# How to solve Microwave Engineering Pozar chapter 5 example 1 with ADS

#### John_2016

Joined Nov 23, 2016
55

#### John_2016

Joined Nov 23, 2016
55
Since near short circuit impedances are prone to increase noise on signals and may damage power supplies, POZAR suggests the criterion displayed on the right, how to decide whether first next-to-load circuit element has to be shunt or series, when matching single frequency with 2 elements L-shape networks: The decision whether series-shunt or shunt-series topology to be used is made considering the need to avoid SC, OC, or unnecessarily long impedance trajectories along the Smith chart.

· If load inside 1+jx, then (in order to reduce impedance) start with shunt.

· If load outside 1+jx, (to increase impedance) with series.

The following script puts ZL on Smith Chart, tells whether ZL is inside or outside 1+jx, and calculates match X and B:

clc;clear all;
ZL=200-1j*100;Z0=100;f0=5e8; % Hz

Ceq=1/(2*pi*f0*mag(ZL)); % 3.183pF at 500MHz for ADS LEMtch assistant
sm1=smithchart;hold all;
gamma_L=(ZL-Z0)/(ZL+Z0);

% show ZL on Smith chart adding text showing values
if imag(ZL)<0 sign1='-';
else sign1='+';
end
hold all;plot(real(gamma_L),imag(gamma_L),'ro','LineWidth',1.5); str1=['ZL =' num2str(real(ZL)) sign1 'j' num2str(abs(imag(ZL))) ' \rightarrow'];
text(real(gamma_L),imag(gamma_L)+.01,str1,'Color','blue', 'FontSize',20,'HorizontalAlignment','right','VerticalAlignment','middle');
RL=real(ZL);XL=imag(ZL);
if abs(real(ZL/Z0))>=1 % ZL inside 1+jx
disp(' ZL inside 1+jx');
B1=1/(RL^2+XL^2)*(XL+(RL/Z0)^.5*(RL^2+XL^2-Z0*RL)^.5)
B2=1/(RL^2+XL^2)*(XL-(RL/Z0)^.5*(RL^2+XL^2-Z0*RL)^.5)
X1=1/B1+XL*Z0/RL-Z0/(B1*RL) ; X2=1/B2+XL*Z0/RL-Z0/(B2*RL)
elseif abs(real(ZL/Z0))<=1 % ZL outside 1+jx
disp(' ZL outside 1+jx');X1=(RL*(Z0-RL))^.5-XL; X2=-(RL*(Z0-RL))^.5-XL
B1=1/Z0*((Z0-RL)/RL)^.5; B2=-1/Z0*((Z0-RL)/RL)^.5
end

[C1 ctype]=B2LC(B1,f0) % 1st solution
[L1 ltype]=X2LC(X1,f0)
[L2 ctype]=B2LC(B2,f0) % 2nd solution
[C2 ltype]=X2LC(X2,f0)

Results

ZL inside 1+jx
B1 =

0.002898979485566

B2 =
-0.006898979485566

X1 =
1.224744871391589e+02

X2 =
-1.224744871391589e+02

C1 = 9.227738300997709e-13
L1 = 3.898484006168380e-08
ltype =L [Henry]

C2 = 2.167378326912196e+07
ctype =L [Henry]

C2 = 3.847649490485592e+11

To simplify reactance translation into capacitance or inductance the following functions B2LC.m and X2LC.m can be used: function [LC char1]=B2LC(B_,f1)
% B2LC translates shunt reactance to capacitive or inductive
% impedance depending upon the sign of the input reactance

if B_>=0
end
if B_<0
LC=1/(abs(B_)*(2*pi*f1)); char1='L [Henry]';
end;end

function [LC char1]=X2LC(X_,f1)
% B2LC translates shunt reactance to capacitive or inductive
% impedance depending upon the sign of the input reactance

if X_>=0
LC=X_/(2*pi*f1); char1='L [Henry]';
end
if X_<0
end;end   SPICE and MATLAB: Simscape Electronics (previously SimElectronics https://uk.mathworks.com/help/physmod/elec/ ) is one of MATLAB's beach head toolbox in Industry electronic circuits simulation areas where specialist simulators have and still are in control of the simulation market. Efforts have been made to interface MATLAB to Spice, among many:

· 'Orcad PSICE with circuit Analysis' by F.Monssen PearsonAmazon (https://www.amazon.ca/Spice-Circuit-Analysis-Monssen/dp/0675222850) compares same basic circuits with Spice and MATLAB.

· Non-convergence circuit simulation problems are briefly mentioned in book 'Inside SPICE' by R.Kielkowski.

· 'Introduction to Linear Circuit Analysis DC to RF MATLAB and SPICE examples' by L.Moura I.Darwazeh has a script to build custom grid Smith charts (https://www.elsevier.com/books/intr...nalysis-and-modelling/moura/978-0-7506-5932-1).

· Sommerhage's PSPICE 6.0 ¬® MATLAB interface (https://uk.mathworks.com/matlabcentral/fileexchange/25028-matlab-<->-pspice-interface). But the popular SPICE engine methodology is being gradually assimilated into this toolbox, see Simscape Electronics (https://uk.mathworks.com/help/pdf_doc/physmod/elec/elec_ref.pdf).

[POZAR] criterion for choosing L-shape match networks seems clear (pg 229), yet in [MEDLEY] (https://www.amazon.com/Microwave-RF-Circuits-Synthesis-Propagation/dp/0890065462) slightly different criteria is suggested:

One can see that for instance case b) the load (the resistors in each of these 6 cases is the load ZL) can have any complex value, may be inside 1+jx and the 1st matching component is a shunt inductance. Or case d) where 1st matching component is a shunt capacitance.

The literature reference that covers all possibilities, to calculate 2 elements L-shape matching networks, is the analytical solution of [BENHAGI], whatever the topology, either starting with shunt or series next to the load, there are always possible reactance values that approach Zin to match:

Following, 2 matching solutions with active components: Active components are the missing cornerstone in many circuit design engineering modules, yet are the preferred choice in miniaturised systems like the majority of modern hand held mobile communications chip based systems.

Some ways to build negative resistance, with non-foster circuits (NFC) [RC0], Negative Impedance Converters (NIC) [Linvill53] and Frequency Dependant Negative Resistors (FDNR) do not show up or even are referred to in [POZAR].    