impedance match question from 'RF circuit design 2nd edn'

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1

Hi, I am reading RF circuit design and have run into an annoying road block. Example 4-7 on page 90 explains how to use a Smith Chart to calculate the component values of an L network for an impedance match between a 25-j15 ohms source and a 100-j25 ohms load.

I double checked the results from the Smith Chart against my own calculations and they are quite different. Can someone help me understand where I've gone wrong?

Q= Sqaure root of (Rp/Rs-1) = Sqrt((100/25)-1) = Sqrt(3) = 1.732

Xp = Rp/Q = 100/1.732 = 57.737 Ohms capacitive reactance

Xs = RsQ = 251.732 = 43.301 Ohms inductive reactance

I add an extra 40 Ohms to Xs to series resonate with the -j15 and -j25 capacitive reactances of the source and load.

Xs = 57.737 + 40 = 97.737 Ohms

However the results from the Smith Chart example are Xs (inductor) = 60 Ohms, Xp (cap) = 68.5 Ohms.

Whats going on?

2

I'm assuming you mean this book?

I'm not sure if this is the best forum to ask these kind of questions... You could try All About Circuits, they haven an RF subforum, IIRC.

Pieter

3

PieterP:
I'm assuming you mean this book?

Yes, that's the 1st edn. Example 4-7 on page 93.

Thanks for the heads up about "All about circuits" forum, looks like they have heaps of good stuff.

4

I see what I did wrong. I should have converted the loads series capacitance into its equivalent parallel capacitance and then absorbed it into the shunt capacitor. Which only serves as an example of how much easier it is to use a Smith Chart. Now, how to mark the post as solved?

5

boggydew:
Hi, I am reading RF circuit design and have run into an annoying road block. Example 4-7 on page 90 explains how to use a Smith Chart to calculate the component values of an L network for an impedance match between a 25-j15 ohms source and a 100-j25 ohms load.

While there should be no problem with at least somebody being able to help you regarding Smith Charts and impedance matching, you need to be very specific about your matching network. Just having 'L network' is vague. So nobody would probably be able to help unless you draw a diagram that clearly defines this 'L network'. Assume people don't have this book you mentioned....or the time to review that section.