosen values in the running example: 12 micro-H for the secondary and 1.2 micro-H for the primary. Their respective reactances are 528 and 53 ohms. The series reactance of the capacitor will likewise be 528 ohms at ideal resonance, and hence, each section must be able to provide half this value, just as in the parallel tuner. For a total capacitance of 43 pF, each section must be able to reach 86 pF. However, the capacitor cannot be a simple split stator-common rotor model, but must be a pair of independent units mechanically driven as a unit. Some apparent split stator models are actually of this design and use a jumper for achieving a common rotor, which is then grounded for balance across the line. With the series connection, the capacitor sections must each float (that is, be well insulated from a common ground).</p>
|
||||
<p>From one perspective, the equations that drive a series circuit look quite different from those that drive the parallel circuits we have been examining. Yet, as an exercise in "what goes around comes around," let's look at these equations.</p>
|
||||
<p>For a series tuned inductively coupled tuner, where the secondary is presumed to be resonant, the input or primary impedance is a function of the reactance of the mutual inductance and the load resistance:</p>
|
||||
<center>
|
||||
<img src="link4e4.gif" width="215" height="79" border="2" vspace="5" hspace="9">
|
||||
</center>where RA is the coupled primary impedance, XM is the reactance of the mutual inductance, and RL is the value of the resistive load, with all values in ohms.
|
||||
<p>Once more, XM is related to the coefficient of coupling (k) in this way:</p>
|
||||
<center>
|
||||
<img src="link4e5.gif" width="250" height="59" border="2" vspace="5" hspace="9">
|
||||
</center>where XLP is the reactance of the primary inductor and XLS is the reactance of the secondary inductor, both in ohms. This equivalence allows us to replace the term XM2 in equation (4) with its counterpart:
|
||||
<center>
|
||||
<img src="link4e6.gif" width="241" height="76" border="2" vspace="5" hspace="9">
|
||||
</center>where all terms have the same meanings as previously noted.
|
||||
<p>Unlike a parallel tuned circuit, the loaded or working Q of a series-tuned circuit is</p>
|
||||
<center>
|
||||
<img src="link4e7.gif" width="209" height="68" border="2" vspace="5" hspace="9">
|
||||
</center>If we replace the terms XLS and RL with Q, we obtain
|
||||
<center>
|
||||
<img src="link4e8.gif" width="234" height="56" border="2" vspace="5" hspace="9">
|
||||
</center>which is the same equation we used for analyzing parallel-tuned circuits in the last two episodes.
|
||||
<p>Series-tuned couplers are normally used with low coefficients of coupling to effect matches of low impedances to the coupler input impedance. If we let the desired value of RA be the same as the value of the primary inductor reactance (about 50 ohms),</p>
|
||||
<center>
|
||||
<img src="link4e9.gif" width="244" height="107" border="2" vspace="5" hspace="9">
|
||||
</center>where all values are as previously defined.
|
||||
<p>Using equation (9) with our running example circuit values, we can develop a small table of reasonable values of k to effect a 50-ohms match with various load resistances.</p>
|
||||
<pre> Values of k for a 50-ohms Match with Various Loads
|
||||
|
||||
Load Resistance Loaded Q Required k
|
||||
(RL) (XLS/RL) for 50-ohms match
|
||||
100 5.3 0.44
|
||||
50 10.6 0.31
|
||||
25 21.1 0.22
|
||||
10 52.8 0.14
|
||||
|
||||
Table 3. Values of k for a 50-ohms match with various loads where XLS = 528 ohms.</pre>
|
||||
<p>The table clearly shows the progression of values, but also shows a rapidly increasing Q as the load resistance to be matched goes down. High Q has the same effect with series- tuned circuits as with parallel-tuned circuits: the required settings become very narrow and must be changed with small excursions of the operating frequency.</p>
|
||||
<p>Additionally, the presence of reactance in the load has the effect of requiring the tuning capacitor to be reset to restore resonance. Where the load reactance is capacitive, the overall component reactance at resonance can be maintained, because shifting the capacitor to a higher capacitance setting reduces its reactance to compensated for the line reactance: the net capacitive reactance is the same as the inductor's reactance at resonance. However, if the load reactance is inductive, it adds to the reactance of the secondary coil. This situation requires a change in the capacitor setting to a smaller value to match the combined inductive reactance to restore resonance. The effective reactance at resonance is higher, thus increasing the circuit Q and increasing the inconveniences (and possible problems) associated with high Q.</p>
|
||||
<p>The most convenient way in most typical amateur circumstances to rid the load of its high reactance with a series tuned coupler is to alter the line length. However, in doing so, we can usually find a line length with a higher load resistance as well as a lower load reactance. Since parallel tuned coupler designs are available for loads of 50 ohms or even slightly less, the end result has been a gradual decline in the use of series-tuned coupler circuits.</p>
|
||||
<p>In the end, the parallel-tuned link coupler, with either a tapped secondary or a capacitor- divider for handling a wide range of load impedances, is the circuit of choice for inductive couplers. The tapped secondary version, while useful for manual operation in multi-band units, is often used with single-band couplers, say, for 160 meters. Once the right settings are found, no further manual changes in taps are normally needed during operation. Such tuners are also cheaper to build, since soldering taps to coil turns is normally less expensive and easier to accomplish than finding a suitable differential capacitor for the alternative load network.</p>
|
||||
<p>For multi-band couplers, the capacitor divider provides continuous front panel adjustment for changes of load impedance. With a multi-section ceramic wafer switch to set the inductor size for each band, along with the tuned circuit variable capacitor and the optional series input capacitor, this design can be reset from band to band quickly as one changes operating frequencies.</p>
|
||||
<p>We have now looked into the basic theory and fundamental circuitry of inductively coupled ATUs. The remaining questions we need to examine concern component values and ratings, construction practices, and measurements to assure best results. Perhaps we can do all this in just one more session.<br>
|
||||
<br></p>
|
||||
<center>
|
||||
<img src="../images/colorbar.gif" align="middle" width="540" height="4">
|
||||
</center><br>
|
||||
<br>
|
||||
<p><i>Updated 11-28-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.</i><br>
|
||||
<br></p>
|
||||
<center>
|
||||
<img src="../images/colorbar.gif" align="middle" width="540" height="4">
|
||||
</center><br>
|
||||
<br>
|
||||
<a href="link5.html"><img src="../images/return.gif" align="bottom" width="40" height="40"> Go to Part 5: Components, Construction, and Measurement</a><br>
|
||||
<br>
|
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<a href="link0.html"><img src="../images/rtnhome.gif" align="bottom" width="40" height="40"> Return to Index</a><br>
|
||||
<br>
|
||||
<br>
|
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<p class="topics-footer">Topics: <a href='../topics.html#matching'>Matching</a></p><br>
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<title>Link-Coupled Antenna Tuners Part V: Components, Construction, and Measurement</title>
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<h1><img src="../images/elect.gif" align="left" width="145" height="75" border="2" vspace="5" hspace="9"><img src="../images/w4rnlwwr.gif" align="right" width="99" height="83" border="2" vspace="5" hspace="10"><br>
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Part V: Components, Construction,<br>
|
||||
and Measurement</h1>
|
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</center>
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<center>
|
||||
<h3>L. B. Cebik, W4RNL</h3>
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</center><br>
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<br>
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<center>
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<img src="../images/colorbar.gif" align="middle" width="540" height="4">
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<br>
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The remaining questions we need to examine with respect to inductively coupled ATUs are component values and ratings, construction practices, and measurements to assure best results. Let's look at these questions, one at a time. We shall be focusing upon parallel-tuned secondaries, with either taps on the inductor secondary or a capacitor-divider to accommodate a wide range of load impedances. Figure 1 provides an abbreviated schematic diagram of both types of circuits. We shall use CP, CS, and CD to sort out the capacitors in the primary, secondary, and (if used) divider circuit. LP and LS will designated the inductor primary and secondary windings.
|
||||
<center>
|
||||
<img src="link5-1.gif" width="458" height="435" border="2" vspace="5" hspace="9">
|
||||
</center>
|
||||
<center>
|
||||
<h3>Component Values</h3>
|
||||
</center>There is no magic set of values for the components in an inductively coupled tuner. Instead, there are a few situations we want to avoid and then a set of reasonable compromises to make. The situation to avoid is having too high a value of CS relative to LS. Lower values of inductance carry with them lower values of inductive reactance. This, in turn, lowers the Q of the coil for resonant combinations on the ham bands, resulting in greater power losses in the coil.
|
||||
<p>The 1960 <i>ARRL Antenna Book</i> recommends a secondary component reactance value of about 500 ohms as a reasonable compromise. This value tends to yield higher Q inductors whose physical size is not too much different than the physical size of variable capacitors having the desired characteristics. Here is a table of the resulting values, not only for the secondary components, but for the primary components as well (assuming a 50-ohms matching with the transmitter). I have extended the list to include the WARC bands.</p>
|
||||
<pre> Recommended Component Values for a Link-Coupled Tuner
|
||||
Band LS CS LP CP
|
||||
160 42 micro-H 170 pF 4.2 micro-H 1700 pF
|
||||
80-75 22 90 2.2 900
|
||||
40 12 45 1.2 450
|
||||
30 8 32 0.8 320
|
||||
20 6 23 0.6 225
|
||||
17 4.5 18 0.45 180
|
||||
15 4 15 0.4 150
|
||||
12 3.2 13 0.32 130
|
||||
10 2.9 12 0.29 120
|
||||
|
||||
Table 1. Recommended component values for a link-coupled tuner.</pre>
|
||||
<p>These recommended values tell us several very practical things. First on the list is the reason why commercial ATU manufacturers rarely try to cover 160 meters with an all-band tuner. The 160-meter coil will be roughly twice as large--for any given power level--as he 80-10-meter coil. Likewise, the tuning capacitor will be large. In the primary circuit, the series capacitor may require either ganging two variables or adding fixed capacitors in parallel with a 1000 pF unit.</p>
|
||||
<p>In general, the component size question for 160-meter tuners also inclines builders to using a tapped coil secondary circuit (instead of the capacitor-divider system). Taps every 2 or 3 turns down to a coil size of 50% of the full length should suffice for most loads encountered. For a specific antenna system, once the correct taps are found, they should not need to be changed. Indeed, it may be possible to use a good ceramic wafer rotary switch to move between taps.</p>
|
||||
<p>Second on our list of lessons from the recommended values is the practicality of an 80-10 meter link coupled tuner. For a very simple design, coil taps may be used, but the capacitor divider system may prove far superior in terms of its continuous range of adjustment. A dual differential capacitor of about 100 pF per section will generally suffice for the capacitor divider.</p>
|
||||
<p>If we use the primary series capacitor, we may be able to combine the 12 and 10 meter positions to save one band switch position. Likewise, the 17 and the 15 meter position may be combined. A 3 section, 6 position ceramic rotary switch should suffice to cover all the bands.</p>
|
||||
<p>Notice that the primary coil should also be tapped for band changing purposes. Depending on the coil construction, some builders may wish to cover more than 2 bands with a single tap, since tapping at partial turns may be physically inconvenient. Tapping the primary is normally done on only one end of the coil. Hence, the position of the primary coil may not be perfectly centered for all bands. This slight imbalance does not produce any significant negative effects.</p>
|
||||
<p>The series circuit may be altered to use lower values of series capacitance by increasing the size of the primary inductor. Values up to double or triple the recommended value may be used on 80 meters to make use of series capacitors in the 350-500 pF range. As the frequency is increased, the coil taps may be brought closer to their optimum recommended values, since the required resonating capacitance would fall within the range of the smaller unit selected.</p>
|
||||
<p>As one increases frequency toward the high end of the HF spectrum, the range of the capacitors is not optimum for smooth tuning. Even though circuit Q may be satisfactorily low, control positions may be very sharp. Ideally, one should consider separate tuners for 80-20 meters and for 20-10 meters. The latter unit may use smaller capacitors and more widely spaced inductor turns. However, for all-band doublets and similar wide-ranging antennas, the 80-10 meter ATU is usually the design of choice.</p>
|
||||
<p>In principle, if space is available, paralleling a high value and a low value variable capacitor can provide more optimal control of capacitance. Both capacitors should have the same voltage rating. At 14 MHz and above, the larger capacitor is switched out of the circuit. Below 20 meters, the smaller capacitor is set at mid-range, with main tuning done with the larger capacitor. The smaller capacitor may then be used as a "fine tuning" control. Since this system requires extra space, an alternative is to use a reduction drive with the main tuning capacitor.</p>
|
||||
<p>The capacitance values given in the chart are the total capacitance across the parallel- tuned secondary circuit. Split-stator or ganged capacitors are normally used to preserve balance across the circuit. Each section should have a capacitance of twice the listed value so that the series combination equals the recommended value.</p>
|
||||
<p>Varying the circuit values does little harm to coupling efficiency so long as sufficient flexibility is maintained in the primary series resonant circuit and in the secondary load impedance transformation circuit. Limitations show up chiefly in the range of load impedances that the coupler can effectively handle, and careful line-length adjustment can usually provide load values within the capabilities of the coupler.</p>
|
||||
<center>
|
||||
<h3>Component Specifications</h3>
|
||||
</center>The best way to look at the components, is one at a time.
|
||||
<p><b>Inductors</b>: For moderate power levels up to 200 watts or so, air-wound inductors with a diameter of 2 to 2.5" and 8 turns per inch (tpi) are very practical. They provide reasonably sized inductors with good Q across the HF range. Inductor Q will normally decrease at the highest frequencies in the range. For 160 meters, a coil of larger diameter may be required to hold its length within reason.</p>
|
||||
<p>Placement of the link at the center of the secondary usually follows one of two physical designs. In simpler designs, the link may be several turns of the main coil stock. The turns adjacent to the limit of the link are tied together to provide continuity in the secondary. Although this system will work, it limits the range of coefficients of coupling. Tighter coupling can be obtained by placing the primary inductor over the secondary. For fixed links using typical air- wound inductor stock, a nonconductive adhesive can bind together the support bars of the coils.</p>
|
||||
<p>The current which the parallel-tuned secondary coil must handle can be estimated from the following simple equation:</p>
|
||||
<center>
|
||||
<img src="link5e1.gif" width="234" height="84" border="2" vspace="5" hspace="9">
|
||||
</center>where IC is the estimated maximum circulating current in amps, QL is the loaded or working Q of the coupler, P is the power level in watts, and RL is the load resistance in ohms at resonance. For a maximum Q of about 10, a power level of 100 watts, and load resistance of 5000 ohms, the maximum current will about 1.4 A. If we use the ideal case in our running example of a load resistance of 1500 ohms and a Q of 2.8, the current is only 0.7 A.
|
||||
<p>Increasing the power to 1500 watts from 100 watts increases the circulating current by the square root of the power ratio. For the two sample cases, the maximum current will be 5.4 A and 2.7 A, respectively. For high power applications, #12 wire is generally satisfactory for these levels, while #14 wire may be used at mid-level powers.</p>
|
||||
<p>For very low power levels, such as those encountered in QRP work (5 watts or less), it is theoretically possible to use wire as fine as #20 or #22. However, at very low power levels, every effort should be made to minimize power loss. The high power wire sizes do not guarantee minimum loss, but only that power losses in the inductor wire are not problematical. Minimum loss wire sizes would be larger, and at QRP levels #18 wire or larger is always in order for inductors with minimal losses.</p>
|
||||
<p>The current in the primary winding is a function of the coil reactance and the power level. For example, if we use a coil with a reactance of about 50 ohms, the current at 100 watts power will be about 1.4 A. Viewed another way, the current will be about the same as the maximum circulating current in the secondary tank circuit. Hence, wire size recommendations applicable to the secondary are also applicable to the primary.</p>
|
||||
<p><b>Capacitors</b>: The chief problem facing inductors is heat from the conversion of RF currents. This problem has a time domain, and brief periods of excessive current are often without harm. With capacitors, the chief problem is arc-over, which may result from virtually instantaneous peak voltages across the capacitor plates.</p>
|
||||
<p>The voltage across the primary series capacitor will be a function of the capacitor reactance and the power level. If a 50-ohms capacitive reactance is used, then at 100 watts, the voltage peak will be 1.4 times the r.m.s. voltage across the capacitor or about 100 volts. At 1500 watts, this peak voltage will increase by the square root of the power increase to about 385 volts. These levels are within the abilities of various sizes of receiving capacitors, which are often employed to achieve the high values of capacitance needed at 80 meters.</p>
|
||||
<p>If the 80 meter capacitance is reduced to 1/3 of the recommended 1000 pF, the capacitive reactance will increase by a factor of 3. In this case, the peak voltage at the 100 watt power level will be about 170 volts. At 1500 watts, the peak voltage reaches about 665 volts. More widely spaced capacitor plates will be required.</p>
|
||||
<p>In the parallel-tuned secondary circuit, the peak voltage is simply 1.4 times the r.m.s. voltage across the tuned circuit. The line voltage is a function of power level and load resistance, where</p>
|
||||
<center>
|
||||
<img src="link5e2.gif" width="246" height="55" border="2" vspace="5" hspace="9">
|
||||
</center>For the example using a load of 5000 ohms at 100 watts, the peak voltage is about 1000 volts. Where the load is 1500 ohms at the same power level, the peak voltage drops to 540 volts. At the 1500 watt power level, these peak voltages increase to 3870 and 2100 volts, respectively. However, off-resonance voltage peaks may be considerably higher.
|
||||
<p>The actual arc-over voltage for a capacitor depends on many factors, including the sharpness of the edge of the capacitor plates and the air quality and humidity around the capacitor. In general, capacitors are chosen with a good reserve. 1500-volt units are common at 100 watts, 3 kV units at 250 watts, and 7 kV of higher units for the legal amateur power limit. These values provide about a 2:1 safety margin in balanced circuits using split stator or ganged capacitors, where each unit of the whole capacitor sees only half the total peak voltage across the line.</p>
|
||||
<p>An often overlooked aspect of capacitor construction is the size of the capacitor frame and its materials. Large, closely space metallic frames can restrict the minimum value of capacitance obtained by a variable capacitor. E. F. Johnson units used in their Match Box series of link tuners employed the minimum metal frame to support the capacitor and permitted very low values of minimum capacitance. These or similar units are desirable in tuners designed to cover the entire 80 to 10 meter range of amateur bands, especially in the parallel tuned secondary of the coupler.</p>
|
||||
<p>Capacitor construction is equally important in maintaining circuit balance with respect to ground. Split-stator capacitors provide an inherently balanced structure, with roughly equal influences on both sides of the circuit from stray capacitance to a metal case or other metallic objects in the circuit. Single-section capacitors, while usable, tend to unbalance the circuit by coupling more capacitance through the larger structure of the frame than through the set of plates not connected to the frame.</p>
|
||||
<p>For capacitor-divider circuits, the capacitors form a series chain of 4 units across the line. Each unit sees about a fourth of the total line voltage. However, with considerable reactance on the line, the voltage across each unit may be somewhat higher. Therefore, the voltage rating of the dual differential capacitor is usually set to be the same as for the split-stator tuning capacitor.</p>
|
||||
<p>When an inductive coupler is undergoing initial tuning, the control combinations may result in very high voltages across capacitors in the circuit. Therefore, initial tune-up should always be done at the lowest power possible to prevent component arc-over.</p>
|
||||
<p><b>Rotary Switches</b>: Rotary switches used to change bands or coil taps should have large, well-spaced contacts. The material should be ceramic, rated for RF service. For medium power levels, standard 1.25" wafers are normally satisfactory. For high power, use larger switching wafers with more widely spaced and large contacts.</p>
|
||||
<p>Shorting switches--that is, switches that connect together all preceding switch positions-- are preferable to simple switches that leave preceding switch positions open. Shorting out the unused turns in the secondary coil normally results in fewer problems with power losses from circulating currents in those turns. However, only experiment can usually determine whether the interturn capacitance in combination with the inductance of the unused turns may result in a resonance at some harmonic of the operating frequency. For this reason, some designers add an additional coil position on multi-band tuners, roughly tuned to 5 to 5.5 MHz. Although this tap might prove useful on some occasion with particularly troublesome 80 or 40 meter loads, its chief function is to reduce the size of shorted inductor sections when operating above 40 meters.</p>
|
||||
<p><b>Terminals</b>: The input terminal for most ATUs will a standard coaxial cable fitting. Output terminals should be ceramic feed-through types. Ring or U terminals are normally used for both inside and outside connections to the threaded shaft that runs through the dual ceramic pillars. Steatite, developed three quarters of a century ago, is still the usual ceramic of choice for RF service in the HF bands.</p>
|
||||
<center>
|
||||
<h3>Construction and Operation</h3>
|
||||
</center>The inductively coupled tuner is essentially a combination of passive circuits and produces no power of its own. Therefore, the shielding practices normally used for power producing equipment are to a large measure optional with antenna tuners. Perfectly operational tuners may be laid out on breadboards or placed within attractive wooden or clear acrylic cabinets. Perhaps the only operational caution with unshielded layouts is to insulate control shafts in order to prevent shock haxards and hand-capacitance effects. Safety to shack visitors (or to the operator) is a strong reason for enclosing the tuner.
|
||||
<p>If a metal case is used, it should be large enough to permit all components to be well spaced from metallic surfaces. This precaution reduces the introduction of stray capacitance, which can reduce the flexibility of the variable controls, especially at higher frequencies. With metal cabinets, long, sturdy ceramic stand-off insulating posts must be used for components that require isolation from ground.</p>
|
||||
<p>Component layout should follow good RF practice, with attention to maintaining secondary circuit balance. Hence, leads to and from comparable points on either side of the center of the secondary should be as short as possible and of roughly equal length and proximity to adjacent components. Leads in the secondary should use wire of the same size as the coil winding. It is possible to space switch wafers to achieve this physical balance, and the rest is largely a matter of component placement.</p>
|
||||
<p>The primary side should use short heavy leads. If the coil primary assembly is at some distance from the coax fitting, a length of coaxial cable may be used to connect the two.</p>
|
||||
<p>A common ground of the smallest spread provides the least potential for excessive current circulating in this path. Even when metal cases are used and form the ground bus, care should be taken to use contact points in closest proximity to each other, commensurate with the use of short leads.</p>
|
||||
<p>Input and output measurement circuits, if internal to the tuner, should be isolated from the fields surrounding the main components of the tuner. The DC and meter portions of the measuring circuits are best isolated by placing them in grounded metal boxes as far as possible from the main coil and capacitors.</p>
|
||||
<p>The input side of the coupler is normally an unbalanced circuit. It requires a common ground. Ideally, this ground should be common with the other station equipment ground as well as the station earth ground.</p>
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<p>The balanced secondary of the tuner presents the user with some options. Ordinarily, the center of the coil is left ungrounded (or "floating"), largely due to difficulties presented by the centering of the link over the center of the secondary inductor. The center of the split-stator tuning capacitor and the junction of capacitor-divider differential units are often grounded as a matter of construction convenience when using metal cases or chassis. This connection is, however, optional. (However, it is good practice to connect the junction of the differential capacitors to the common rotor of the main tuning capacitor.)</p>
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<p>Grounding the center of the of the secondary circuit provides a common reference for the two sides of the feedline and the secondary circuit. However, it also provides a point of direct coupling for out-of-band signals. Such coupling is significantly reduced if all secondary components are left floating. Home constructors may wish to experiment to determine the better system for their individual situations. A floating secondary may be especially useful with 160- meter tuners, where strong AM broadcast band stations require all the filtering possible.</p>
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<p>Tuning up the coupler is a matter of finding the correct control settings for maximum output and a 1:1 SWR at the input. Initial tuning is largely trial and error in the absence of definitive knowledge of the load resistance and reactance. For a tuner using a tapped secondary inductor, a trial balanced pair of taps is the starting point (at low power, of course). The secondary capacitor is resonated, as indicated by a dip in the SWR metering circuit that is in the primary line either inside or outside the tuner. The series capacitor is then adjust to the lowest SWR, followed by a series of alternate tweakings" of the primary and secondary capacitors. If the initial taps do not result in a 1:1 SWR, the next adjacent set should be tried--and so on until the match is obtained.</p>
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||||
<p>The goal is to use the set of taps closest to the outer limits of the secondary inductor that permit a perfect match. These taps represent the lowest working Q for the circuit and thus provide the largest bandwidth for satisfactory operation without further control adjustment. Ordinarily, they also provide maximum power output. However, as noted along the way, it is possible--although unusual--to find a perfect match while most of the current is circulating within the components rather than going to the line.</p>
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<p>For the capacitor-divider coupler, the coil tap is usually fixed by a band switch. Adjustment involves alternate changes to the series primary capacitor, the secondary resonating capacitor, and the differential capacitor. However, the aim is the same: the lowest Q (and broadest tuning) that still permits a perfect input SWR reading. Since an opaque case and simple reference marks tend to obscure what is happening with the capacitor-divider, the bandwidth of an adjustment set may be the only indication that the most satisfactory match has been obtained.</p>
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<p>All final setting should be logged and attached to the tuner case. Not only do they ease the adjustment when changing frequencies, they also provide a reference for antenna system diagnosis. If the required settings drift with time, vary radically with certain weather changes, or change suddenly to a new permanent set, antenna and feedline maintenance is indicated.</p>
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<center>
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<h3>Measurement</h3>
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</center>Two measurements are important to any coupler: the match of the input circuit with the line to the transmitter (and receiver) and the relative power output. Ordinarily, we make the first of these measurements and simply presume that the second needs no measurement. The ordinary is simply not good radio practice.
|
||||
<p>The input monitor usually consists of an SWR metering circuit mounted within the tuner cabinet or placed in the line between the tuner and the transmitter. Either system works well. Since SWR circuits are legion, no further comment on them is required, except perhaps for the reminder that the DC metering portion of the circuit should be well shielded from the fields of the tuner components.</p>
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<p>Output measuring has long been unnecessarily difficult, since standard recommendation call for RF ammeters, which are difficult to find, especially in the ranges useful for the wide variety of amateur power levels. For higher power, light sources coupled to high-voltage positions along the line have provided an alternative power output indication.</p>
|
||||
<p>Since the coupler may encounter a wide range of load impedances whose actual values are not easily determined, true power output is not the measurement of choice. Rather, efficient operation of the coupler is a matter of achieving the highest possible power output for any given input. Hence, a relative power output indicator is sufficient for most non-laboratory applications.</p>
|
||||
<p>For any given load impedance, both the current and the voltage will rise as power is increased. Both rise as the square root of the power increase. Therefore, a simple voltage sampler may be connected to the output terminals of the coupler and left in the line permanently. The sample voltage can be rectified, filtered, and then measured with a voltmeter. For relative readings, where we wish to track the rise and fall of the voltage as we adjust tuning controls, an analog meter is preferable.</p>
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<center>
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<img src="link5-2.gif" width="430" height="426" border="2" vspace="5" hspace="9">
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<p>Figure 2 shows the basic schematic diagram of a relative output meter. High value voltage dividers go from each terminal to ground. The resistors should be in the Megohms, but the exact values should be determined experimentally relative to the range of impedances and power levels used by a particular station. Diodes provide full-wave rectification of the sampled RF. At levels higher than QRP, use high-voltage diodes as a protection from reverse voltage breakdown. The potentially high impedance of the output circuit dictates a higher level of filtering than usually applied to low impedance circuits.</p>
|
||||
<p>In this basic circuit, a simple potentiometer may act as a sensitivity control and thus be the only element within the "Amp. & Control" box in Figure 2. An FET op amp in a voltage follower circuit provides the voltage and current the voltmeter. It is wise to add zener diode or other protection to prevent meter damage from excessive voltage levels.</p>
|
||||
<p>The circuit is open to innumerable improvements in the "Amp. & Control" section, especially for automating the meter range for the wide variety of sample voltage levels that the tuner may provide. A second voltage divider might be used as a reference to one of the bargraph LED driver chips to obtain up to ten decades of control. The chip output would not only light an LED telling the operator which decade was in use, but as well trigger a control chip that inserted the correct voltage reducing resistor for each step rise in power level. Of course, such improvements require a modicum of power, and all such circuitry requires excellent shielding.</p>
|
||||
<p>The point of this exercise is to move us into contemporary means available for monitoring coupler output without disturbing the balance of the tuner at any power level. By tracking relative power output from the tuner, we can assure that we not only have achieve a correct input-side match, but as well have achieved maximum power output. It is the output that does the work of communicating, not the match.</p>
|
||||
<p>This small tutorial has drawn on a large number of sources in an effort to bring together the principles and practices of inductively coupled tuners. If such tuners are better understood, they may once more take their proper place beside network tuners, each doing the job for which it is best fitted and not being forcefully adapted to a task which it is not well-fit to perform. Despite nearly a half century's effort to make coaxial cable the only ham cable, amateurs are discovering that parallel transmission line has an important place in the array of antenna- transmission line combinations. And wherever parallel transmission line is used, the inductively coupled tuner has a natural home.<br>
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<p><i>Updated 11-28-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.</i><br>
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