VSWR_in and VSWR_out for 3-stage LNA

[JoJo]

I would like to know how to calculate this manually for the entire 3 stages without ADS simulation. I have the equations from Gonzalez p. 194-196:

Gamma_IN = S11 + ((S12*S21*Gamma_L)/(1 - (S22*Gamma_L)));
Gamma_OUT = S22 + ((S12*S21*Gamma_S)/(1 - (S11*Gamma_S)));
Gamma_a = (Za - Z0) / (Za + Z0);
Gamma_b = (Zb - Z0) / (Zb + Z0);
VSWR_IN = (1 + abs(Gamma_a)) / (1 - abs(Gamma_a));
VSWR_OUT = (1 + abs(Gamma_b)) / (1 - abs(Gamma_b));

Assume Z0 = 50 ohms.

From what I was told, you solve Gamma_IN for the 3rd stage first. Then that becomes the load for stage 2. Then Gamma_IN for the 2nd stage becomes the load for the first stage. The opposite is true for Gamma_OUT. What I'm not sure is...is Gamma_L for the 3rd stage 50 ohms or is it Gamma_L for the 3rd stage amplifier which would then be a complex number? Or am I completely off? I tried this in Matlab and my numbers are completely off or rather, much greater than 1. Thanks if anyone can help.

 

[BigBoss]

Gamma_L : Load Reflection Coefficient.If RL=50 Ohm, Gamma_L=0
If RL is Different than 50, Gamma_L may be complex or real.

 

[JoJo]

Cool, I got that part. But when I solve Gamma_IN, does that become the load for stage 2 and so on?

 

[BigBoss]

Cool, I got that part. But when I solve Gamma_IN, does that become the load for stage 2 and so on?

Yes, Gamma_IN will be load of previous stage.

 

[JoJo]

Is my logic for Gamma_a and b also correct? Gamma_a3 for 3rd stage = 0 because Za = Z0 = 50. Then Za for Gamma_a2 = Gamma_IN (of 3rd stage). Basically, my Matlab code looks like this:

GammaIN3 = S11 + ((S12*S21*0)/(1 - (S22*0)));
GammaIN2 = S11 + ((S12*S21*GammaIN3)/(1 - (S22*GammaIN3)));
GammaIN1 = S11 + ((S12*S21*GammaIN2)/(1 - (S22*GammaIN2)));


GammaOUT1 = S22 + ((S12*S21*0)/(1 - (S11*0)));
GammaOUT2 = S22 + ((S12*S21*GammaOUT1)/(1 - (S11*GammaOUT1)));
GammaOUT3 = S22 + ((S12*S21*GammaOUT2)/(1 - (S11*GammaOUT2)));


GammaA3 = 0;
GammaA2 = (GammaIN3 - 1) / (GammaIN3 + 1);
GammaA1 = (GammaIN2 - 1) / (GammaIN2 + 1);

GammaB1 = 0;
GammaB2 = (GammaOUT1 - 1) / (GammaOUT1 + 1);
GammaB3 = (GammaOUT2 - 1) / (GammaOUT2 + 1);

VSWR_IN3 = (1 + abs(GammaA3)) / (1 - abs(GammaA3));
VSWR_IN2 = (1 + abs(GammaA2)) / (1 - abs(GammaA2));
VSWR_IN1 = (1 + abs(GammaA1)) / (1 - abs(GammaA1));

VSWR_OUT1 = (1 + abs(GammaB1)) / (1 - abs(GammaB1));
VSWR_OUT2 = (1 + abs(GammaB2)) / (1 - abs(GammaB2));
VSWR_OUT3 = (1 + abs(GammaB3)) / (1 - abs(GammaB3));

Thanks again for your help, really appreciate it.