refactor: stromspeisung
Removed the cahpter "Frequenzabhängige Stromverteilung" and integrated it in the chapter "Strom- und Spannungsspeisung II"
This commit is contained in:
Matthias Jung
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|
||||
</svg>
|
||||
|
After Width: | Height: | Size: 20 KiB |
@@ -0,0 +1,47 @@
|
||||
% Author: Prof. Dr. Matthias Jung, DL9MJ
|
||||
% Year: 2026
|
||||
\begin{circuitikz}
|
||||
\draw[thick, DARCred] (0,0)
|
||||
sin ++(4, 3)
|
||||
cos ++(4,-3);
|
||||
|
||||
% 3. Harmonische
|
||||
\draw[thick, DARCblue] (0,0)
|
||||
sin ++({4/3},+1) cos ++({4/3},-1)
|
||||
sin ++({4/3},+1) cos ++({4/3},-1)
|
||||
sin ++({4/3},+1) cos ++({4/3},-1);
|
||||
|
||||
% 5. Harmonische
|
||||
\draw[thick, DARCgreen] (0,0)
|
||||
sin ++(0.8,+0.6) cos ++(0.8,-0.6)
|
||||
sin ++(0.8,+0.6) cos ++(0.8,-0.6)
|
||||
sin ++(0.8,+0.6) cos ++(0.8,-0.6)
|
||||
sin ++(0.8,+0.6) cos ++(0.8,-0.6)
|
||||
sin ++(0.8,+0.6) cos ++(0.8,-0.6);
|
||||
|
||||
% 7. Harmonische
|
||||
\draw[thick, DARCorange] (0,0)
|
||||
sin ++({4/7},{+3/7}) cos ++({4/7},{-3/7})
|
||||
sin ++({4/7},{+3/7}) cos ++({4/7},{-3/7})
|
||||
sin ++({4/7},{+3/7}) cos ++({4/7},{-3/7})
|
||||
sin ++({4/7},{+3/7}) cos ++({4/7},{-3/7})
|
||||
sin ++({4/7},{+3/7}) cos ++({4/7},{-3/7})
|
||||
sin ++({4/7},{+3/7}) cos ++({4/7},{-3/7})
|
||||
sin ++({4/7},{+3/7}) cos ++({4/7},{-3/7});
|
||||
|
||||
\draw[very thick] (0,0) coordinate(start)
|
||||
to [short] ++( 3.9, 0)
|
||||
to [short] ++( 0,-0.8);
|
||||
\draw[very thick] (8,0) coordinate(end)
|
||||
to [short] ++(-3.9, 0)
|
||||
to [short] ++( 0,-0.8);
|
||||
|
||||
\node[DARCred, anchor=south west] at (6,{3/sqrt(2)}) {\qty{3.5}{\mega\hertz}};
|
||||
\node[DARCblue, fill=white, inner sep=1pt, anchor=south west]
|
||||
at (2,{1/sqrt(2)}) {\qty{10.5}{\mega\hertz}};
|
||||
\node[DARCgreen, fill=white, inner sep=1pt, anchor=south west]
|
||||
at (4.8,{1/sqrt(2)}) {\qty{17.5}{\mega\hertz}};
|
||||
\node[DARCorange, anchor=north] at ({8/7},0) {\qty{24.5}{\mega\hertz}};
|
||||
|
||||
\DARCmeasure{start}{end}{0,-1}{0}{$\qty{40}{\meter}$}
|
||||
\end{circuitikz}
|
||||
@@ -1,8 +0,0 @@
|
||||
Für die folgenden Fragen muss man nur die Wellenlänge der dargestellten Stromverteilungen bestimmen und kann diese dann in die entsprechende Frequenz umrechnen.
|
||||
|
||||
%TODO: Die in den Prüfungsfragen dargestellten Stromverteilungen sind falsch. Sobald diese korrigiert sind, sollte der Text nochmal erklärt werden.
|
||||
|
||||
[question:AG203]
|
||||
[question:AG204]
|
||||
[question:AG205]
|
||||
[question:AG206]
|
||||
@@ -1,11 +1,28 @@
|
||||
Ein mittengespeister Halbwellendipol ist nicht nur bei seiner Grundfrequenz stromgespeist, sondern auch bei *ungeradzahligen* Vielfachen seiner Grundfrequenz, wie in Abbildung [ref:e_stromverteilungen].
|
||||
|
||||
Ein mittengespeister Halbwellendipol ist nicht nur bei seiner Grundfrequenz stromgespeist, sondern auch bei *ungeradzahligen* Vielfachen seiner Grundfrequenz, wie in Abbildung [ref:e_stromverteilungen] gezeigt. So besitzt beispielsweise ein für das $\qty{80}{\meter}$-Band ausgelegter Dipol mit einer Grundfrequenz von $\qty{3,5}{\mega\hertz}$ weitere Resonanzen näherungsweise bei $3\cdot\qty{3,5}{\mega\hertz}=\qty{10,5}{\mega\hertz}$ und $5\cdot\qty{3,5}{\mega\hertz}=\qty{17,5}{\mega\hertz}$ und ist an diesen Freqeuenzen stromgespeist und niederohmig.
|
||||
[question:AG207]
|
||||
|
||||
Bei *geraden* Vielfachen hingegen, ergibt sich eine Spannungsspeisung, da dann der Speisepunkt an einem Spannungsbauch liegt.
|
||||
Bei *geraden* Vielfachen hingegen, ergibt sich eine Spannungsspeisung, da dann der Speisepunkt an einem Spannungsbauch liegt. Bei einem $\qty{80}{\meter}$-Dipol liegt bei einer Anregung von $2\cdot\qty{3,5}{\mega\hertz}=\qty{7}{\mega\hertz}$ oder $4\cdot\qty{3,5}{\mega\hertz}=\qty{14}{\mega\hertz}$, am mittigen Speisepunkt Stromminimum und damit eine hohe Impedanz. Diese Frequenzen sind bei einem einfachen mittengespeisten Dipol daher nicht ohne Weiteres nutzbar. Im Abschnitt "Traps" werden wir eine möglichkeit kennenlernen, wie man zusätzliche Resonanzen gezielt auf solchen Frequenzen erzeugen kann.
|
||||
|
||||
[question:AG208]
|
||||
|
||||
<margin>
|
||||
[picture:1050:e_stromverteilungen:Stromverteilungen bei verschiedenen Grundfrequenzen]
|
||||
[picture:1050:a_stromverteilungen:Stromverteilungen bei verschiedenen Grundfrequenzen]
|
||||
</margin>
|
||||
|
||||
---
|
||||
|
||||
Die Abbildung [ref:a_stromverteilungen_b] zeigt die Stromverteilungen für eine Grundfrequenz von $\qty{3,5}{\mega\hertz}$ und ganzzahlige Vielfache. Die Abbildung [ref:a_stromverteilungen_c] zeigt die Stromverteilungen für die Grundfrequenz und ihre ungeradzahligen Vielfachen. Die Abbildungen zeigen schematisch den *Betrag der Stromverteilung*. Die Höhe der dargestellten Strombäuche dient nur der Veranschaulichung und stellt keine absolute Stromstärke dar.
|
||||
|
||||
Die Anzahl des Vielfachen lässt sich direkt an der Anzahl der Strombäuche erkennen: Zwei Strombäuche entsprechen dem Zweifachen der Grundfrequenz, drei Strombäuche dem Dreifachen der Grundfrequenz usw.
|
||||
|
||||
Für die folgenden Fragen betrachten wir wieder den bereits bekannten $\qty{80}{\meter}$-Dipol mit einer Gesamtlänge von etwa $\qty{40}{\meter}$. Seine Grundfrequenz liegt näherungsweise bei $\qty{3,5}{\mega\hertz}$. Um die jeweils dargestellte Anregungsfrequenz zu bestimmen, genügt es daher, die Anzahl der Strombäuche zu zählen und mit der Grundfrequenz von $\qty{3,5}{\mega\hertz}$ zu multiplizieren.
|
||||
|
||||
<margin>
|
||||
[picture:1137:a_stromverteilungen_b:Stromverteilungen für Grundfrequenz von $\qty{3,5}{\mega\hertz}$ und ganzzahligen Vielfachen]
|
||||
[picture:1138:a_stromverteilungen_c:Stromverteilungen für Grundfrequenz von $\qty{3,5}{\mega\hertz}$ und ungeradzahligen Vielfachen]
|
||||
</margin>
|
||||
|
||||
[question:AG203]
|
||||
[question:AG204]
|
||||
[question:AG205]
|
||||
[question:AG206]
|
||||
@@ -1,4 +1,4 @@
|
||||
Multibandantennen, die gezielt auf mehreren Bändern resonant sind, haben wir bereits kennengelernt, z. B. die endgespeiste Antenne mit 1:49-Transformator. Ein mittengespeister Halbwellendipol kann neben seiner Grundfrequenz grundsätzlich auch auf ungeradzahligen Vielfachen dieser Frequenz resonant sein. So besitzt beispielsweise ein für das $\qty{80}{\meter}$-Band ausgelegter Dipol mit einer Grundfrequenz von $\qty{3,5}{\mega\hertz}$ weitere Resonanzen näherungsweise bei $\qty{10,5}{\mega\hertz}$ und $\qty{17,5}{\mega\hertz}$.
|
||||
Multibandantennen, die gezielt auf mehreren Bändern resonant sind, haben wir bereits kennengelernt, z. B. die endgespeiste Antenne mit 1:49-Transformator. Kommen wir wieder auf unser Beispiel aus dem Abschnitt "Strom- und Spannungsspeisung II" zurück: Ein mittengespeister Halbwellendipol kann neben seiner Grundfrequenz grundsätzlich auch auf ungeradzahligen Vielfachen dieser Frequenz resonant sein. So besitzt beispielsweise ein für das $\qty{80}{\meter}$-Band ausgelegter Dipol mit einer Grundfrequenz von $\qty{3,5}{\mega\hertz}$ weitere Resonanzen näherungsweise bei $\qty{10,5}{\mega\hertz}$ und $\qty{17,5}{\mega\hertz}$.
|
||||
|
||||
Bei geradzahligen Vielfachen der Grundfrequenz, beispielsweise bei $\qty{7}{\mega\hertz}$ oder $\qty{14}{\mega\hertz}$, liegt am mittigen Speisepunkt dagegen ein Stromminimum und damit eine hohe Impedanz. Diese Frequenzen sind bei einem einfachen mittengespeisten Dipol daher nicht ohne Weiteres nutzbar. Eine Möglichkeit, zusätzliche Resonanzen gezielt auf solchen Frequenzen zu erzeugen, ist der sogenannte *Sperrkreis-Dipol*, der auch als *Trap-Dipol* bezeichnet wird.
|
||||
|
||||
|
||||
@@ -0,0 +1,7 @@
|
||||
Der Dipol hat eine Gesamtlänge von etwa $\qty{40}{\meter}$ und entspricht damit näherungsweise einem Halbwellendipol für das $\qty{80}{\meter}$-Band. Seine Grundfrequenz beträgt ungefähr $\qty{3,5}{\mega\hertz}$.
|
||||
|
||||
Die Stromkurve *a* besitzt insgesamt $\num{8}$ Strombäuche. Die Anregungsfrequenz entspricht daher dem Achtfachen der Grundfrequenz:
|
||||
|
||||
$f = 8 \cdot \qty{3,5}{\mega\hertz} = \qty{28}{\mega\hertz}$.
|
||||
|
||||
Die Stromkurve *a* gilt somit für eine Anregung mit $\qty{28}{\mega\hertz}$.
|
||||
@@ -0,0 +1,7 @@
|
||||
Der Dipol hat eine Grundfrequenz von ungefähr $\qty{3,5}{\mega\hertz}$.
|
||||
|
||||
Die Stromkurve *b* besitzt insgesamt $\num{4}$ Strombäuche. Die Anregungsfrequenz entspricht daher dem Vierfachen der Grundfrequenz:
|
||||
|
||||
$f = 4 \cdot \qty{3,5}{\mega\hertz} = \qty{14}{\mega\hertz}$.
|
||||
|
||||
Die Stromkurve *b* gilt somit für eine Anregung mit $\qty{14}{\mega\hertz}$.
|
||||
@@ -0,0 +1,7 @@
|
||||
Der Dipol hat eine Grundfrequenz von ungefähr $\qty{3,5}{\mega\hertz}$.
|
||||
|
||||
Die Stromkurve *c* besitzt insgesamt $\num{2}$ Strombäuche. Die Anregungsfrequenz entspricht daher dem Zweifachen der Grundfrequenz:
|
||||
|
||||
$f = 2 \cdot \qty{3,5}{\mega\hertz} = \qty{7}{\mega\hertz}$.
|
||||
|
||||
Die Stromkurve *c* gilt somit für eine Anregung mit $\qty{7}{\mega\hertz}$.
|
||||
@@ -0,0 +1,7 @@
|
||||
Die Stromkurve *d* besitzt nur einen Strombauch über die gesamte Länge des Dipols. Sie entspricht daher der Grundschwingung des etwa $\qty{40}{\meter}$ langen Halbwellendipols.
|
||||
|
||||
Die Anregungsfrequenz beträgt somit ungefähr
|
||||
|
||||
$f = \qty{3,5}{\mega\hertz}$.
|
||||
|
||||
Die Stromkurve *d* gilt daher für eine Anregung mit $\qty{3,5}{\mega\hertz}$.
|
||||
+2
-9
@@ -964,13 +964,6 @@
|
||||
"class": "A",
|
||||
"video_url": null
|
||||
},
|
||||
{
|
||||
"title": "Traps",
|
||||
"ident": "traps",
|
||||
"status": "alpha",
|
||||
"class": "A",
|
||||
"video_url": null
|
||||
},
|
||||
{
|
||||
"title": "Yagi-Uda-Antenne III",
|
||||
"ident": "yagi_uda_3",
|
||||
@@ -1014,8 +1007,8 @@
|
||||
"video_url": null
|
||||
},
|
||||
{
|
||||
"title": "Frequenzabhängige Stromverteilung",
|
||||
"ident": "frequenzabhaengige_stromverteilung",
|
||||
"title": "Traps",
|
||||
"ident": "traps",
|
||||
"status": "alpha",
|
||||
"class": "A",
|
||||
"video_url": null
|
||||
|
||||
+2
-9
@@ -1547,13 +1547,6 @@
|
||||
"class": "A",
|
||||
"video_url": null
|
||||
},
|
||||
{
|
||||
"title": "Traps",
|
||||
"ident": "traps",
|
||||
"status": "alpha",
|
||||
"class": "A",
|
||||
"video_url": null
|
||||
},
|
||||
{
|
||||
"title": "Yagi-Uda Antenne II",
|
||||
"ident": "yagi_uda_2",
|
||||
@@ -1618,8 +1611,8 @@
|
||||
"video_url": null
|
||||
},
|
||||
{
|
||||
"title": "Frequenzabhängige Stromverteilung",
|
||||
"ident": "frequenzabhaengige_stromverteilung",
|
||||
"title": "Traps",
|
||||
"ident": "traps",
|
||||
"status": "alpha",
|
||||
"class": "A",
|
||||
"video_url": null
|
||||
|
||||
+2
-9
@@ -2280,13 +2280,6 @@
|
||||
"class": "A",
|
||||
"video_url": null
|
||||
},
|
||||
{
|
||||
"title": "Traps",
|
||||
"ident": "traps",
|
||||
"status": "alpha",
|
||||
"class": "A",
|
||||
"video_url": null
|
||||
},
|
||||
{
|
||||
"title": "Yagi-Uda Antenne II",
|
||||
"ident": "yagi_uda_2",
|
||||
@@ -2351,8 +2344,8 @@
|
||||
"video_url": null
|
||||
},
|
||||
{
|
||||
"title": "Frequenzabhängige Stromverteilung",
|
||||
"ident": "frequenzabhaengige_stromverteilung",
|
||||
"title": "Traps",
|
||||
"ident": "traps",
|
||||
"status": "alpha",
|
||||
"class": "A",
|
||||
"video_url": null
|
||||
|
||||
Reference in New Issue
Block a user