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Electromagnetic Waves & Antennas Toolbox

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Electromagnetic Waves & Antennas Toolbox



06 Feb 2004 (Updated )

Companion Software

% impedmat.m - mutual impedance matrix of array of parallel dipole antennas
% Usage: Z = impedmat(L,a,d)  
% L = lengths of dipoles in wavelengths = [L1,L2,...,LK]
% a = radii of dipoles in wavelengths = [a1,a2,...,aK]                    
% d = [x,y] or [x] coordinates of dipoles in wavelengths, d is Kx2 or Kx1 or 1xK           
% Z = mutual impedance matrix referred to the input terminals of the antennas
% notes: L may not contain multiples of lambda
%        the linear dipoles are z-directed and their centers lie on the xy-plane
%        d is the matrix of the [x,y] locations of the antennas and is Kx2, that is, 
%        d = [x1,y1; x2,y2; ...; xK,yK]. If the antennas are along the x-axis then 
%        d is the vector of x-coordinates only and can be entered either as a column 
%        or row vector, d=[x1,x2,...,xK]
%        the current distributions on the antennas are assumed to sinusoidal, 
%        for example, on the p-th antenna, Ip(z) = Ip * sin(k*(Lp/2-abs(z)))
%        uses IMPED to calculate the mutual impedances

% S. J. Orfanidis - 1999 -

function Z = impedmat(L,a,d)

if nargin==0, help impedmat; return; end

if ~isempty(find(L==fix(L))),                       % check if any of the L's is integer
   error('L may not contain multiples of lambda'); 

K = length(L);                                      % number of antennas

if max(size(d))~=K,
    error('d must have size Kx2 or Kx1 or 1xK');
if min(size(d))==1,
    d = [d(:),zeros(K,1)];                          % make d into [x,y] pairs

Z = zeros(K,K);

for p=1:K,
  for q=p:K,                                        % upper triangular part of Z
    if q==p,
      b = a(p);                                     % self-impedances
      b = norm(d(p,:)-d(q,:));                      % distance between p,q dipoles
    Zpq = imped(L(p),L(q),b);                       % mutual impedance between p,q dipoles
    Z(p,q) = Zpq; 
    Z(q,p) = Zpq;                                   % reciprocity

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