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Analytic and ADS solutions Smith chart is handy, but only for a single frequency or narrow band. Analytic approach provides solutions in a given bandwidth. Solving quadratic algebraic equation (next page). May convert into a simple program, e.g., Matlab Based on Smith/analytic solution, ADS may finalize the design, layout and implementation EEE 591/445 Lecture 18 1

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Shunt Double-Stub Matching: Design Equations ( 29 d t β tan = ( 29 ( 29 2 2 0 1 2 0 2 2 0 2 1 0 0 sin L L L L Y B t B t t G G Y t t Y G d - - + - + = ( 29 ( 29 t G Y G t G Y G t Y B t t G Y G t Y B B L L L L L L L 0 2 2 0 2 0 2 2 2 0 2 0 1 1 1 + - + ± = - + ± + - = EEE 591/445 2 Lecture 18 Basic equations (5.19) (5.22) (5.23) (5.21)
Shunt Double-Stub Matching: Design Equations - = = S s S o B Y l Y B l 0 0 tan a 2 1 : n realizatio stub circuit - Short tan a 2 1 : n realizatio stub circuit - Open π λ If either length is negative simply add λ /2 to give a physically realizable length. 2 1 or B B B S = EEE 591/445 3 Lecture 18 (5.24a) (5.24b)

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function [d,ls] = stub1_shsc(zL) % design single-stub matching networks to match normalized load impedance % uses shunt SC stub % % inputs % zL = normalized load impedance % % outputs % d(i) = distance in wavelengths from load to stub; two solutions i=1,2. % ls(i) = length of SC stub; two solutions i=1,2. % initialize the variables d = NaN*ones(1,2); ls = NaN*ones(1,2); t = NaN*ones(1,2); rL = real(zL); xL = imag(zL); % determine values of d using (5.9) and (5.10) if rL==1, t(1) = -xL/2; else t(1) = (xL + sqrt(rL*((1-rL)^2+xL^2)))/(rL-1); t(2) = (xL - sqrt(rL*((1-rL)^2+xL^2)))/(rL-1); end d = atan(t)/(2*pi); k = find(d<=0);
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