refactor: swr-meter
This commit is contained in:
Matthias Jung
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<path fill-rule="nonzero" fill="rgb(100%, 100%, 100%)" fill-opacity="1" stroke-width="0.3985" stroke-linecap="butt" stroke-linejoin="miter" stroke="rgb(0%, 0%, 0%)" stroke-opacity="1" stroke-miterlimit="10" d="M 122.797083 -183.799981 C 122.797083 -182.921954 122.087606 -182.212476 121.209579 -182.212476 C 120.331552 -182.212476 119.622074 -182.921954 119.622074 -183.799981 C 119.622074 -184.674088 120.331552 -185.383566 121.209579 -185.383566 C 122.087606 -185.383566 122.797083 -184.674088 122.797083 -183.799981 Z M 122.797083 -183.799981 " transform="matrix(0.996552, 0, 0, -0.996552, 6.329417, 6.169655)"/>
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<g clip-path="url(#clip-3)">
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<path fill-rule="nonzero" fill="rgb(88.233948%, 31.373596%, 13.723755%)" fill-opacity="1" stroke-width="1.59404" stroke-linecap="butt" stroke-linejoin="miter" stroke="rgb(88.233948%, 31.373596%, 13.723755%)" stroke-opacity="1" stroke-miterlimit="10" d="M 5.706738 0.000293328 L 0.795273 3.018512 L 0.795273 -3.017925 Z M 5.706738 0.000293328 " transform="matrix(0.996552, 0, 0, -0.996552, 44.352, 36.36748)"/>
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</svg>
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|
After Width: | Height: | Size: 26 KiB |
@@ -0,0 +1,60 @@
|
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% Author: Dr. Matthias Jung, DL9MJ
|
||||
% Year: 2026
|
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\begin{tikzpicture}
|
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\draw(0,0)
|
||||
to [short, o-] ++ (1,0) coordinate(x1)
|
||||
coordinate(h1);
|
||||
\draw[DARCgreen](h1)
|
||||
to [american inductor, name={L1}, inductors/width=2.0, inductors/coils=8] ++ (2,0) coordinate(h2);
|
||||
\draw(h2)
|
||||
to [short, -o] ++ (1,0)
|
||||
to [open,-o] ++(0,-1) node[rground] {};
|
||||
\draw(0,0)
|
||||
to [open,-o, name={h3}] ++(0,-1) node[rground] {};
|
||||
\draw[DARCgreen](x1)
|
||||
to [open] ++(0,-1) coordinate(ll1)
|
||||
to [american inductor, draw=DARCgreen, name={L2}, inductors/width=2.0, inductors/coils=8, v={$U_\mathrm{I}$}] ++ (2,0)
|
||||
coordinate(ll2);
|
||||
\draw[DARCorange](L1.south west)
|
||||
to [open] ++(0,-0.2)
|
||||
to [C] ++(0,-0.5)
|
||||
to [open] (L2.north west);
|
||||
\draw[DARCorange](L1.south)
|
||||
to [open] ++(0,-0.2)
|
||||
to [C] ++(0,-0.5)
|
||||
to [open] (L2.north);
|
||||
\draw[DARCorange](L1.south east)
|
||||
to [open] ++(0,-0.2)
|
||||
to [C] ++(0,-0.5)
|
||||
to [open] (L2.north east);
|
||||
\draw(L2.south)
|
||||
to [open, -o] ++(0,-2)
|
||||
node [rground](gnd){};
|
||||
\draw(ll1)
|
||||
to [short, -o] ++(0,-0.5) coordinate(left);
|
||||
\draw(ll2)
|
||||
to [short, -o] ++(0,-0.5) coordinate(right);
|
||||
\draw(left)
|
||||
to [open] ++(-0.125,0) coordinate(left1);
|
||||
\draw(left)
|
||||
to [open] ++(+0.125,0) coordinate(left2);
|
||||
\draw(right)
|
||||
to [open] ++(-0.125,0) coordinate(right1);
|
||||
\draw(right)
|
||||
to [open] ++(+0.125,0) coordinate(right2);
|
||||
\draw(gnd)
|
||||
to [open] ++(-0.125,0) coordinate(gnd1);
|
||||
\draw(gnd)
|
||||
to [open] ++(+0.125,0) coordinate(gnd2);
|
||||
%
|
||||
\draw[DARCorange](left1)
|
||||
to [open, v={$U_\mathrm{C}$}, draw=DARCorange] (gnd1);
|
||||
\draw[DARCorange](right2)
|
||||
to [open, v^={$U_\mathrm{C}$}, draw=DARCorange] (gnd2);
|
||||
\draw[DARCgreen](left2)
|
||||
to [open, draw=DARCgreen, v^={$\frac{U_\mathrm{I}}{2}$}] (gnd2);
|
||||
\draw[DARCgreen](gnd1)
|
||||
to [open, draw=DARCgreen, v^={$\frac{U_\mathrm{I}}{2}$}] (right1);
|
||||
%
|
||||
\draw[ultra thick, -Triangle, DARCred] (h3.center) -- ++(0.75,0);
|
||||
\end{tikzpicture}
|
||||
@@ -0,0 +1,128 @@
|
||||
<?xml version="1.0" encoding="UTF-8"?>
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<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" width="255.118pt" height="200.307pt" viewBox="0 0 255.118 200.307">
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<defs>
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<g>
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<g id="glyph-0-0">
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<path d="M 1.828125 0.09375 C 3.578125 0.09375 4.203125 -1.046875 4.5 -2.640625 L 4.984375 -5.09375 C 5.03125 -5.34375 5.171875 -5.484375 5.546875 -5.5 L 5.765625 -5.515625 C 5.8125 -5.515625 5.84375 -5.546875 5.84375 -5.59375 L 5.875 -5.765625 L 5.859375 -5.78125 C 5.453125 -5.78125 5.109375 -5.765625 4.921875 -5.765625 C 4.71875 -5.765625 4.375 -5.78125 3.984375 -5.78125 L 3.953125 -5.765625 L 3.921875 -5.59375 C 3.921875 -5.546875 3.953125 -5.515625 3.984375 -5.515625 L 4.203125 -5.5 C 4.5 -5.484375 4.609375 -5.40625 4.609375 -5.21875 C 4.609375 -5.1875 4.609375 -5.140625 4.59375 -5.09375 L 4.078125 -2.46875 C 3.890625 -1.46875 3.53125 -0.28125 2.078125 -0.28125 C 1.65625 -0.28125 1.34375 -0.46875 1.140625 -0.71875 C 0.953125 -0.96875 0.90625 -1.25 0.90625 -1.53125 C 0.90625 -1.8125 0.953125 -2.125 1.015625 -2.40625 L 1.53125 -5.109375 C 1.59375 -5.359375 1.734375 -5.484375 2.09375 -5.5 L 2.3125 -5.515625 C 2.359375 -5.515625 2.390625 -5.546875 2.390625 -5.59375 L 2.4375 -5.765625 L 2.40625 -5.78125 C 2.015625 -5.78125 1.65625 -5.765625 1.3125 -5.765625 C 0.96875 -5.765625 0.640625 -5.78125 0.234375 -5.78125 L 0.203125 -5.765625 L 0.171875 -5.59375 C 0.171875 -5.546875 0.203125 -5.515625 0.234375 -5.515625 L 0.453125 -5.5 C 0.734375 -5.484375 0.859375 -5.421875 0.859375 -5.234375 C 0.859375 -5.1875 0.859375 -5.15625 0.84375 -5.109375 L 0.265625 -2.109375 C 0.21875 -1.875 0.203125 -1.671875 0.203125 -1.484375 C 0.203125 -0.203125 1.15625 0.09375 1.828125 0.09375 Z M 1.828125 0.09375 "/>
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</g>
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<g id="glyph-1-0">
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<path d="M 1.359375 -0.875 L 1.359375 -3.734375 C 1.359375 -4.328125 1.484375 -4.359375 1.984375 -4.390625 C 2.03125 -4.421875 2.03125 -4.578125 1.984375 -4.625 C 1.671875 -4.609375 1.328125 -4.609375 1.0625 -4.609375 C 0.828125 -4.609375 0.46875 -4.609375 0.140625 -4.625 C 0.09375 -4.578125 0.09375 -4.421875 0.140625 -4.390625 C 0.640625 -4.359375 0.75 -4.328125 0.75 -3.734375 L 0.75 -0.875 C 0.75 -0.28125 0.640625 -0.25 0.140625 -0.21875 C 0.09375 -0.171875 0.09375 -0.03125 0.140625 0.015625 C 0.453125 0 0.8125 0 1.0625 0 C 1.328125 0 1.65625 0 1.984375 0.015625 C 2.03125 -0.03125 2.03125 -0.171875 1.984375 -0.21875 C 1.484375 -0.25 1.359375 -0.28125 1.359375 -0.875 Z M 1.359375 -0.875 "/>
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</g>
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<g id="glyph-1-1">
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</svg>
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|
After Width: | Height: | Size: 26 KiB |
@@ -0,0 +1,60 @@
|
||||
% Author: Dr. Matthias Jung, DL9MJ
|
||||
% Year: 2026
|
||||
\begin{tikzpicture}
|
||||
\draw(0,0)
|
||||
to [short, o-] ++ (1,0) coordinate(x1)
|
||||
coordinate(h1);
|
||||
\draw[DARCgreen](h1)
|
||||
to [american inductor, name={L1}, inductors/width=2.0, inductors/coils=8] ++ (2,0) coordinate(h2);
|
||||
\draw(h2)
|
||||
to [short, -o] ++ (1,0)
|
||||
to [open,-o, name={h3}] ++(0,-1) node[rground] {};
|
||||
\draw(0,0)
|
||||
to [open,-o] ++(0,-1) node[rground] {};
|
||||
\draw[DARCgreen](x1)
|
||||
to [open] ++(0,-1) coordinate(ll1)
|
||||
to [american inductor, draw=DARCgreen, name={L2}, inductors/width=2.0, inductors/coils=8, v<={$U_\mathrm{I}$}] ++ (2,0)
|
||||
coordinate(ll2);
|
||||
\draw[DARCorange](L1.south west)
|
||||
to [open] ++(0,-0.2)
|
||||
to [C] ++(0,-0.5)
|
||||
to [open] (L2.north west);
|
||||
\draw[DARCorange](L1.south)
|
||||
to [open] ++(0,-0.2)
|
||||
to [C] ++(0,-0.5)
|
||||
to [open] (L2.north);
|
||||
\draw[DARCorange](L1.south east)
|
||||
to [open] ++(0,-0.2)
|
||||
to [C] ++(0,-0.5)
|
||||
to [open] (L2.north east);
|
||||
\draw(L2.south)
|
||||
to [open, -o] ++(0,-2)
|
||||
node [rground](gnd){};
|
||||
\draw(ll1)
|
||||
to [short, -o] ++(0,-0.5) coordinate(left);
|
||||
\draw(ll2)
|
||||
to [short, -o] ++(0,-0.5) coordinate(right);
|
||||
\draw(left)
|
||||
to [open] ++(-0.125,0) coordinate(left1);
|
||||
\draw(left)
|
||||
to [open] ++(+0.125,0) coordinate(left2);
|
||||
\draw(right)
|
||||
to [open] ++(-0.125,0) coordinate(right1);
|
||||
\draw(right)
|
||||
to [open] ++(+0.125,0) coordinate(right2);
|
||||
\draw(gnd)
|
||||
to [open] ++(-0.125,0) coordinate(gnd1);
|
||||
\draw(gnd)
|
||||
to [open] ++(+0.125,0) coordinate(gnd2);
|
||||
%
|
||||
\draw[DARCorange](left1)
|
||||
to [open, v={$U_\mathrm{C}$}, draw=DARCorange] (gnd1);
|
||||
\draw[DARCorange](right2)
|
||||
to [open, v^={$U_\mathrm{C}$}, draw=DARCorange] (gnd2);
|
||||
\draw[DARCgreen](left2)
|
||||
to [open, draw=DARCgreen, v^<={$\frac{U_\mathrm{I}}{2}$}] (gnd2);
|
||||
\draw[DARCgreen](gnd1)
|
||||
to [open, draw=DARCgreen, v^<={$\frac{U_\mathrm{I}}{2}$}] (right1);
|
||||
%
|
||||
\draw[ultra thick, -Triangle, DARCred] (h3.center) -- ++(-0.75,0);
|
||||
\end{tikzpicture}
|
||||
@@ -15,6 +15,7 @@ Eine Antenne mit einem Speisewiderstand von $\qty{100}{\ohm}$ verursacht bei Spe
|
||||
Zur Beantwortung der folgenden Frage müssen wir uns außerdem daran erinnern, dass der Widerstand eines Faltdipols knapp $\qtyrange{240}{300}{\ohm}$ beträgt.
|
||||
|
||||
[question:AG405]
|
||||
[question:AI403]
|
||||
|
||||
Ein trügerischer Effekt ist die Auswirkung von Leitungsdämpfung auf das Stehwellenverhältnis. Je mehr Verluste eine Leitung aufweist, umso kleiner (also "besser") kann das Stehwellenverhältnis auf dieser Leitung ausfallen. Dies liegt daran, dass eine verlustbehaftete Leitung sowohl die vorlaufende als auch die rücklaufende Leistung reduziert. Selbst wenn am Ende einer Leitung keine Antenne angeschlossen ist (Leerlauf oder Kurzschluss), und dort $\qty{100}{\percent}$ der Energie reflektiert wird, also das Stehwellenverhältnis dort $\infty$ beträgt, so kann man am anderen Ende ein deutlich besseres Stehwellenverhältnis messen. Geht z. B. in Hin-Richtung die Hälfte der Leistung verloren und in Rück-Richtung erneut die Hälfte verloren, so reduziert sich die Energie auf ein Viertel ($\frac{1}{2} \cdot \frac{1}{2} = \frac{1}{4}$). Entsprechend zeigt ein Stehwellenmessgerät an der Senderseite des Kabels ein Stehwellenverhältnis von $\num{3}$ an, was $\qty{25}{\percent}$ reflektierter Leistung entspricht, obwohl am Ende $\qty{100}{\percent}$ reflektiert werden – es kommen jedoch nur $\qty{25}{\percent}$ am Stehwellenmessgerät an.
|
||||
|
||||
|
||||
@@ -1,8 +1,48 @@
|
||||
Ein Stehwellenmessgerät koppelt einen Teil der vorlaufenden Leistung und einen Teil der rücklaufenden Leistung aus und zeigt diesen an. Durch eine geeignete Skala (z. B. mittels eines Kreuzzeigerinstruments) lässt sich das Stehwellenverhältnis ablesen.
|
||||
In der Klasse E haben wir das SWR-Meter und seine Anwendung bereits kennengelernt. In der Klasse A wollen wir verstehen, wie ein Stehwellenmessgerät intern funktioniert. Ein SWR-Meter besteht in der Regel aus zwei Richtkopplern. Zu nächst wollen wir uns mit deren Funktionsweise vertraut machen.
|
||||
|
||||
Ein *Richtkoppler* dient dazu, einen kleinen Teil eines HF-Signals aus einer Speiseleitung auszukoppeln. Seine Besonderheit besteht darin, dass er dabei unterscheiden kann, in welche Richtung sich die Welle auf der Leitung ausbreitet. Dazu wird das Signal auf zwei unterschiedliche Arten erfasst. Über eine kapazitive Kopplung wird eine Spannung $U_C$ gewonnen, die von der Spannung auf der Speiseleitung abhängt. Gleichzeitig erzeugt die induktive Kopplung eine Spannung $U_I$, die vom Strom auf der Speiseleitung abhängt. Der Richtkoppler wird so dimensioniert, dass die kapazitiv und induktiv gewonnenen Signalanteile an seinen Ausgängen gleich groß sind. An den beiden Ausgängen werden diese Anteile jedoch mit unterschiedlichem Vorzeichen miteinander kombiniert.
|
||||
|
||||
Bei einer Welle, die sich in einer bestimmten Richtung auf der Leitung ausbreitet, z. B. von links nach rechts wie in Abbildung [ref:a_richtkoppler_rechts_links] dargestellt, addieren sich die kapazitiv und induktiv gewonnenen Spannungen an einem Ausgang. Am anderen Ausgang sind sie gegensinnig und heben sich im Idealfall gegenseitig auf. Das Signal erscheint daher hauptsächlich an nur einem der beiden Ausgänge.
|
||||
|
||||
<margin>
|
||||
[picture:1109:a_richtkoppler_rechts_links:Richtkoppler, die Welle läuft von links nach rechts]
|
||||
</margin>
|
||||
|
||||
---
|
||||
|
||||
Kehrt sich die Ausbreitungsrichtung der Welle um, wie z. B. von rechts nach links wie in Abbildung [ref:a_richtkoppler_rechts_links] dargestellt, kehrt sich auch die Richtung des Stroms relativ zur Spannung um. Dadurch ändert die induktiv gekoppelte Spannung $U_I$ ihr Vorzeichen, während sich die kapazitiv gekoppelte Spannung $U_C$ entsprechend der Leitungsspannung ergibt.
|
||||
|
||||
<margin>
|
||||
[picture:1110:a_richtkoppler_rechts_links:Richtkoppler, die Welle läuft von rechts nach links]
|
||||
</margin>
|
||||
|
||||
Damit vertauschen sich auch die beiden Ausgänge des Richtkopplers: Der Ausgang, an dem sich die beiden Anteile zuvor addiert haben, wird nun weitgehend ausgelöscht, während sie sich am anderen Ausgang addieren.
|
||||
|
||||
Auf diese Weise kann ein Richtkoppler zwischen einer *vorlaufenden Welle* in Richtung Antenne und einer *rücklaufenden Welle* in Richtung Sender unterscheiden.
|
||||
|
||||
---
|
||||
|
||||
Diese Eigenschaft der Richtkoppler wird in einem *Stehwellenmessgerät* beziehungsweise *SWR-Meter* genutzt: Man misst hierzu die die Ausgangsspannungen zweier in die Leitung eingeschleifter Richtkoppler, die in gegensätzlicher Richtung betrieben werden. Die HF-Spannungen an den Ausgängen der Richtkoppler werden mit Dioden gleichgerichtet und geglättet. Dadurch entstehen Gleichspannungen, die mit einem Messinstrument angezeigt werden können.
|
||||
|
||||
[question:AI401]
|
||||
|
||||
Die Abbildung [ref:a_rswr_meter] zeigt den prinzipiellen Aufbau eines Stehwellenmessgeräts mit zwei Richtkopplern. Dabei nehmen wir an, dass sich der Sender auf der linken und die Antenne auf der rechten Seite befindet.
|
||||
|
||||
[question:AI402]
|
||||
|
||||
Für die folgende Frage brauchen wir uns nur daran zu erinnern, dass das Stehwellenverhältnis auch dem Impedanzverhältnis entspricht, sofern der Lastwiderstand ein reiner Wirkwiderstand ist.
|
||||
Der obere Leiter ist Teil der Speiseleitung zwischen Sender und Antenne. An ihm werden zwei Größen erfasst: Über die kapazitive Kopplung wird ein kleiner Anteil der HF-Spannung ausgekoppelt. Über die induktive Kopplung wird gleichzeitig ein Anteil gewonnen, der vom Strom auf der Speiseleitung abhängt.
|
||||
|
||||
[question:AI403]
|
||||
Die jeweils nicht zur Messung verwendete Seite der Koppelleitung wird mit einem *Abschlusswiderstand* abgeschlossen. Dieser Widerstand entspricht näherungsweise dem Wellenwiderstand $Z_0$ der Koppelleitung. Dadurch wird die dort ankommende HF-Leistung aufgenommen und nicht wieder in die Koppelleitung zurückreflektiert. Solche Reflexionen würden die Trennung zwischen vorlaufender und rücklaufender Welle verschlechtern.
|
||||
|
||||
Diese beiden Signalanteile werden im Richtkoppler miteinander kombiniert. Für eine Welle, die vom Sender zur Antenne läuft, addieren sie sich in einem der beiden Koppler, während sie sich im anderen weitgehend gegenseitig aufheben. Bei einer Welle in der entgegengesetzten Richtung ist es genau umgekehrt.
|
||||
|
||||
Die beiden nahezu spiegelbildlich aufgebauten Schaltungsteile können dadurch unterschiedliche Laufrichtungen erfassen:
|
||||
|
||||
* Der eine Richtkoppler liefert ein Signal proportional zur *vorlaufenden Welle* vom Sender zur Antenne.
|
||||
* Der andere Richtkoppler liefert ein Signal proportional zur *rücklaufenden Welle* von der Antenne zum Sender.
|
||||
|
||||
Die ausgekoppelten Signale sind zunächst HF-Wechselspannungen. Die Dioden richten diese Spannungen gleich, und die Kondensatoren glätten sie. Dadurch entstehen Gleichspannungen, die mit den beiden Messwerken eines Kreuzzeigerinstruments angezeigt werden können, oder durch einen Mikrocontroller mit A/D-Umsetzer gemessern werden können. Die einstellbaren Widerstände dienen dabei zum Abgleich beziehungsweise zur Kalibrierung der Anzeige. Sie sind von den Abschlusswiderständen der Koppelleitungen zu unterscheiden, die für einen reflexionsarmen Abschluss mit $Z_0$ sorgen.
|
||||
|
||||
<margin>
|
||||
[picture:499:a_rswr_meter:SWR-Meter mit zwei Richtkopplern]
|
||||
</margin>
|
||||
|
||||
@@ -0,0 +1,13 @@
|
||||
Die eingespeiste Leistung beträgt $\qty{100}{\watt}$. Auf dem Weg zum Leitungsende wird sie durch die Leitungsdämpfung von $\qty{3}{\decibel}$ auf die Hälfte reduziert:
|
||||
|
||||
$P_\mathrm{Ende}=\qty{100}{\watt}\cdot 10^{-\frac{3}{10}}\approx\qty{50}{\watt}$.
|
||||
|
||||
Bei einem Leerlauf oder einem Kurzschluss wird die am Leitungsende ankommende Leistung vollständig reflektiert. Daher werden dort etwa
|
||||
|
||||
$\qty{50}{\watt}$
|
||||
|
||||
reflektiert.
|
||||
|
||||
Auf dem Rückweg zum Sender wird die reflektierte Leistung durch die Leitung erneut um $\qty{3}{\decibel}$ gedämpft. Am Leitungseingang würden daher nur noch etwa $\qty{25}{\watt}$ zurückkommen.
|
||||
|
||||
Gefragt ist jedoch nach der am Leitungsende reflektierten Leistung. Diese beträgt etwa $\qty{50}{\watt}$.
|
||||
@@ -0,0 +1,25 @@
|
||||
Mit einer künstlichen $\qty{50}{\ohm}$-Antenne beträgt das SWR am Leitungseingang etwa $\num{1}$. Damit wissen wir zunächst, dass die Antennenleitung selbst in Ordnung ist.
|
||||
|
||||
Mit der angeschlossenen Antenne wird dagegen ein SWR von $\num{3}$ gemessen. Für das SWR gilt mit der Spannung der vorlaufenden Welle $U_\mathrm{V}$ und der rücklaufenden Welle $U_\mathrm{R}$:
|
||||
|
||||
$s=\frac{U_\mathrm{V}+U_\mathrm{R}}{U_\mathrm{V}-U_\mathrm{R}}.$
|
||||
|
||||
Bei $s=\num{3}$ ergibt sich daraus, dass die Spannung der rücklaufenden Welle halb so groß wie die der vorlaufenden Welle ist:
|
||||
|
||||
$\frac{U_\mathrm{R}}{U_\mathrm{V}}=\frac{3-1}{3+1}=\num{0,5}.$
|
||||
|
||||
Da die Leistung proportional zum Quadrat der Spannung ist, beträgt die rücklaufende Leistung am Leitungseingang damit
|
||||
|
||||
$\num{0,5}^2=\num{0,25}$
|
||||
|
||||
der vorlaufenden Leistung. Von den eingespeisten $\qty{10}{\watt}$ kommen am Leitungseingang also etwa
|
||||
|
||||
$\qty{10}{\watt}\cdot\num{0,25}=\qty{2,5}{\watt}$
|
||||
|
||||
als rücklaufende Leistung an.
|
||||
|
||||
Die Leitung besitzt auf jedem Weg eine Dämpfung von $\qty{3}{\decibel}$. Von den eingespeisten $\qty{10}{\watt}$ erreichen daher nur etwa $\qty{5}{\watt}$ die Antenne. Auf dem Rückweg wird die reflektierte Leistung wiederum halbiert.
|
||||
|
||||
Damit am Leitungseingang noch $\qty{2,5}{\watt}$ rücklaufende Leistung ankommen, müssen an der Antenne ungefähr $\qty{5}{\watt}$ reflektiert worden sein. Dies entspricht praktisch der gesamten dort ankommenden Leistung.
|
||||
|
||||
Die Antenne nimmt somit so gut wie keine HF-Leistung auf und ist fehlerhaft.
|
||||
@@ -0,0 +1,21 @@
|
||||
Wird die Antenne abgeklemmt, liegt am Leitungsende ein Leerlauf vor. Die dort ankommende HF-Leistung wird vollständig reflektiert.
|
||||
|
||||
Die Leitung besitzt eine Dämpfung von $\qty{5}{\decibel}$ auf dem Hinweg und nochmals $\qty{5}{\decibel}$ auf dem Rückweg. Die reflektierte Welle wird auf ihrem gesamten Weg also um
|
||||
|
||||
$\qty{5}{\decibel}+\qty{5}{\decibel}=\qty{10}{\decibel}$
|
||||
|
||||
gedämpft. Eine Dämpfung von $\qty{10}{\decibel}$ entspricht bei der Leistung einem Faktor von $\num{10}$. Von den eingespeisten $\qty{10}{\watt}$ kommen daher am Leitungseingang noch
|
||||
|
||||
$P_\mathrm{R}=\frac{\qty{10}{\watt}}{10}=\qty{1}{\watt}$
|
||||
|
||||
als rücklaufende Leistung an.
|
||||
|
||||
Die vorlaufende Leistung am Leitungseingang beträgt $\qty{10}{\watt}$. Da die Leistung proportional zum Quadrat der Spannung ist, beträgt das Verhältnis der rücklaufenden zur vorlaufenden Spannung
|
||||
|
||||
$\frac{U_\mathrm{R}}{U_\mathrm{V}} =\sqrt{\frac{\qty{1}{\watt}}{\qty{10}{\watt}}} \approx\num{0,316}.$
|
||||
|
||||
Das Stehwellenverhältnis ergibt sich damit zu
|
||||
|
||||
$s= \frac{U_\mathrm{V}+U_\mathrm{R}} {U_\mathrm{V}-U_\mathrm{R}} = \frac{1+\num{0,316}}{1-\num{0,316}} \approx\num{1,92}.$
|
||||
|
||||
Am Leitungseingang ist daher trotz des Leerlaufs am Leitungsende nur ein SWR von etwa $\num{1,92}$ zu messen.
|
||||
@@ -0,0 +1,15 @@
|
||||
Der Faltdipol besitzt einen Speisewiderstand von etwa $\qtyrange{240}{300}{\ohm}$. Der Wellenwiderstand der verwendeten Leitung beträgt $\qty{75}{\ohm}$.
|
||||
|
||||
Da der Antennenwiderstand größer als der Wellenwiderstand der Leitung ist, ergibt sich das SWR näherungsweise zu
|
||||
|
||||
$s=\frac{R_\mathrm{a}}{Z}$.
|
||||
|
||||
Für die beiden Grenzen des angegebenen Bereichs erhält man
|
||||
|
||||
$s_\mathrm{min}=\frac{\qty{240}{\ohm}}{\qty{75}{\ohm}}=\num{3,2}$
|
||||
|
||||
und
|
||||
|
||||
$s_\mathrm{max}=\frac{\qty{300}{\ohm}}{\qty{75}{\ohm}}=\num{4}$.
|
||||
|
||||
Auf der Leitung ist daher ein SWR von etwa $\numrange{3,2}{4}$ zu erwarten.
|
||||
@@ -0,0 +1,11 @@
|
||||
Der Lastwiderstand beträgt $\qty{150}{\ohm}$, während Messgerät und Sender für einen Wellenwiderstand von $\qty{50}{\ohm}$ ausgelegt sind.
|
||||
|
||||
Da der Lastwiderstand größer als der Wellenwiderstand ist, ergibt sich das Stehwellenverhältnis zu
|
||||
|
||||
$s=\frac{R_\mathrm{L}}{Z}$.
|
||||
|
||||
Damit folgt
|
||||
|
||||
$s=\frac{\qty{150}{\ohm}}{\qty{50}{\ohm}}=3$.
|
||||
|
||||
Das Stehwellenmessgerät muss daher ein SWR von $\num{3}$ anzeigen.
|
||||
Reference in New Issue
Block a user