# How to solve Microwave Engineering Pozar chapter 05 exercise 17 with MATLAB

Question:  Literature source [POZAR] available here:
https://www.amazon.co.uk/Microwave-Engineering-David-M-Pozar/dp/0470631554

There's also a solutions manual available here:
https://www.scribd.com/doc/176505749/Microwave-engineering-pozar-4th-Ed-solutions-manual MATLAB script source pozar_05_exercise_17.m and all necessary support functions included in .zip here attached file pozar_05_exercise_17.zip

This question is again the kind that one thinks the Symbolic Toolbox is going to be the perfect tool but again
the Symbolic Toolbox returns 9 DIN4 pages full of a Symbolic expression that cannot be called a solution. let alone
handled without a crane.

Luckily it can be solved numerically, as shown in the attached script and notes.

Firstly it's convenient to find out Z1 and Z2 to validate the sought expressions
• Z1(ZL,Z0)
• Z2(ZL,Z0)
z1=Z1/Z0;z2=Z2/Z0

z1 z2 turn out to be 1.1067 and 1.3554

the frequency response of |Γ| is As shown in the attached script, the ABCD expressions can be manipulated to obtain the following that in turn reveals (Z2/Z1) Z2_ov_Z1 = 1.224563802132642

From here all that's left is to calculate the characteristic impedance of the λ/4 section next to load Z2, from [POZAR] 253pg.

gamma_n(2)==(ZL_ov_Z0-z2)/(ZL_ov_Z0+z2)

John BG
jgb2012@sky.com

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