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Design >> RF Design >> why is S11 changes when the loading changes?
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Message started by dog1 on Nov 20^th, 2013, 4:36am

Title: why is S11 changes when the loading changes?
Post by dog1 on Nov 20^th, 2013, 4:36am

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!

Title: Re: why is S11 changes when the loading changes?
Post by tm123 on Nov 20^th, 2013, 6:33am

You must have feedback from output to input. Depending on the type of transistor you are using the effects of C_mu (capacitance from collector to base of an NPN) or Cdg (capacitance from drain to gate of an MOS) can easily change your S11. This is a common problem in high frequency circuit design.

Title: Re: why is S11 changes when the loading changes?
Post by dog1 on Nov 20^th, 2013, 7:28am

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.

Title: Re: why is S11 changes when the loading changes?
Post by tm123 on Nov 20^th, 2013, 9:26am

I disagree with your reasoning. A non-zero S12 means that the input impedance is a function of output impedance/loading. If the input impedance is a function of the output impedance/loading then the S11 is also a function of the output impedance/loading.

To me, the definition of S11 is 'input reflection coefficient with the output terminated with a known impedance', lets say 50 ohms. The definition is not 'input reflection coefficient with output reflection coefficient set to zero'.

Title: Re: why is S11 changes when the loading changes?
Post by dog1 on Nov 21^st, 2013, 5:33am

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.

Title: Re: why is S11 changes when the loading changes?
Post by tm123 on Nov 21^st, 2013, 10:52am

Let's take a specific example to answer your original question. If you have a 2 port network that has non-zero S12, the input/output impedances of the network are 50 ohms, and you terminate both the input and output with 50 ohms. So you will have no reflection at the input or output and thus perfect S11/S22. Now change the output termination to 100 ohms. What do you expect will happen?

Title: Re: why is S11 changes when the loading changes?
Post by aaron_do on Nov 21^st, 2013, 5:44pm

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

Title: Re: why is S11 changes when the loading changes?
Post by dog1 on Nov 22^nd, 2013, 1:45am

Hi:

thanks for your answers. Aaron I see you are making a good point. But since what I changed is the port impedance at port 2, and S11 is referred to the port impedance at port 1, so at first glance I think it shouldn't really matter. TM123, what I mean is that I can change the port impedance at port 2, say, from 50ohm to 200ohm, but if the output impedance is 60ohm, then when calculating S11, the system should automatically adjust for that and assume 60ohm at port 2.

Title: Re: why is S11 changes when the loading changes?
Post by aaron_do on Nov 22^nd, 2013, 1:58am

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

Title: Re: why is S11 changes when the loading changes?
Post by tm123 on Nov 22^nd, 2013, 8:08am

I still disagree with your comment "but if the output impedance is 60ohm, then when calculating S11, the system should automatically adjust for that and assume 60ohm at port 2. " The output impedance could be viewed as arbitrary, having some real and imaginary component. To find the S11, you terminate the output with the system characteristic impedance, let's say 50 ohms, and inject a wave a port 1 and measure the reflected wave at port 1.

After re-reading the S11 definition you posted previously I think you have it backwards. It should read: If a2=0, then S11 is defined as b1/a1. However, a2=0 is not a necessary condition to find S11, it just simplifies the S11 equation. As we said previously if the impedance at port 2 is not equal to the load (not impedance matched) and you have non-zero S12 (which it sounds like you do in this case), then a2 is not 0 but your S11 simulation/measurement is still valid and it is a function of the load.

Hope this helps.

Tim

Title: Re: why is S11 changes when the loading changes?
Post by dog1 on Nov 25^th, 2013, 8:07am

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.

Title: Re: why is S11 changes when the loading changes?
Post by aaron_do on Nov 25^th, 2013, 4:12pm

Hi,

Quote:

I think it doesn't matter what is used as port 2, you have to ensure that the output is matched to the load.

Maybe this is your misunderstanding. In the first place, I think I wrote the equation out wrongly as I was just writing from memory. It should be

S11 = b1/a1 | a2 = 0

The condition a2 = 0 does not make any assumptions about whether or not the output is matched to the load. It is only matched to the load if you go out of your way to design the circuit so that it matches. This condition only says that the load should be matched to the "reference impedance". However, in this case, the reference impedance is defined by the port itself. So it is always matched. For example, if the port 2 reference impedance is 1kohm, the condition a2=0 implies that the load impedance should equal to 1kohm, not Rout.

regards,
Aaron

Title: Re: why is S11 changes when the loading changes?
Post by dog1 on Nov 26^th, 2013, 7:21am

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! :) :D