Hi:

I m designing an LNA and I find that when I change the loading impedance (of the output port) or add a parallel or serial inductance at the output, the S11 changes. But shouldn't S11 by definition be the ratio between the input and reflected wave UNDER THE CONDITION THAT THE OUTPUT PORT IS MATCHED(so that there is no reflected wave at the output), so I assume that it shouldn't change with the loading condition.

Thanks!

Yes, thanks. It is true that my S12 isn't 0. But the thing is I cannot understand Why that should have an impact on my S11 when the loading port's impedance changes. Because from definition of S11, when simulating for S11, the output should be in a matched condition (Otherwise I think it should be called the input reflection coefficient if the output is not matched). So although I might change my loading impedance in the test bench, I think the simulator should correct for it and thus it should have no effect on S11, which is intrinstic to the two-port and I think should have no relation to components external to the two-port.

Thanks for ur reply. But I still think that I was right.
the definition of S parameters is (from wiki) attached. It can be seen that S11=b1/a1 when a2=0, that is, matched load at the output. And I think that whatever I connected to port 2 shouldn't matter.

It is indeed true that the loading may have an impact on the input impedance, same for input reflection coefficient. But that is twhy they are different from the S11 and Z11, since S11 and Z11 are defined with respect to the two-port only and even if u take a two-port network and connect it with nothing, u can still define the S11 and Z11.

Hi dog1,


I think your misunderstanding is that you are assuming the port impedance is 50 ohm, and that when you change the load, the s-parameters is still calculated based on a 50-ohm load.

In fact every port can have its own port impedance, and S-parameters is defined that way. When you see S11 changing, you are actually seeing the S-parameters for a different set of port impedances. For better insight, read the paper, "Power Waves and the Scattering Matrix" from IEEExplore.


regards,
Aaron

Hi dog1,


you're not quite right there. S11 is not based on just one port. It is based on both ports. So adjusting the port impedance of one port will affect S11, S21, S12, and S22.

For instance,

S11 = b1/a1 | b2 = 0

the condition b2 = 0 means no reverse power from port 2, but it is based on the impedance that you defined for port 2, not port 1.


regards,
Aaron

Hi

 Thanks for the reply and sorry for the late response. However, I am still not convinced.
 Aaron, S11 = b1/a1 | b2 = 0, b1, a1 is referred to port 1, and to keep b2=0, I think it doesn't matter what is used as port 2, you have to ensure that the output is matched to the load. Yet you cannot change the two-port circuit itself, which means that the output load have to be changed (automatically) in order to match the output impedance of the circuit. So changing the loading port shouldn't matter.
 tm123, I think you are half right. however, I think that if the LNA can be described as a linear two port system, which I think is typically the case(actually I am just playing with an common source, and Using sp analysis in spectre, so I think linearity shouldn't be a problem), then the S parameter matrix should be enough to describe the behavior of the circuit. That is,  S11= b1/a1 |a2=0 should stand as long as the LNA can be described as a linear two port system, even if in the test bench a2 isn't 0. put it another way, although in the test bench a2 isn't zero because I do not have output impedance match, when calculating S11, I can assume that the circuit is loaded by a matched load and use S11= b1/a1 and it should gives me the same result.

True that! I think your understanding is right and that I was wrong to say that the output is matched. Thanks for both of your answers!!!

Cheer!