exercise 5.12
ZIP with MATLAB scripts and note:
exercise 5.12 notes:
12.1.- single shunt short circuit stub.
Additional shunt open single stub calculation also available
% calculating lengths
clc;clear all;close all;
delete('pozar_05_12_vars.mat') % avoid append or variables overlap in .mat
% 12.1
ZL=200;YL=ZL;Z0=100;Y0=1/Z0;RL=real(ZL);XL=imag(ZL);GL=real(YL);BL=imag(YL);
% when RL~=Z0
t1=(XL+((RL*((Z0-RL)^2+XL^2))/Z0)^.5)/(RL-Z0);
t2=(XL-((RL*((Z0-RL)^2+XL^2))/Z0)^.5)/(RL-Z0);
% when RL=Z0
D1_TL=1/(2*pi)*atan(t1);if t1<0 D1_TL=D1_TL+.5; end
D2_TL=1/(2*pi)*atan(t2);if t2<0 D2_TL=D2_TL+.5; end
D1_TL
D2_TL
B1=(RL^2*t1-(Z0-XL*t1)*(XL+Z0*t1))/(Z0*(RL^2+(XL+Z0*t1)^2))
B2=(RL^2*t2-(Z0-XL*t2)*(XL+Z0*t2))/(Z0*(RL^2+(XL+Z0*t2)^2))
D1stub_sc=1/(2*pi)*atan(Y0/B1); if (Y0/B1)<0 D1stub_sc=D1stub_sc+.5; end
D1stub_oc=-1/(2*pi)*atan(B1/Y0); if atan(B1/Y0)>0 D1stub_oc=D1stub_oc+.5; end
D2stub_sc=1/(2*pi)*atan(Y0/B2); if (Y0/B2)<0 D2stub_sc=D2stub_sc+.5; end
D2stub_oc=-1/(2*pi)*atan(B2/Y0); if atan(B2/Y0)>0 D2stub_oc=D2stub_oc+.5; end
D1stub_sc
D1stub_oc
D2stub_sc
D2stub_oc
% storing results in variables for frequency BW comparison last point of this exercise:
D1_TL_shunt_singlestub=D1_TL;D2_TL_shunt_singlestub=D2_TL;
D1stub_sc_shunt_singlestub=D1stub_sc;D2stub_sc_shunt_singlestub=D2stub_sc;
D1stub_oc_shunt_singlestub=D1stub_oc;D2stub_oc_shunt_singlestub=D2stub_oc;
if (isempty(dir('pozar_05_12_vars.mat')))
save('pozar_05_12_vars.mat','D1_TL_shunt_singlestub','D2_TL_shunt_singlestub',...
'D1stub_sc_shunt_singlestub','D2stub_sc_shunt_singlestub',...
'D1stub_oc_shunt_singlestub','D2stub_oc_shunt_singlestub');
else
save('pozar_05_12_vars.mat','D1_TL_shunt_singlestub','D2_TL_shunt_singlestub',...
'D1stub_sc_shunt_singlestub','D2stub_sc_shunt_singlestub',...
'D1stub_oc_shunt_singlestub','D2stub_oc_shunt_singlestub','-append');
end
t1 = 1.414213562373095
t2 = -1.414213562373095
D1_TL = 0.152043361992348
D2_TL = 0.347956638007652
B1 = 0.007071067811865
B2 = -0.007071067811865
D1stub_sc = 0.152043361992348
D1stub_oc = 0.402043361992348
D2stub_sc = 0.347956638007652
D2stub_oc = 0.097956638007652
From 12.1 throughout 12.8 finding transmission line length D_TL and stub length Dstub either shorted or open.
In 12.9 we are going to measure and compare frequency bandwidths.
In order to reuse plotting loops, saving and retrieving TL and stub lengths to .mat file pozar_05_12_vars.mat.
12.2.- single series short circuit stub (added calculations for series open single stub)
%% 12.2 single series short circuit stub (added calculations for series open single stub)
% when GL=~Y0
t1=(BL+((GL*((Y0-GL)^2+BL^2))/Y0)^.5)/(GL-Y0)
t2=(BL-((GL*((Y0-GL)^2+BL^2))/Y0)^.5)/(GL-Y0)
% when GL=Y0
if t1>=0 D1_TL=1/(2*pi)*atan(t1); elseif t1<0 D1_TL=1/(2*pi)*atan(t1)+.5; end
if t2>=0 D2_TL=1/(2*pi)*atan(t2); elseif t2<0 D2_TL=1/(2*pi)*atan(t2)+.5; end
D1_TL
D2_TL
X1=1/Y0*(GL^2*t1-(Y0-t1*BL)*(BL+t1*Y0))/(GL^2+(BL+Y0*t1)^2)
X2=1/Y0*(GL^2*t2-(Y0-t2*BL)*(BL+t2*Y0))/(GL^2+(BL+Y0*t2)^2)
D1stub_sc=1/(2*pi)*atan(-X1/Z0);if atan(X1/Z0)<0 D1stub_sc=D1stub_sc+.5;end
D1stub_oc=1/(2*pi)*atan(Z0/X1);if atan(Z0/X1)<0 D1stub_oc=D1stub_oc+.5;end
D2stub_sc=1/(2*pi)*atan(-X2/Z0);if atan(X2/Z0)<0 D2stub_sc=D2stub_sc+.5;end
D2stub_oc=1/(2*pi)*atan(Z0/X2);if atan(Z0/X2)<0 D2stub_oc=D2stub_oc+.5;end
D1_TL
D2_TL
D1stub_sc
D2stub_sc
D1stub_oc
D2stub_oc
% storing results in variables with different names for frequency BW comparison last point exercise
D1_TL_series_singlestub=D1_TL;D2_TL_series_singlestub=D2_TL;
D1stub_sc_series_singlestub=D1stub_sc;
D2stub_sc_series_singlestub=D2stub_sc;
D1stub_oc_series_singlestub=D1stub_oc;
D2stub_oc_series_singlestub=D2stub_oc;
if (isempty(dir('pozar_05_12_vars.mat')))
save('pozar_05_12_vars.mat','D1_TL_series_singlestub','D2_TL_series_singlestub',...
'D1stub_sc_series_singlestub','D2stub_sc_series_singlestub',...
'D1stub_oc_series_singlestub','D2stub_oc_series_singlestub');
else save('pozar_05_12_vars.mat','D1_TL_series_singlestub','D2_TL_series_singlestub',...
'D1stub_sc_series_singlestub','D2stub_sc_series_singlestub',...
'D1stub_oc_series_singlestub','D2stub_oc_series_singlestub','-append');
end
% to cell 12.9.2
t1 = -0.707106781186548
t2 = 0.707106781186548
D1_TL = 0.402043361992348
D2_TL = 0.097956638007652
X1 = 70.710678118654755
X2 = -70.710678118654755
D1stub_sc = 0.097956638007652
D2stub_sc = 0.402043361992348
D1stub_oc = 0.347956638007652
D2stub_oc = 0.152043361992348
12.3.- double shunt short circuit stubs (added shunt open double stub calculations)
% 12.3 double shunt short circuit stubs (added shunt open double stub calculations)
ZL=200;Z0=100;Y0=1/Z0;YL=1/ZL;GL=real(YL);BL=imag(YL);D_TL=1/8;t=tan(2*pi*D_TL)
B11=-BL+1/t*(Y0+((1+t^2)*GL*Y0-GL^2*t^2)^.5)
B12=-BL-1/t*(Y0-((1+t^2)*GL*Y0-GL^2*t^2)^.5)
B21=(-Y0*(Y0*GL*(1+t^2)-GL^2*t^2)^.5+GL*Y0)/(GL*t)
B22=(Y0*(Y0*GL*(1+t^2)-GL^2*t^2)^.5+GL*Y0)/(GL*t)
D11stub_oc=1/(2*pi)*atan(B11/Y0);if atan(B11/Y0)<0 D11stub_oc=D11stub_oc+.5; end;
D12stub_oc=1/(2*pi)*atan(B12/Y0);if atan(B12/Y0)<0 D12stub_oc=D12stub_oc+.5; end;
D21stub_oc=1/(2*pi)*atan(B21/Y0);if atan(B21/Y0)<0 D21stub_oc=D21stub_oc+.5; end;
D22stub_oc=1/(2*pi)*atan(B22/Y0);if atan(B22/Y0)<0 D22stub_oc=D22stub_oc+.5; end;
D11stub_sc=-1/(2*pi)*atan(Y0/B11);if atan(Y0/B11)>0 D11stub_sc=D11stub_sc+.5; end;
D12stub_sc=-1/(2*pi)*atan(Y0/B12);if atan(Y0/B12)>0 D12stub_sc=D12stub_sc+.5; end;
D21stub_sc=-1/(2*pi)*atan(Y0/B21);if atan(Y0/B21)>0 D21stub_sc=D21stub_sc+.5; end;
D22stub_sc=-1/(2*pi)*atan(Y0/B22);if atan(Y0/B22)>0 D22stub_sc=D22stub_sc+.5; end;
D11stub_oc
D12stub_oc
D21stub_oc
D22stub_oc
D11stub_sc
D12stub_sc
D21stub_sc
D22stub_sc
% storing results
D1_TL_shunt_doublestub=D_TL;
D11stub_oc_shunt_doublestub=D11stub_oc;
D12stub_oc_shunt_doublestub=D12stub_oc;
D21stub_oc_shunt_doublestub=D21stub_oc;
D22stub_oc_shunt_doublestub=D22stub_oc;
D11stub_sc_shunt_doublestub=D11stub_sc;
D12stub_sc_shunt_doublestub=D12stub_sc;
D21stub_sc_shunt_doublestub=D21stub_sc;
D22stub_sc_shunt_doublestub=D22stub_sc;
if (isempty(dir('pozar_05_12_vars.mat')))
save('pozar_05_12_vars.mat',...
'D11stub_oc_shunt_doublestub','D12stub_oc_shunt_doublestub',...
'D21stub_oc_shunt_doublestub','D22stub_oc_shunt_doublestub',...
'D11stub_oc_shunt_doublestub','D12stub_oc_shunt_doublestub',...
'D21stub_oc_shunt_doublestub','D22stub_oc_shunt_doublestub');
else
save('pozar_05_12_vars.mat',...
'D11stub_oc_shunt_doublestub','D12stub_oc_shunt_doublestub',...
'D21stub_oc_shunt_doublestub','D22stub_oc_shunt_doublestub',...
'D11stub_oc_shunt_doublestub','D12stub_oc_shunt_doublestub',...
'D21stub_oc_shunt_doublestub','D22stub_oc_shunt_doublestub','-append')
end
t = 1.000000000000000
B11 = 0.018660254037844
B12 = -0.001339745962156
B21 = -0.007320508075689
B22 = 0.027320508075689
D11stub_oc = 0.171703373799962
D12stub_oc = 0.478803499409917
D21stub_oc = 0.399427713574991
D22stub_oc = 0.194155807330508
D11stub_sc = 0.4217033737999
D12stub_sc = 0.228803499409917
D21stub_sc = 0.149427713574991
D22stub_sc = 0.444155807330508
12.4.- double shunt open circuit stubs
(added shunt open stub calculations)
D_TL=1/8;t=tan(2*pi*D_TL)
X11=-XL+1/t*(Z0+((1+t^2)*RL*Z0-RL^2*t^2)^.5)
X12=-XL+1/t*(Z0-((1+t^2)*RL*Z0-RL^2*t^2)^.5)
X21=1/(RL*t)*(+Z0*(Z0*RL*(1+t^2)-RL^2*t^2)^.5+RL*Z0)
X22=1/(RL*t)*(-Z0*(Z0*RL*(1+t^2)-RL^2*t^2)^.5+RL*Z0)
D11stub_oc=1/(2*pi)*atan(Z0/X11);if atan(Z0/X11)<0 D11stub_oc=D11stub_oc+.5; end;
D12stub_oc=1/(2*pi)*atan(Z0/X12);if atan(Z0/X12)<0 D12stub_oc=D12stub_oc+.5; end;
D21stub_oc=1/(2*pi)*atan(Z0/X21);if atan(Z0/X21)<0 D21stub_oc=D21stub_oc+.5; end;
D22stub_oc=1/(2*pi)*atan(Z0/X22);if atan(Z0/X22)<0 D22stub_oc=D22stub_oc+.5; end;
D11stub_sc=-1/(2*pi)*atan(X11/Z0);if atan(X11/Z0)>0 D11stub_sc=D11stub_sc+.5; end;
D12stub_sc=-1/(2*pi)*atan(X12/Z0);if atan(X12/Z0)>0 D12stub_sc=D12stub_sc+.5; end;
D21stub_sc=-1/(2*pi)*atan(X21/Z0);if atan(X21/Z0)>0 D21stub_sc=D21stub_sc+.5; end;
D22stub_sc=-1/(2*pi)*atan(X22/Z0);if atan(X22/Z0)>0 D22stub_sc=D22stub_sc+.5; end;
D11stub_oc
D12stub_oc
D21stub_oc
D22stub_oc
D11stub_sc
D12stub_sc
D21stub_sc
D22stub_sc
% storing results
D_TL_series_doublestub=D_TL
D11stub_sc_series_doublestub=D11stub_sc;
D12stub_sc_series_doublestub=D12stub_sc;
D21stub_sc_series_doublestub=D21stub_sc;
D22stub_sc_series_doublestub=D22stub_sc;
D11stub_oc_series_doublestub=D11stub_oc;
D12stub_oc_series_doublestub=D12stub_oc;
D21stub_oc_series_doublestub=D21stub_oc;
D22stub_oc_series_doublestub=D22stub_oc;
if (isempty(dir('pozar_05_12_vars.mat')))
save('pozar_05_12_vars.mat',...
'D11stub_oc_series_doublestub','D12stub_oc_series_doublestub',...
'D21stub_oc_series_doublestub','D22stub_oc_series_doublestub',...
'D11stub_oc_series_doublestub','D12stub_oc_series_doublestub',...
'D21stub_oc_series_doublestub','D22stub_oc_series_doublestub');
else
save('pozar_05_12_vars.mat',...
'D11stub_oc_series_doublestub','D12stub_oc_series_doublestub',...
'D21stub_oc_series_doublestub','D22stub_oc_series_doublestub',...
'D11stub_oc_series_doublestub','D12stub_oc_series_doublestub',...
'D21stub_oc_series_doublestub','D22stub_oc_series_doublestub','-append')
end
t = 1.000000000000000
X11 = 1.000000000000000e+02
X12 = 1.000000000000000e+02
X21 = 1.000000000000000e+02
X22 = 1.000000000000000e+02
D11stub_oc = 0.125
D12stub_oc = 0.125
D21stub_oc = 0.125
D22stub_oc = 0.125
D11stub_sc = 0.375
D12stub_sc = 0.375
D21stub_sc = 0.375
D22stub_sc = 0.375
While 12.3 and 12.4 have constant TL length to avoid complicating calculations, if instead D3=1/4, 3/8, or 1.2/8 then this equation approach doesn't work, stub lengths come up complex which is one of the limitations for not using the Smith chart or simulator with optimiser.
12.5.- D_TL=1/8.2
D112stub_oc = 0.0966
D122stub_oc = 0.1593
D212stub_oc = 0.1080
D222stub_oc = 0.1388
D112stub_sc = 0.3466
D122stub_sc = 0.4093
D212stub_sc = 0.3580
D222stub_sc = 0.3888
12.6.- D_TL=1/10
D113stub_oc = 0.0561
D123stub_oc = 0.2438
D213stub_oc = 0.0723
D223stub_oc = 0.1519
D113stub_sc = 0.3061
D123stub_sc = 0.4938
D213stub_sc = 0.3223
D223stub_sc = 0.4019
12.7.- D_TL=1/11
D114stub_oc = 0.0476
D124stub_oc = 0.2705
D214stub_oc = 0.0628
D224stub_oc = 0.1514
D114stub_sc = 0.2976
D124stub_sc = 0.0205
D214stub_sc = 0.3128
D224stub_sc = 0.4014
12.8.- D_TL=1/12
D115stub_oc = 0.0416
D125stub_oc = 0.2916
D215stub_oc = 0.0558
D225stub_oc = 0.1494
D115stub_sc = 0.2916
D125stub_sc = 0.0416
D215stub_sc = 0.3058
D225stub_sc = 0.3994
12.9.- best BW? with D=L0/lambda, lambda0=c/f0, L0=D*lambda0, then
2*pi/lambda*D*lambda0=2*pi*f/c*D*c/f0
beta*L0=2*pi*D=2*pi*D*f/f0
input impedance for ideal stubs and TL:
Zin_stub_sc=1j*Z0*tan(2*pi*L*f/c)
Zin_stub_oc=Z0/(1j*tan(2*pi*L*f/c))
Zin_TL=(ZL+1j*tan(2*pi*D*f/f0))/(Z0+1j*ZL*tan(2*pi*D*f/f0))
%% 12.9.1
% run Shift+Enter at least 12.1 first to generate stub and TL lengths
load pozar_05_12_vars.mat
ZL=200;Z0=100;Y0=1/Z0;YL=1/ZL;GL=real(YL);BL=imag(YL);
c=3e8;f0=2e9;df=1e5;f1=1e9;f2=3e9;f=[f1:df:f2];
s11=zeros(1,numel(f));s11_mod=zeros(1,numel(f));
ZinTL=Z0*(ZL+1j*Z0*tan(2*pi*D1_TL_shunt_singlestub ...
*f/f0))./(Z0+1j*ZL*tan(2*pi*D1_TL_shunt_singlestub *f/f0));
Zin_stb_sc=1j*Z0*tan(2*pi*D1stub_sc_shunt_singlestub*f/f0); % shunt stub
Zin=1./(ZinTL.^-1+Zin_stb_sc.^-1);
s11=[s11_mod;(Zin-Z0)./(Zin+Z0)];
s11_mod=[s11_mod;abs((Zin-Z0)./(Zin+Z0))];
ZinTL=Z0*(ZL+1j*Z0*tan(2*pi*D1_TL_shunt_singlestub ...
*f/f0))./(Z0+1j*ZL*tan(2*pi*D1_TL_shunt_singlestub *f/f0));
Zin_stb_sc=Z0./(1j*tan(2*pi*D1stub_oc_shunt_singlestub*f/f0)); % series stub
Zin=1./(ZinTL.^-1+Zin_stb_sc.^-1);
s11=[s11_mod;(Zin-Z0)./(Zin+Z0)];
s11_mod=[s11_mod;abs((Zin-Z0)./(Zin+Z0))];
ZinTL=Z0*(ZL+1j*Z0*tan(2*pi*D2_TL_shunt_singlestub ...
*f/f0))./(Z0+1j*ZL*tan(2*pi*D2_TL_shunt_singlestub *f/f0));
Zin_stb_sc=1j*Z0*tan(2*pi*D2stub_sc_shunt_singlestub*f/f0); % shunt stub
Zin=1./(ZinTL.^-1+Zin_stb_sc.^-1);
s11=[s11_mod;(Zin-Z0)./(Zin+Z0)];
s11_mod=[s11_mod;abs((Zin-Z0)./(Zin+Z0))];
ZinTL=Z0*(ZL+1j*Z0*tan(2*pi*D2_TL_shunt_singlestub ...
*f/f0))./(Z0+1j*ZL*tan(2*pi*D2_TL_shunt_singlestub *f/f0));
Zin_stb_sc=Z0./(1j*tan(2*pi*D2stub_oc_shunt_singlestub*f/f0)); % series stub
Zin=1./(ZinTL.^-1+Zin_stb_sc.^-1);
s11=[s11_mod;(Zin-Z0)./(Zin+Z0)];
s11_mod=[s11_mod;abs((Zin-Z0)./(Zin+Z0))];
s11_mod(1,:)=[];
s11(1,:)=[];
% s11_oc2=s11(4,:)'; smithchart(s11_oc2); %
for k=1:1:size(s11_mod,1)
figure(1);plot(f,s11_mod(k,:));hold all;
end
grid on
title('short/open shunt single stub |s11|')
legend('DTL1 D1 sc','DTL1 D2 oc','DTL2 D2 sc','DTL2 D2 oc','Location','northwest')
for k=1:1:size(s11_mod,1)
figure(2);plot(f,10*log10(s11_mod(k,:)));axis([1e9 3e9 -35 0]);hold all;
end
grid on;grid minor
title('short/open shunt single stub 10log(|s11|)')
legend('DTL1 D1 sc','DTL1 D2 oc','DTL2 D2 sc','DTL2 D2 oc','Location','northwest')
for k=1:1:size(s11_mod,1)
figure(3);plot(f,20*log10(s11_mod(k,:)));axis([1.7e9 2.3e9 -20 -10]);hold all;
end
grid on;grid minor
title('20dB Return Loss BW for short/open shunt single stub')
legend('DTL1 D1 sc','DTL1 D2 oc','DTL2 D2 sc','DTL2 D2 oc','Location','northwest')
measuring Return Loss below -20dB bandwidth:
a=10*log10(s11_mod(1,:));a_below20=a(a<-20);
[nx,f_below20]=find(a<-20);f_bw=f(f_below20);
figure(2);plot(f_bw,a_below20,'bo')
BW_band_RL20dB_singleshuntstub=[min(f_bw) max(f_bw)]
BW_RL20dB_singleshuntstub=...
abs(min(f_bw)-max(f_bw))
save('pozar_05_12_vars.mat',…
'BW_band_RL20dB_singleshuntstub',…
'BW_RL20dB_singleshuntstub')
BW_band_RL20dB_singleshuntstub =
1.0e+09 *
1.983100000000000
2.017200000000000
BW_RL20dB_singleshuntstub =
34100000
what happens when crossing TL length and stub lengths?
% run Shift+Enter at least 12.1 first to generate stub and TL lengths
load pozar_05_12_vars.mat
ZL=200;Z0=100;Y0=1/Z0;YL=1/ZL;GL=real(YL);BL=imag(YL);
c=3e8;f0=2e9;df=1e5;f1=1e9;f2=3e9;f=[f1:df:f2];
DTL=[D1_TL_shunt_singlestub D2_TL_shunt_singlestub]
Dstb=[D1stub_sc_shunt_singlestub D1stub_oc_shunt_singlestub;
D2stub_sc_shunt_singlestub D2stub_oc_shunt_singlestub];
s11=zeros(1,numel(f));s11_mod=zeros(1,numel(f));
for k=1:1:numel(DTL)
for s=1:1:size(Dstb,1)
ZinTL=Z0*(ZL+1j*Z0*tan(2*pi*DTL(k)*(f)/f0))./(Z0+1j*ZL*tan(2*pi*DTL(k)*(f)/f0));
Zin_stb_sc=1j*Z0*tan(2*pi*Dstb(k,s)*(f)/f0);
Zin=1./(ZinTL.^-1+Zin_stb_sc.^-1);
s11=[s11_mod;(Zin-Z0)./(Zin+Z0)];
s11_mod=[s11_mod;abs((Zin-Z0)./(Zin+Z0))];
end
end
s11_mod(1,:)=[];s11(1,:)=[];
for k=1:1:size(s11_mod,1)
figure(1);plot(f,s11_mod(k,:));hold all;
end
grid on
title('short/open shunt single stub |s11|')
legend('DTL1 D1 sc','DTL1 D2 oc','DTL2 D2 sc','DTL2 D2 oc','Location','northwest')
for k=1:1:size(s11_mod,1)
figure(2);plot(f,10*log10(s11_mod(k,:)));axis([1e9 3e9 -35 0]);hold all;
end
grid on;grid minor
title('short/open shunt single stub 10log(|s11|)')
legend('DTL1 D1 sc','DTL1 D2 oc','DTL2 D2 sc','DTL2 D2 oc','Location','northwest')
for k=1:1:size(s11_mod,1)
figure(3);plot(f,20*log10(s11_mod(k,:)));axis([1.7e9 2.3e9 -20 -10]);hold all;
end
grid on;grid minor
title('20dB Return Loss BW for short/open shunt single stub')
legend('DTL1 D1 sc','DTL1 D2 oc','DTL2 D2 sc','DTL2 D2 oc','Location','northwest')
One way to manually fix the previously crossed open circuit stub lengths:
load pozar_05_12_vars.mat
ZL=200;Z0=100;Y0=1/Z0;YL=1/ZL;GL=real(YL);BL=imag(YL);
c=3e8;f0=2e9;df=1e5;f1=1e9;f2=3e9;f=[f1:df:f2];
DTL=[D1_TL_shunt_singlestub D2_TL_shunt_singlestub]
Dstb=[D1stub_sc_shunt_singlestub...
D1stub_oc_shunt_singlestub+.054; % |s11| manual correction D2stub_sc_shunt_singlestub...
D2stub_oc_shunt_singlestub-.054]; % |s11| manual correction
s11=zeros(1,numel(f));s11_mod=zeros(1,numel(f));
for k=1:1:numel(DTL)
for s=1:1:size(Dstb,1)
ZinTL=...
Z0*(ZL+1j*Z0*tan(2*pi*DTL(k)*(f)/f0))./(Z0+1j*ZL*tan(2*pi*DTL(k)*(f)/f0));
Zin_stb_sc=1j*Z0*tan(2*pi*Dstb(k,s)*(f)/f0);
Zin=1./(ZinTL.^-1+Zin_stb_sc.^-1);
s11=[s11_mod;(Zin-Z0)./(Zin+Z0)];
s11_mod=[s11_mod;abs((Zin-Z0)./(Zin+Z0))];
end
end
s11_mod(1,:)=[];
s11(1,:)=[];
for k=1:1:size(s11_mod,1)
figure(1);plot(f,s11_mod(k,:));hold all;
end
grid on
title('short shunt single stub')
legend('DTL1 D1 sc','DTL1 D2 oc','DTL2 D2 sc','DTL2 D2 oc','Location','northwest')
for k=1:1:size(s11_mod,1)
figure(2);plot(f,10*log10(s11_mod(k,:)));axis([1e9 3e9 -35 0]);hold all;
end
grid on;grid minor
title('short shunt single stub')
legend('DTL1 D1 sc','DTL1 D2 oc','DTL2 D2 sc','DTL2 D2 oc','Location','northwest')
% s11_oc2=s11(4,:)'; smithchart(s11_oc2);
for k=1:1:size(s11_mod,1)
figure(3);plot(f,20*log10(s11_mod(k,:)));axis([1.7e9 2.3e9 -20 -10]);hold all;
end
grid on;grid minor
title('20dB Return Loss BW for short/open shunt single stub')
legend('DTL1 D1 sc','DTL1 D2 oc','DTL2 D2 sc','DTL2 D2 oc','Location','northwest')
% measuring badnwidths
BW_band_RL20dB_singleshuntstub=[0 0];BW_RL20dB_singleshuntstub(1)=0
for k=1:1:size(s11_mod,1)
a=10*log10(s11_mod(k,:));
a_below20=a(a<-20);
[nx,f_below20]=find(a<-20);
f_bw=f(f_below20);
% figure(2);plot(f_bw,a_below20,'bo')
BW_band_RL20dB_singleshuntstub= [BW_band_RL20dB_singleshuntstub;
min(f_bw) max(f_bw)];
BW_RL20dB_singleshuntstub= [BW_RL20dB_singleshuntstub;
abs(min(f_bw)-max(f_bw))];
end
BW_band_RL20dB_singleshuntstub(1,:)=[];BW_RL20dB_singleshuntstub(1)=[];
BW_band_RL20dB_sinheshuntstub
BW_RL20dB_singleshuntstub
% storing
save('pozar_05_12_vars.mat',...
'BW_band_RL20dB_singleshuntstub', BW_RL20dB_singleshuntstub')
BW_band_RL20dB_singleshuntstub =
1.0e+09 *
1.983100000000000 2.017200000000000
1.991200000000000 2.009000000000000
1.992500000000000 2.007400000000000
1.989200000000000 2.010700000000000
BW_RL20dB_singleshuntstub =
34100000
17800000
14900000
21500000
the line s11_oc2=s11(4,:)'; smithchart(s11_oc2); only used for test, if attempting to plot more than one sij on Smith chart with command
smithchart, feed a 2x2xN matrix, otherwise hold all doesn't work and only one sij is plotted on the Smith chart.
12.9.2
load pozar_05_12_vars.mat
ZL=200;Z0=100;Y0=1/Z0;YL=1/ZL;GL=real(YL);BL=imag(YL);
c=3e8;f0=2e9;df=1e5;f1=1e9;f2=3e9;f=[f1:df:f2];
s11=zeros(1,numel(f));s11_mod=zeros(1,numel(f));
ZinTL=Z0*(ZL+1j*Z0*tan(2*pi*D1_TL_series_singlestub ...
*f/f0))./(Z0+1j*ZL*tan(2*pi*D1_TL_series_singlestub *f/f0));
Zin_stb_sc=Z0*1j*tan(2*pi*D1stub_sc_series_singlestub*f/f0); % SC stub
Zin=ZinTL+Zin_stb_sc; s11=[s11_mod;(Zin-Z0)./(Zin+Z0)];
s11_mod=[s11_mod;abs((Zin-Z0)./(Zin+Z0))];
ZinTL=Z0*(ZL+1j*Z0*tan(2*pi*D1_TL_series_singlestub ...
*f/f0))./(Z0+1j*ZL*tan(2*pi*D1_TL_series_singlestub *f/f0));
Zin_stb_sc=Z0./(1j*tan(2*pi*D1stub_oc_series_singlestub*f/f0)); % OC stub
Zin=ZinTL+Zin_stb_sc;s11=[s11_mod;(Zin-Z0)./(Zin+Z0)];
s11_mod=[s11_mod;abs((Zin-Z0)./(Zin+Z0))];
ZinTL=Z0*(ZL+1j*Z0*tan(2*pi*D2_TL_series_singlestub ...
*f/f0))./(Z0+1j*ZL*tan(2*pi*D2_TL_series_singlestub *f/f0));
Zin_stb_sc=1j*Z0*tan(2*pi*D2stub_sc_series_singlestub*f/f0); % SC stub
Zin=ZinTL+Zin_stb_sc;s11=[s11_mod;(Zin-Z0)./(Zin+Z0)];
s11_mod=[s11_mod;abs((Zin-Z0)./(Zin+Z0))];
ZinTL=Z0*(ZL+1j*Z0*tan(2*pi*D2_TL_series_singlestub ...
*f/f0))./(Z0+1j*ZL*tan(2*pi*D2_TL_series_singlestub *f/f0));
Zin_stb_sc=Z0./(1j*tan(2*pi*D2stub_oc_series_singlestub*f/f0)); % OC stub
Zin=ZinTL+Zin_stb_sc; s11=[s11_mod;(Zin-Z0)./(Zin+Z0)];
s11_mod=[s11_mod;abs((Zin-Z0)./(Zin+Z0))];
s11_mod(1,:)=[];s11(1,:)=[];
for k=1:1:size(s11_mod,1)
figure(1);plot(f,s11_mod(k,:));hold all;
end
grid on
title('short/open series single stub |s11|')
legend('DTL1 D1 sc','DTL2 D1 oc','DTL1 D2 sc','DTL2 D2 oc','Location','northwest')
for k=1:1:size(s11_mod,1)
figure(2);plot(f,10*log10(s11_mod(k,:)));axis([1e9 3e9 -35 0]);hold all;
end
grid on;grid minor
title('short/open series single stub 10log(|s11|)')
legend('DTL1 D1 sc','DTL2 D1 oc','DTL1 D2 sc','DTL2 D2 oc','Location','northwest')
for k=1:1:size(s11_mod,1)
figure(3);plot(f,20*log10(s11_mod(k,:)));axis([1.7e9 2.3e9 -20 -10]);hold all;
end
grid on;grid minor
title('20dB Return Loss BW for short/open series single stub')
legend('DTL1 D1 sc','DTL2 D1 oc','DTL1 D2 sc','DTL2 D2 oc','Location','northwest')
measuring Return Loss below -20dB bandwidth,
plotting points of a single |s11|dB trace below -20dB:
a=10*log10(s11_mod(1,:));a_below20=a(a<-20)
[nx,f_below20]=find(a<-20);f_bw=f(f_below20)
figure(2);plot(f_bw,a_below20,'bo')
BW_band_RL20dB_singleseriestub=[min(f_bw) max(f_bw)]
% measuring 1 bandwidth
BW_band_RL20dB_singleseriestub=[0 0];
BW_RL20dB_singleseriestub(1)=0;
% measuring BW of all calculated single series stub matches
for k=1:1:size(s11_mod,1)
a=10*log10(s11_mod(k,:)); a_below20=a(a<-20);
[nx,f_below20]=find(a<-20); f_bw=f(f_below20);
% figure(2);plot(f_bw,a_below20,'bo')
BW_band_RL20dB_singleseriestub=...
[BW_band_RL20dB_singleseriestub;
min(f_bw) max(f_bw)];
BW_RL20dB_singleseriesstub=...
[BW_RL20dB_singleseriesstub;
abs(min(f_bw)-max(f_bw))];
end
BW_band_RL20dB_singleseriestub=[];
BW_RL20dB_singleseriestub(1)=[];
BW_band_RL20dB_doubleshuntstub
BW_RL20dB_doubleshuntstub
% storing
save('pozar_05_12_vars.mat',...
'BW_band_RL20dB_doubleshuntstub',…
'BW_RL20dB_doubleshuntstub')
BW_band_RL20dB_singleseriestub =
1.0e+09 *
1.988900000000000
2.011100000000000
BW_RL20dB_singleseriestub =
22200000
BW_band_RL20dB_singleseriestub =
1.0e+09 *
1.988900000000000 2.011100000000000
1.991200000000000 2.008900000000000
1.993300000000000 2.006500000000000
1.989100000000000 2.010700000000000
BW_RL20dB_singleseriestub =
17700000
13200000
21600000
22200000
17700000
13200000
21600000
12.9.3.- double shunt short circuit stubs (added shunt open double stub calculations)
c=3e8;f0=2e9;df=1e5;f1=1e9;f2=3e9;f=[f1:df:f2];
s11=zeros(1,numel(f));s11_mod=zeros(1,numel(f));
Zin_stb1_sc=Z0*1j*tan(2*pi*(D11stub_sc_shunt_doublestub)*f/f0); % sc
Y1=YL+1./Zin_stb1_sc;
ZinTL=Z0*(1./Y1+1j*Z0.*tan(2*pi*D_TL_shunt_doublestub*f/f0)) ...
./(Z0+1j*1./Y1.*tan(2*pi*D_TL_shunt_doublestub*f/f0));
Z_stb2_sc=Z0*1j*tan(2*pi*(D21stub_sc_shunt_doublestub)*f/f0); % sc
Zin=1./(1./ZinTL+1./Z_stb2_sc);
s11=[s11_mod;(Zin-Z0)./(Zin+Z0)];
s11_mod=[s11_mod;abs((Zin-Z0)./(Zin+Z0))];
Zin_stb1_sc=Z0*1j*tan(2*pi*(D12stub_sc_shunt_doublestub)*f/f0); % sc
Y1=YL+1./Zin_stb1_sc;
ZinTL=Z0*(1./Y1+1j*Z0.*tan(2*pi*D_TL_shunt_doublestub*f/f0)) ...
./(Z0+1j*1./Y1.*tan(2*pi*D_TL_shunt_doublestub*f/f0));
Z_stb2_sc=Z0*1j*tan(2*pi*(D22stub_sc_shunt_doublestub)*f/f0); % sc
Zin=1./(1./ZinTL+1./Z_stb2_sc);
s11=[s11_mod;(Zin-Z0)./(Zin+Z0)];
s11_mod=[s11_mod;abs((Zin-Z0)./(Zin+Z0))];
Zin_stb1_oc=Z0./(1j*tan(2*pi*(D11stub_oc_shunt_doublestub)*f/f0)); % oc
Y1=YL+1./Zin_stb1_oc;
ZinTL=Z0*(1./Y1+1j*Z0.*tan(2*pi*D_TL_shunt_doublestub*f/f0)) ...
./(Z0+1j*1./Y1.*tan(2*pi*D_TL_shunt_doublestub*f/f0));
Z_stb2_oc=Z0./(1j*tan(2*pi*(D21stub_oc_shunt_doublestub)*f/f0)); % oc
Zin=1./(1./ZinTL+1./Z_stb2_oc);
s11=[s11_mod;(Zin-Z0)./(Zin+Z0)];
s11_mod=[s11_mod;abs((Zin-Z0)./(Zin+Z0))];
Zin_stb1_oc=Z0./(1j*tan(2*pi*(D12stub_oc_shunt_doublestub)*f/f0)); % oc
Y1=YL+1./Zin_stb1_oc;
ZinTL=Z0*(1./Y1+1j*Z0.*tan(2*pi*D_TL_shunt_doublestub*f/f0)) ...
./(Z0+1j*1./Y1.*tan(2*pi*D_TL_shunt_doublestub*f/f0));
Z_stb2_oc=Z0./(1j*tan(2*pi*(D22stub_oc_shunt_doublestub)*f/f0)); % oc
Zin=1./(1./ZinTL+1./Z_stb2_oc);
s11=[s11_mod;(Zin-Z0)./(Zin+Z0)];
s11_mod=[s11_mod;abs((Zin-Z0)./(Zin+Z0))];
s11_mod(1,:)=[];s11(1,:)=[];
for k=1:1:size(s11_mod,1)
figure(1);plot(f,s11_mod(k,:));hold all;
end
grid on
title('short/open shunt double stub |s11|')
legend('D11sc D21sc','D12sc D22sc','D11oc D21oc', …
'D12oc D22oc','Location','northwest')
for k=1:1:size(s11_mod,1)
figure(2);plot(f,10*log10(s11_mod(k,:)));axis([1e9 3e9 -35 0]);hold all;
end
grid on;grid minor
title('short/open shunt double stub 10 log|s11|')
legend('D11sc D21sc','D12sc D22sc','D11oc D21oc', …
'D12oc D22oc','Location','northwest')
for k=1:1:size(s11_mod,1)
figure(3);plot(f,20*log10(s11_mod(k,:)));axis([1.7e9 2.3e9 -20 -10]);hold all;
end
grid on;grid minor
title('20dB Return Loss BW for short/open shunt double stub')
legend('D11sc D21sc','D12sc D22sc','D11oc D21oc', ...
D12oc D22oc','Location','northwest')
2 stubs improves BW, smaller amount of trace points below -20dB compared to traces from single stubs matching.
% plotting trace points below -20dB
a=10*log10(s11_mod(1,:))
a_below20=a(a<-20)
[nx,f_below20]=find(a<-20)
f_bw=f(f_below20)
figure(2);plot(f_bw,a_below20,'bo')
BW_band_RL20dB_doubleshuntstub=[0 0];
BW_RL20dB_doubleshuntstub=0;
% measuring all bandwidths
for k=1:1:size(s11_mod,1)
a=10*log10(s11_mod(k,:));
a_below20=a(a<-20);
[nx,f_below20]=find(a<-20);
f_bw=f(f_below20);
% figure(2);plot(f_bw,a_below20,'bo')
BW_band_RL20dB_doubleshuntstub=...
[BW_band_RL20dB_doubleshuntstub;min(f_bw) max(f_bw)];
BW_RL20dB_doubleshuntstub=...
[BW_RL20dB_doubleshuntstub;abs(min(f_bw)-max(f_bw))];
end
BW_band_RL20dB_doubleshuntstub(1,:)=[];
BW_RL20dB_doubleshuntstub(1)=[];
BW_band_RL20dB_doubleshuntstub
BW_RL20dB_doubleshuntstub0
% storing
save('pozar_05_12_vars.mat',...
'BW_band_RL20dB_doubleshuntstub','BW_RL20dB_doubleshuntstub')
BW_band_RL20dB_doubleshuntstub =
1.0e+09 *
0 0
1.999200000000000 2.000800000000000
1.992800000000000 2.007200000000000
1.998400000000000 2.001600000000000
1.991500000000000 2.008700000000000
BW_RL20dB_doubleshuntstub =
0
1600000
14400000
3200000
17200000
12.4.- double series short circuit stubs. Added series open double stub calculations.
since there is only one stub length for each stub this simplifies calculations and graphs.
load pozar_05_12_vars.mat
ZL=200;Z0=100;Y0=1/Z0;YL=1/ZL;GL=real(YL);BL=imag(YL);XL=imag(ZL);GL=real(YL);BL=imag(YL);
c=3e8;f0=2e9;df=1e5;f1=1e9;f2=3e9;f=[f1:df:f2];
s11=zeros(1,numel(f));s11_mod=zeros(1,numel(f));
Zin_stb1_sc=Z0*1j*tan(2*pi*(D11stub_sc_series_doublestub)*f/f0); % short circuit stub
Z1=ZL+Zin_stb1_sc;
ZinTL=Z0*(Z1+1j*Z0.*tan(2*pi*D_TL_series_doublestub*f/f0))...
./(Z0+1j*Z1.*tan(2*pi*D_TL_series_doublestub*f/f0));
Z_stb2_sc=Z0*1j*tan(2*pi*(D22stub_sc_series_doublestub)*f/f0); % sc
Zin=ZinTL+Z_stb2_sc;s11=[s11_mod;(Zin-Z0)./(Zin+Z0)];
s11_mod=[s11_mod;abs((Zin-Z0)./(Zin+Z0))];
s11_mod(1,:)=[];s11(1,:)=[];
for k=1:1:size(s11_mod,1)
figure(1);plot(f,s11_mod(k,:));hold all;
end
grid on
title('short/open series double stub |s11|')
legend('D11sc D21sc','D12sc D22sc','D11oc D21oc','D12oc D22oc','Location','northwest')
for k=1:1:size(s11_mod,1)
figure(2);plot(f,10*log10(s11_mod(k,:)));axis([1e9 3e9 -35 0]);hold all;
end
grid on;grid minor
title('short/open series double stub 10 log|s11|')
legend('D11sc D21sc','D12sc D22sc','D11oc D21oc','D12oc D22oc','Location','northwest')
for k=1:1:size(s11_mod,1)
figure(3);plot(f,20*log10(s11_mod(k,:)));axis([1.7e9 2.3e9 -20 -10]);hold all;
end
grid on;grid minor
title('20dB Return Loss BW for short/open series double stub')
legend('D11sc D21sc','D12sc D22sc','D11oc D21oc','D12oc D22oc','Location','northwest')
% plotting trace points below -20dB
a=10*log10(s11_mod(1,:))
a_below20=a(a<-20)
[nx,f_below20]=find(a<-20)
f_bw=f(f_below20)
figure(2);plot(f_bw,a_below20,'bo')
BW_band_RL20dB_doubleseriestub=[0 0];BW_RL20dB_doubleseriestub=0;
% measuring all bandwidths and storing
for k=1:1:size(s11_mod,1)
a=10*log10(s11_mod(k,:));
a_below20=a(a<-20);
[nx,f_below20]=find(a<-20);
f_bw=f(f_below20);
% figure(2);plot(f_bw,a_below20,'bo')
BW_band_RL20dB_doubleseriestub=...
[BW_band_RL20dB_doubleseriestub;min(f_bw) max(f_bw)];
BW_RL20dB_doubleseriestub=[BW_RL20dB_doubleseriestub;abs(min(f_bw)-max(f_bw))];
end
BW_band_RL20dB_doubleseriestub(1,:)=[];BW_RL20dB_doubleseriestub(1)=[];
BW_band_RL20dB_doubleseriestub
BW_RL20dB_doubleseriestub
save('pozar_05_12_vars.mat','BW_band_RL20dB_doubleseriestub','BW_RL20dB_doubleseriestub')
