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Design >> RF Design >> why input is matched when complex conjugate match?
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Message started by dog1 on Oct 20^th, 2014, 6:58am

Title: why input is matched when complex conjugate match?
Post by dog1 on Oct 20^th, 2014, 6:58am

I have a confusion about input matching. I know that S11=0 when input is complex matched. On the other hand, the equation for S11 is S11=(Zin-Z0)/(Zin+Z0), it is 0 when Z0=Zin, not its complex conjugate. Why is that?

Thanks!

Title: Re: why input is matched when complex conjugate match?
Post by totowo on Nov 13^th, 2014, 11:17pm

" S11=0 when input is complex matched" . It's wrong.
You should distinguish between "complex match" and "transmission line match". They are NOT identical.

I'd like to show you an example:
Zs=25 Ohm, Zload=100 ohm, connected with a lamda/4 length lossless transmission line (Z0=50);
Obviously, Gamma_s or Gamma_L is not equal to 0;
but they are conjugate matching in any position of the transmission line.

dog1 wrote on Oct 20^th, 2014, 6:58am:

Title: Re: why input is matched when complex conjugate match?
Post by dog1 on Nov 14^th, 2014, 9:52am

Thanks for your answer. I was thinking the same way. It is just that Cadence report S11=0 (<-300 dB) when the input is complex conjugate matched (I chose a complex Zs for a port and added a complex load impedance), and I cannot get through this.

Title: Re: why input is matched when complex conjugate match?
Post by aaron_do on Nov 15^th, 2014, 12:53am

Complex conjugate is for maximum power transfer. Impedance match is for minimum reflection.

Aaron

Title: Re: why input is matched when complex conjugate match?
Post by dog1 on Nov 15^th, 2014, 3:58am

@totowo I think I didn't make myself clear. I mean I also think they are not the same thing. But in your example, I think that the cadence would be giving S11=0 and that is understandable. because in your case, if a input port (Rs=25) is connected to a 1/4 transmission line (Zo=50) loaded with Rl=100, then the reference impedance the simuator assumes is 25. and the input impedance it sees at the input port is 25, so S11=0. What I am confused is that when the source impedance is complex, why is the simulator giving S11=0 when it is complex conjugate matched instead of just Zs(==Z0)=Zin?

@aaron I agree with you. But why is cadence giving S11=0 when it is complex conjugate matched instead of just Zs(==Z0)=Zin? Does that have something to do with how cadence defines the reference impedance? (I never get clear how the "port" is defined when its impedance is complex in cadence)

Thanks!

Regards,

Chen

Title: Re: why input is matched when complex conjugate match?
Post by totowo on Nov 16^th, 2014, 5:27pm

1. Don't use complex impedance in PORT of cadence...In my experience it seems to move the imag part into the load and only take the real part as source impedance (Zs);

2. In cadence port, an implicit condition is the reference impedance (Z0) is identical to source impedance (Zs). Thus in cadence simulation, Gamma_s or Gamma_L is always equal to 0.

In one word, don't use cadence to validate the MW fundamental theory, because it will make you more confused :)

dog1 wrote on Nov 15^th, 2014, 3:58am:

Title: Re: why input is matched when complex conjugate match?
Post by dog1 on Nov 19^th, 2014, 9:18am

Thanks! I agree that probably it is probably the "port" that is messing things up.

Chen