Modeling Input Impedance of MESFET Using Series RLC Circuit

[roeb]

Hi,

I'm trying to model the input impedance of a MESFET by using a series RLC circuit.

For example I have the following reflection coefficients:
.575 angle(-138) at 6 GHz
.617 angle(170) at 8 GHz
.610 angle(128) at 10 GHz

As you can see, as the frequency changes so too does the angle. Does anyone have any suggestions for how I can analytically or graphically determine a fairly close approximation using a series RLC?

Right now I'm trying to plot the 3 frequencies and the reflection coefficients on a Smith Chart and come up some values but the best I've been able to do so far is
.61 angle(-150)
.59 angle(178)
.61 angle(164)

using L = .442 nH, C = .917 pF and R = 12.85 ohms.

I'd like to get some more accuracy but it seems my method is not working too well.

Thanks,
roeb

 

[uWave_Matt]

Graphically, your reflection coefficients on the smith chart should give S11 which should be your normalized input impedance. Just multiply by 50 (or whatever your characteristic impedance is) to get actual input impedance.

 

[roeb]

Hi, thanks for your reply.

I understand how to match a single frequency, but I'm having trouble getting a 'good' match for the range of frequencies. What I want is a single RLC network that can approximate the reflection coefficients over 6-10 GHz.

http://img29.imageshack.us/img29/7175/temppic.png

I'm manually tuning the LC values (pretty much keeping R constant) but it's rather tedious and I can't get all that close. I realize that I'll never get a perfect match, but it seems that I should be able to iteratively solve this so that I can get a bit better.

 

[uWave_Matt]

Hi, thanks for your reply.

I understand how to match a single frequency, but I'm having trouble getting a 'good' match for the range of frequencies. What I want is a single RLC network that can approximate the reflection coefficients over 6-10 GHz.

I'm manually tuning the LC values (pretty much keeping R constant) but it's rather tedious and I can't get all that close. I realize that I'll never get a perfect match, but it seems that I should be able to iteratively solve this so that I can get a bit better.

Actually, if you want to use just one tuned section and widen your BW, the only thing I can think of is over-damping it to lower the Q factor. You'll choose resonance to be maybe around 8GHz, then vary your resistor to increase or decrease BW. Higher resistance is higher damping, lower Q, and higher BW.