input return loss for conjugately matched amplifier

Hi all,

I am going through an example for conjugately matching an amplifier in Pozar's microwave engineering book. I can do that all well and fine, however I am having trouble calculating the return loss for the input. I've attached pictures of the example and the finished circuit and stubs length etc.

I know return-loss = -20log(p), where p = abs(gamma). But which gamma is it? I have tried combining gammaS plus the other parts of the input match into an equivalent circuit by using circuit theory then calculating the new gamma with the equivalent circuit impedance, but my answer doesn't match the results in the book or in ADS.

From ADS, at 4 GHz, the simultaneous-match Gamma is 0.017/31.6. So from playing around with ADS, it looks to me that I need to work out smGamma. So any help with this would be much appreciated.

Thanks,

Hakim

Here GammaIn is a function of S11 AND other stuffs, so GammaIn of the circuit without matching circuit.So that, GammaIn can be found by s-parameters of the active device only.Therefore GammaIn of the whole circuit is totally different than that.

I have realised that I need to calculate the S-Parameters of the circuit. But not too sure how to do it. Found stuff on shifting reference planes and adding the admittances of open circuits but still not getting the right input return loss when worked out the new S11.

Okay, I have gone back to my high frequency lecture notes. I have attached the document. So on step 7 for the example that contiues from page 2, it shifts the reference planes using the method shown converts to Y params then adds on the open circuit stubs reactances, then converts back to S matrix where S11 and S22 can be used to calculate the return loss. Now in the second document I have attached shows my working out in mathcad, but it doesn't match the values in the lecture notes.

Can anyone help explain this procedure or provide an alternative?

ELE4021+ELE8058_AGS-10.pdflecture-10-returnloss.pdf

Sorry I uploaded my matlab commands. Here are my mathcad (more readable):

lecture-10-page2-example-returnloss.pdf

Realised I can just take make ABCD parameters of the stubs and TL's, then convert the S parameters of the transistor to ABCD as well, then multiply it all. After multiplying convert back to S-params, then the input return loss is -20log(|S11|).