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refactor: unerwünschte Aussendungen 3

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Matthias Jung
2026-08-27 23:37:18 +02:00
parent 6314597cf6
commit b87c041aa1
7 changed files with 929 additions and 7 deletions
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contents/drawings/1139.svg
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contents/drawings/1139.tex
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% Author: Prof. Dr. Matthias Jung, DL9MJ
% Year: 2026
%
% Vergleich der Grenzwerte nach ETSI und AFuV 33/2007 (2)
% Angaben in dBc
\begin{tikzpicture}
\begin{axis}[
axis on top,
height=5cm,
scale only axis,
width=\linewidth*\getDarcImageFactor,
xmin=0.15,
xmax=3000,
ymin=-75,
log ticks with fixed point,
xmode=log,
xlabel={Frequenz in \unit{\mega\hertz}},
ylabel={Grenzwert in dBc},
%xtick={0.15,1.5,15,150,1500,3000},
%xticklabels={
% $0{,}15$,
% $1{,}5$,
% $15$,
% $150$,
% $1500$,
% $3000$
%},
ytick={-75,-70,-65,-60,-55,-50,-45,-40,-35,-30},
%grid=major,
%major grid style={
% draw=DARCgray!35,
% line width=0.4pt
%},
legend style={
at={(0.5,-0.2)},
anchor=north,
draw=none,
legend columns=4,
font=\footnotesize,
/tikz/every even column/.append style={column sep=0.1cm}
}
]
% AFU Bänder:
%2,2km
\fill[color=DARCgray!50!white](axis cs: 0.1357,-100) rectangle (0.1378,100);
%630m
\fill[color=DARCgray!50!white](axis cs: 0.472,-100) rectangle (0.479,100);
%160m
\fill[color=DARCgray!50!white](axis cs: 1.81,-100) rectangle (2.0,-100);
%80m
\fill[color=DARCgray!50!white](axis cs: 3.50,-100) rectangle (3.8,100);
%60m
\fill[color=DARCgray!50!white](axis cs: 5.3515,-100) rectangle (5.3665,100);
%40m
\fill[color=DARCgray!50!white](axis cs: 7.0,-100) rectangle (7.2,100);
%30m
\fill[color=DARCgray!50!white](axis cs: 10.1,-100) rectangle (10.15,100);
%20m
\fill[color=DARCgray!50!white](axis cs: 14.0,-100) rectangle (14.35,100);
%17m
\fill[color=DARCgray!50!white](axis cs: 18.068,-100) rectangle (18.168,100);
%15m
\fill[color=DARCgray!50!white](axis cs: 21.0,-100) rectangle (21.45,100);
%12m
\fill[color=DARCgray!50!white](axis cs: 24.89,-100) rectangle (24.99,100);
%10m
\fill[color=DARCgray!50!white](axis cs: 28.0,-100) rectangle (29.7,100);
%6m
\fill[color=DARCgray!50!white](axis cs: 50.0,-100) rectangle (52.0,100);
%4m
\fill[color=DARCgray!50!white](axis cs: 70.0,-100) rectangle (70.5,100);
%2m
\fill[color=DARCgray!50!white](axis cs: 144.0,-100) rectangle (146.0,100);
%70cm
\fill[color=DARCgray!50!white](axis cs: 430.0,-100) rectangle (440.0,100);
%23cm
\fill[color=DARCgray!50!white](axis cs: 1240.0,-100) rectangle (1300.0,100);
%13cm
\fill[color=DARCgray!50!white](axis cs: 2320.0,-100) rectangle (2450.0,100);
% --------------------------------------------------------------------------
% ETSI, 5 W
%
% -(43 + 10 log10(5 W)) = -49.9897 dBc
% Im Diagramm sinnvoll auf -50 dBc gerundet.
% --------------------------------------------------------------------------
\addplot[
DARCgreen,
very thick
]
coordinates {
(0.15,-50)
(3000,-50)
};
\addlegendentry{ETSI: \qty{5}{\watt}}
% --------------------------------------------------------------------------
% ETSI, 100 W
%
% Rechnerisch:
% -(43 + 10 log10(100 W)) = -63 dBc
%
% Unterhalb 30 MHz gilt laut Tabelle jedoch der absolute Grenzwert
% von -50 dBc.
% --------------------------------------------------------------------------
\addplot[
DARCorange,
very thick
]
coordinates {
(0.15,-50)
(30,-50)
(30,-63)
(3000,-63)
};
\addlegendentry{ETSI: \qty{100}{\watt}}
% --------------------------------------------------------------------------
% ETSI, 750 W
%
% Rechnerisch:
% -(43 + 10 log10(750 W)) = -71.75 dBc
%
% Unterhalb 30 MHz: -50 dBc
% Ab 30 MHz: -70 dBc
% --------------------------------------------------------------------------
\addplot[
DARCred,
very thick
]
coordinates {
(0.15,-50)
(30,-50)
(30,-70)
(3000,-70)
};
\addlegendentry{ETSI: \qty{750}{\watt}}
% --------------------------------------------------------------------------
% Vfg. 33/2007 (2)
%
% 0.15 ... 1.7 MHz: -60 dBc
% 1.7 ... 35 MHz: -40 dBc
%
% 35 ... 50 MHz:
%
% -(40 + 129.1 log10(f / 35))
%
% 50 ... 1000 MHz: -60 dBc
% 1000 ... 3000 MHz: -50 dBc
% --------------------------------------------------------------------------
\addplot[
DARCblue,
very thick
]
coordinates {
(0.15,-60)
(1.7,-60)
(1.7,-40)
(35,-40)
};
\addlegendentry{Vfg. 33/2007 (2)}
% Übergang von 35 MHz bis 50 MHz
\addplot[
DARCblue,
very thick,
domain=35:50,
samples=100,
forget plot
]
{
-(40 + 129.1 * ln(x/35) / ln(10))
};
% Ab 50 MHz
\addplot[
DARCblue,
very thick,
forget plot
]
coordinates {
(50,-60)
(1000,-60)
(1000,-50)
(3000,-50)
};
\end{axis}
\end{tikzpicture}
contents/drawings/1139.txt
+1
View File
@@ -0,0 +1 @@
TODO
contents/drawings/1140.svg
+191
View File
@@ -0,0 +1,191 @@
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contents/drawings/1140.tex
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% Author: Prof. Dr. Matthias Jung, DL9MJ
% Year: 2024
\begin{circuitikz}[european]
\def\base{2.0}
\draw[ultra thick](1*\base,0.0) -- ++ (0,3.0) coordinate(h1);
\draw[ultra thick, DARCorange](2*\base,0.0) -- ++ (0,2.0) coordinate(h2);
\draw[ultra thick, DARCorange](3*\base,0.0) -- ++ (0,1.5) coordinate(h3);
\draw[ultra thick, DARCorange](4*\base,0.0) -- ++ (0,1.0) coordinate(h4);
\draw[DARCred, dashed] (h1) -- (h1-|h4);
\draw[DARCred, dashed] (h2) -- (h2-|h1);
\draw[DARCred, dashed] (h2) -- (h2-|h4);
\draw[DARCred, Triangle-Triangle] (h1-|h2) -- (h2) node[midway, anchor=west] () {$\Delta \geq \qty{40}{\decibel}$};
\draw(5.25,0.0) ;
\draw(1*\base,0) node[align=center, anchor=north] () {$f_\text{0}$\\1 Harm.};
\draw(2*\base,0) node[align=center, anchor=north] () {1. OW\\2 Harm.};
\draw(3*\base,0) node[align=center, anchor=north] () {2. OW\\3 Harm.};
\draw(4*\base,0) node[align=center, anchor=north] () {3. OW\\4 Harm.};
\draw[-Triangle](0.0,0.0) -- (9.0,0.0) node[anchor=west] () {$f$};
\draw[-Triangle](0.0,0.0) -- (0.0,4.0) node[anchor=south] () {$A$};
\end{circuitikz}
contents/sections/unerwuenschte_aussendungen_2.md
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@@ -40,7 +40,7 @@ Dass dieses Thema sehr wichtig ist, zeigt sich an der großen Zahl von Prüfungs
</margin>
<margin>
[photo:320:e_ua_tiefpass_selbstbau:Selbgebautes Tiefpassfilters]
[photo:320:e_ua_tiefpass_selbstbau:Selbgebautes Tiefpassfilter]
</margin>
---
contents/sections/unerwuenschte_aussendungen_3.md
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@@ -36,26 +36,45 @@ Sollen bestimmte Oberwellen oder Harmonische eines Signals einzeln unterdrückt
---
Laut Amateurfunkverordnung (AFuV) sind unerwünschte Aussendungen auf das geringstmögliche Maß zu beschränken. Die [Verfügung 33](https://50ohm.de/vfg33) von 2007 legt allerdings genaue Grenzwerte fest, welche durch den Funkamateur aber auch von Herstellern kommerzieller Geräte beachtet werden müssen.
Nach der Amateurfunkverordnung (AFuV) sind unerwünschte Aussendungen auf das geringstmögliche Maß zu beschränken. Für selbst gebaute Amateurfunkgeräte sowie für ursprünglich kommerziell vertriebene Geräte, die von einem Funkamateur verändert wurden, legt die [Verfügung 33/2007](https://50ohm.de/vfg33) der Bundesnetzagentur (BNetzA) konkrete Grenzwerte fest. Die Abbildung [ref:a_vfg33] zeigt einen Auszug aus dieser Verfügung mit den zulässigen Grenzwerten für unerwünschte Aussendungen.
Die Grenzwerte sind üblicherweise in $\unit{\dBc}$ angegeben und beschreiben, um wie viele Dezibel eine unerwünschte Aussendung gegenüber dem Trägersignal beziehungsweise dem maximalen Sendesignalpegel des Senders (PEP) abgeschwächt sein muss. Alternativ zur relativen Angabe in $\unit{\dBc}$ kann für unerwünschte Aussendungen auch ein absoluter Grenzwert der Leistung, beispielsweise in $\unit{\dBm}$ oder $\unit{\micro\watt}$, gelten. Maßgeblich ist dabei jeweils der höhere der aus beiden Grenzwerten resultierenden zulässigen Leistungswerte.
Für Amateurfunkgeräte, die kommerziell in der Europäischen Union vertrieben werden, gelten ebenfalls Grenzwerte für unerwünschte Aussendungen. Diese sind EU-weit einheitlich geregelt. Im Unterschied zu den Grenzwerten der Verfügung 33/2007 hängen die zulässigen Werte hierbei teilweise von der Sendeleistung des Geräts ab. Die Abbildung [ref:a_etsi_vfg] stellt die Grenzwerte für kommerziell vertriebene Geräte den Vorgaben der Verfügung 33/2007 gegenüber.
Ein Beispiel verdeutlicht den Unterschied: Für ein kommerziell vertriebenes Handfunkgerät mit einer Sendeleistung von $\qty{5}{\watt}$ gilt im dargestellten Frequenzbereich ein Grenzwert von $\qty{-50}{\dBc}$. Wird dagegen ein entsprechendes $\qty{5}{\watt}$-Gerät für das 2-m- oder 70-cm-Band selbst gebaut, muss nach Verfügung 33/2007 ein Grenzwert von $\qty{-60}{\dBc}$ eingehalten werden.
Bei einer Sendeleistung von $\qty{750}{\watt}$ bleibt dieser Grenzwert für das selbst gebaute Gerät bei $\qty{-60}{\dBc}$. Für ein kommerziell vertriebenes Gerät mit derselben Leistung gilt dagegen ein strengerer Grenzwert von $\qty{-70}{\dBc}$.
Die folgenden Prüfungsfragen beziehen sich auf selbst gebaute oder modifizierte Amateurfunkgeräte und somit auf die Grenzwerte für unerwünschte Aussendungen, wie sie in der Verfügung 33/2007 der Bundesnetzagentur festgelegt sind.
<margin>
[photo:319:a_vfg33:Auszug aus der Verfügung 33 von 2007]
[photo:319:a_vfg33:Auszug aus der Verfügung 33 von 2007.]
[picture:1139:a_etsi_vfg:Vergleich der ETSI Norm EN 301783 mit der Verfügung 33 von 2007. Im Hintergrund sind die Amateurfunkbänder grau hinterlegt.]
</margin>
Für den VHF/UHF/SHF-Bereich von $\qtyrange{50}{1000}{\mega\hertz}$ gilt, dass Nebenaussendungen und Oberwellen mindestens $\qty{60}{\dB}$ gegenüber dem maximalen Sendesignalspitzenpegel des Senders (PEP) gedämpft werden müssen, so lange sich die Leistung der Signale oberhalb eines Pegels von $\qty{0,25}{\micro\watt}$ befindet (vgl. Abbildung [ref:a_uagw]).
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[question:AJ225]
Für den VHF/UHF/SHF-Bereich von $\qtyrange{50}{1000}{\mega\hertz}$ gilt, dass Nebenaussendungen und Oberwellen mindestens $\qty{60}{\dB}$ gegenüber dem maximalen Sendesignalspitzenpegel des Senders (PEP) gedämpft werden müssen, so lange sich die Leistung der Signale oberhalb eines Pegels von $\qty{0,25}{\micro\watt}$ befindet (vgl. Abbildung [ref:a_uagw]).
<margin>
[picture:918:a_uagw:Oberwellendämpfung VHF/UHF/SHF-Bereich]
</margin>
Für den Kurzwellenbereich von $\qtyrange{1,7}{35}{\mega\hertz}$ gilt, dass Nebenaussendungen und Oberwellen mindestens $\qty{40}{\dB}$ gegenüber dem maximalen Sendesignalspitzenpegel des Senders (PEP) gedämpft werden müssen, so lange sich die Leistung der Signale oberhalb eines Pegels von $\qty{0,25}{\micro\watt}$ befindet.
[question:AJ225]
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Für den Kurzwellenbereich von $\qtyrange{1,7}{35}{\mega\hertz}$ gilt, dass Nebenaussendungen und Oberwellen mindestens $\qty{40}{\dB}$ gegenüber dem maximalen Sendesignalspitzenpegel des Senders (PEP) gedämpft werden müssen, so lange sich die Leistung der Signale oberhalb eines Pegels von $\qty{0,25}{\micro\watt}$ befindet (vgl. Abbildung [ref:a_uagw2]).
<margin>
[picture:1140:a_uagw2:Oberwellendämpfung KW-Bereich]
</margin>
[question:AJ224]
%TODO BILD VON DL1COM EINBAUEN
Mit einem Spektrumanalysator lässt sich im Modus spurious emissions eine Messung der Oberwellen bzw. Harmonischen (engl. harmonics) durchführen, wie in Abbildung [ref:a_uagw] dargestellt. Der Spektrumanalysator erfasst dabei automatisch den Pegel des Trägers sowie die Unterdrückung der Harmonischen und zeigt diese zusätzlich auf dem Bildschirm an. Wenn man ein Gerät selbst baut, ist es entscheidend, durch Messungen sicherzustellen, dass die vorgeschriebenen Grenzwerte eingehalten werden. Ein kommerzieller Funkgerätehersteller bestätigt mit der CE-Erklärung zwar die Einhaltung dieser Grenzwerte, dennoch kommt es vor, dass einzelne Geräte die Vorgaben nicht erfüllen – in solchen Fällen kann die Bundesnetzagentur deren Betrieb und Verkauf verbieten.
Mit einem Spektrumanalysator lässt sich im Modus *Spurious Emissions* eine Messung der Oberwellen bzw. Harmonischen (engl. harmonics) durchführen, wie in Abbildung [ref:a_uagw] dargestellt. Der Spektrumanalysator erfasst dabei automatisch den Pegel des Trägers sowie die Unterdrückung der Harmonischen und zeigt diese zusätzlich auf dem Bildschirm an. Wenn man ein Gerät selbst baut, ist es entscheidend, durch Messungen sicherzustellen, dass die vorgeschriebenen Grenzwerte eingehalten werden. Ein kommerzieller Funkgerätehersteller bestätigt mit der CE-Erklärung zwar die Einhaltung dieser Grenzwerte, dennoch kommt es vor, dass einzelne Geräte die Vorgaben nicht erfüllen – in solchen Fällen kann die Bundesnetzagentur deren Betrieb und Verkauf verbieten.
Unerwünschte Aussendungen entstehen nicht nur durch Oberwellen, sondern können auch in der Frequenzaufbereitung von Sendern auftreten – etwa durch unerwünschte Mischprodukte, durch Schwankungen in der Versorgungsspannung oder durch eine Übersteuerung des NF-Signals. Das wollen wir uns im Folgenden noch etwas genauer anschauen.