File:Dipol antenna impedance.png

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Description
English: Impedance of a dipol antenna in relation to length l and diameter d. Where as the given ratios are and .
Deutsch: Impedanz einer Dipolantenne im Bezug zum Länge l und dem Durchmesser d. Das gewählte Verhältnis beträgt 1000 und 10.
Date
Source Own work
Author Menner

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I, the copyright holder of this work, hereby publish it under the following license:
Creative Commons CC-Zero This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication.
The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.

Source code

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#!/usr/bin/octave 

%
% Diagramm zur Dipolantenne mit Länge zu Eingangsimpedanz
%
% aus Krak "Antennen und Strahlungsfelder" bzw. http://rediscoveries.blogspot.de/2011/08/half-wavelength-dipole-that-isnt.html
%
% 2014
%

% Abhängigkeit: pkg install -auto -install specfun


%
% reaktanz()
%

function [R_E, X_E] = reaktanz(h, a)
global k_0;
global Z_0;
global C;

  Term_0 = Z_0 / (4*pi());
  Term_1 = - Ci(2*k_0*h) + C + log(2*k_0*h);
  Term_2 = Si(4*k_0*h) - 2 * Si(2*k_0*h);
  Term_3 = Ci(4*k_0*h) - 2 * Ci(2*k_0*h) + C + log(k_0*h);
  Term_4 = 1 ./ (sin(k_0 * h)).^2;

  R_E = Term_0 * Term_4 .* (2 * Term_1 + sin(2 * k_0 * h) .* Term_2 + cos(2*k_0*h) .* Term_3);


  Term_X_1 = Si( 2 * k_0 * h);
  Term_X_2 = Term_2 * -1;
  Term_X_3 = Ci(4*k_0*h) - 2 * Ci(2*k_0*h) + C + log((k_0 * a).^2) - log(k_0*h);

  X_E = Term_0 * Term_4 .* (2 * Term_X_1 + cos(2 * k_0 * h) .* Term_X_2 + sin(2*k_0*h) .* Term_X_3);

endfunction


%
% M  A  I  N
%

% Normierung
lambda = 1.;

% Länge der Dipolantenne
schritt = 0.01;
% schritt = 0.025
l = schritt:schritt:3*lambda;
ratio = 20;
%l = 0.5;
% l = 0.5*lambda;
%l
h = l/2;

% Freiraumimpedanz nach WP
global Z_0 = 376.730313461; %  Ohm
% Z_0 = 1;

% Euler-Mascheroni-Konstante nach WP
global C = 0.5772156649;

% Kreiswellenzahl
global k_0 = 2*pi()/lambda; % TODO

% http://essay.utwente.nl/61459/1/MSc_P_Prins.pdf
% eta = Z_0 / Z_m = Z_E / Z_0 = Z_S
%printf("Master\n");
%Term_1 = Ci(2*k_0*h) + C + log(2*k_0*h);
%Term_2 = Si(4*k_0*h) - 2 * Si(2*k_0*h);
%Term_3 = - Ci(4*k_0*h) + 2 * Ci(2*k_0*h) + C + log(k_0*h);
%Term_4 = 1 ./ (sin(k_0 * h)).^2;


%R_E

% Kark [Zuh53]
printf("Kark\n");

a_1000 = h/1000;
[R_E, X_E1000] = reaktanz(h, a_1000);
Z_E1000 = sqrt(R_E.^2 + X_E1000.^2);

a_10 = h/10;
[R_E, X_E10] = reaktanz(h, a_10);
Z_E10 = sqrt(R_E.^2 + X_E10.^2);

close();

% set (0, 'DefaultFigurePosition', [1 0.5 * get(0, "screensize")(4:-1:3) get(0, "DefaultFigurePosition")(4)]);

figure('Position',[100, 100, 1200,1000]);

plot( l/lambda, R_E, "k;R;", "linewidth", 2);
hold("on");
plot( l/lambda, X_E1000, "--r;X_{1000};", "linewidth", 2);
plot(l/lambda, Z_E1000, "r;|Z_{1000}|;", "linewidth", 2);
plot( l/lambda, X_E10, "--b;X_{10};", "linewidth", 2);
plot(l/lambda, Z_E10, "b;|Z_{10}|;", "linewidth", 2);

ylim([-250, 250]);
xlabel("Ratio l/\\lambda");
ylabel("Impedance in Ohm");

legend ("location", "southeast");

print("dipol_impedance.png", "-dpng", "-S1600,900")

% printf("Weiter mit beliebiger Taste...\n");
% pause();

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Date/TimeThumbnailDimensionsUserComment
current12:29, 24 August 2014Thumbnail for version as of 12:29, 24 August 20141,600 × 900 (68 KB)Menner (talk | contribs)typo
11:25, 24 August 2014Thumbnail for version as of 11:25, 24 August 20141,600 × 900 (68 KB)Menner (talk | contribs)User created page with UploadWizard

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