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


Literature source [POZAR] available here:

There's also a solutions manual available here:

Answer :

MATLAB script source pozar_05_exercise_17.m and all necessary support functions included in .zip here attached file

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 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.


John BG

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