# Theoritical problem based on impedance matching and amplifier design

Discussion in 'Homework Help' started by alex1234, May 5, 2011.

1. ### alex1234 Thread Starter New Member

Jul 10, 2010
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0
This are problems from Book Microwave Engineering By David Pozar.
I am preparing for an exam based on this subject and stuck with some part of it.

Problem 8.
I calculated ouput reflection coefficent as = 0.85L71(degrees).
I am getting the length of OC Stub to be 0.204(wavelength) and series stub to be 0.203(wavelength).
But in solution its given to be
length of OC Stub to be 0.298(wavelength) and series stub to be 0.107(wavelength).
Here is the link of my solved smith chart solution
Since there multiple correct answers as it depends on the way traveled on smith chart, is my answer correct?

Secondly I have googled for many links which shows impedence matching using lumped elements, but didnt find a single one which shows the same with only impedance chart can any one help me with the designing steps of matched lumped elements using only Z-Smith chart.
In the above book,its given when the impedence lies in 1+jb circle but not when it doesnot lie outside 1+jb circle.

I donot understand how to travel on the same impedence using z-chart only.

It would be also very helpful if there are links which have java applets which can solve any sums based on rf circuits atleast theoritically.

-Thank you.

Last edited: May 5, 2011
2. ### t_n_k AAC Fanatic!

Mar 6, 2009
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Most of us won't have that book at hand. Perhaps you should post a copy of the problem.

3. ### alex1234 Thread Starter New Member

Jul 10, 2010
7
0
Ok, I should have posted it in before as well...
S11=0.65L-140
S12=0.04L60
S21=2.41L50
S22=0.7L-65
All angles are in degrees.
From my calculations Δ=0.393L165,k=1.25 Thus from rollets condition, the device is stable at the operating frequency.
load reflection coefficent as = 0.85L71(degrees).
and from my calculations
length of OC Stub to be 0.204λ and series stub to be 0.203λ.
But in solution its given to be
length of OC Stub to be 0.298λ and series stub to be 0.107λ.
Here is the link of my solved smith chart solution

Q2) 11.9 from the book.
S11=0.61L-170
S12=0
S21=2.24L32
S22=0.72L-83
Since unilateral,source reflection coefficent=S11*=0.61L170
Maximum gain Gtu=12.2dB.
Now since in exams, we are provided only with Z-smith charts, I dont know How to design the matching network by lumped elements using Z-chart only

4. ### t_n_k AAC Fanatic!

Mar 6, 2009
5,448
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Re Q1 - You happen to have found the alternative solution for the two line components. A series line of 0.196λ with an open stub of 0.202λ and Zo load gives the same load reflection coefficient as a series line of 0.107λ and open stub of 0.298λ and Zo load. Either solution is valid.

Your values are slightly different because you used a pencil and paper Smith Chart method which has some inherent uncertainty.

Last edited: May 6, 2011
5. ### t_n_k AAC Fanatic!

Mar 6, 2009
5,448
783
Calculation of L-section (lumped inductor / capacitor) matching networks is not a trivial task and probably unlikely to be tested under exam conditions. If you can demonstrate the use of transmission line matching I would think that would be more than sufficient. What does your professor say regarding this?

I've seen mention (including formulae) of L-section matching procedure in some brief study notes on S parameters by a Nick Gamroth (Google him). There's a small formula error in the notes in reference to output reflection coefficient which he transcribed directly from another source - also with same error. I haven't checked whether his notes on L-section matching are OK but they might be a point of reference for you if you want to follow up on this.

Mar 6, 2009
5,448
783