% stub1.m - single-stub matching
%
% -----------------/-----------|
% main line Z0 / ZL
% ---------------/---/----l----|
% / d
% /___/
%
% Usage: dl = stub1(zL,type)
% dl = stub1(zL) (equivalent to type='ps')
%
% zL = normalized load impedance, zL = ZL/Z0
% type = 'ps','po','ss','so' for parallel/short, parallel/open, series/short, series/open
%
% dl = [d,l] = 2x2 matrix, where each row is a solution
%
% d is length of stub (2x1 vector for two possible solutions)
% l is position of stub from load (2x1 vector for two possible solutions)
%
% notes: d,l are in wavelengths and are reduced mod lambda/2
%
% design method for case 'ps':
% (1-GL)/(1+GL) - j*cot(bd) = 1 gives the conditions
% cos(2bl-thL) = -abs(GL) and
% tan(bd) = -tan(2bl-thL)/2
%
% for a balanced shunt stub, the length of each leg is:
% d_bal = acot(cot(2*pi*d)/2) ('ps' case), d_bal = atan(tan(2*pi*d)/2) ('po' case)
% S. J. Orfanidis - 1999 - www.ece.rutgers.edu/~orfanidi/ewa
function dl = stub1(zL,type)
if nargin==0, help stub1; return; end
if nargin==1, type='ps'; end
GL = z2g(zL,1); % reflection coefficient at load
thL = angle(GL);
switch type,
case 'ps'
bl = thL/2 + [1;-1]*acos(-abs(GL))/2;
bd = atan(-tan(2*bl-thL)/2);
case 'po'
bl = thL/2 + [1;-1]*acos(-abs(GL))/2;
bd = acot(tan(2*bl-thL)/2);
case 'ss'
bl = thL/2 + [1;-1]*acos(abs(GL))/2;
bd = acot(tan(2*bl-thL)/2);
case 'so'
bl = thL/2 + [1;-1]*acos(abs(GL))/2;
bd = atan(-tan(2*bl-thL)/2);
otherwise
fprintf('\nunknown type\n\n');
return
end
l = bl/2/pi;
d = bd/2/pi;
dl = mod([d,l], 0.5);
