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S parameter fundamental questions, please help. (Read 9088 times)
harry_dresden
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S parameter fundamental questions, please help.
Aug 25th, 2009, 5:13pm
 
b1=S11a1+S12a2 ---(1)

In all references (that I can find), says that as long as load impedance equal to characteristic impedance, ZL=Z0, a2 will be 0, from (1), we can then find S11.

1. Say for this two port device under test, [S], has an output impedance of Zout, note that this is not the load impedance, ZL. My question is, assuming the output of [S], Zout is not match to Z0, would there be a reflection? If yes, a2 is not 0,  this means that  the S11 for [S] could not be obtain from (1).

2. Another question on similar context, but from another angle: refer to the figure attached, looking back into the transmission line with characteristic impedance of Z0 from the load, do we really see Z0? Say if the transmission line is quarter wave length, in order to have match (no reflection), we should choose the Z0= root(ZoutZL*), where Zout is the output impedance of [S]. In other words, when we look into the transmission line from the load, we see ZL* not Z0. While most reference never mention that Z0 is observed from that point, it seems to imply it that way as there is no discussion on this equation (Z0= root(ZoutZL*)), which is the condition to achieve match. Sure, we can consider in terms of lump element and the transmission to be negligible short. In this case, the matching condition, should be just ZL*=Zout not ZL=Z0.


Can anybody with a good understanding on this fundamental please help explain these clearly to me?
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« Last Edit: Aug 25th, 2009, 11:32pm by harry_dresden »  

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Frank Wiedmann
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Re: S parameter fundamental questions, please help.
Reply #1 - Aug 26th, 2009, 1:38am
 
The waves used in the definition of the S-parameter matrix are not traveling waves but pseudo-waves defined with respect to an arbitrary reference impedance (usually 50 ohms). Please see the introduction of http://www.mtt.org/measurements/GENERWGCT.PDF for additional details.
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harry_dresden
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Re: S parameter fundamental questions, please help.
Reply #2 - Aug 26th, 2009, 5:00pm
 
hi frank,

thank you for your reference.
yes, in fact a1, a2, b1 and b2 are all power waves, for example a1= Incident voltage/ root(Z0).

my question is in fact a practical one, not a theoretical one. if there is anyone who could help me with the questions, it will be awesome.

thank you in advance. to clarify the question further, I have updated the figure with Zout, which is the output impedance of the two port circuit.
In summary: If Zout is not equal to Z0(or Z0* which is the same for a real value) will there be reflection? If yes, a2 in equation (1) is not zero. S11 could not be obtained from (1). Can anyone please tell me if this is true?



harry
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Frank Wiedmann
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Re: S parameter fundamental questions, please help.
Reply #3 - Aug 27th, 2009, 12:53am
 
Did you actually read and try to understand the article? You are still mixing up traveling waves and pseudo-waves. Especially sections 1 and 3 are extremely relevant for your question. Section 5 is also very interesting because it shows that the frequently used "power waves" are not a very useful definition.

Of course there will be a reflection of the traveling waves if Z0 and Zout are different. However, this is not relevant for the usual definition of the S-parameter matrix, which is defined in terms of pseudo-waves. If Z0 is equal to the reference impedance Zref of the S-parameter matrix, then the pseudo-wave a2 is zero by definition.

I like the following equivalent explanation of the S-parameter matrix: S11 is the input reflection coefficient (Zin-Zref)/(Zin+Zref) of the two port circuit, where Zin is the input impedance when the output is terminated with Zref. S21 is 2*Vout/V0 when the output is terminated with Zref and the input is connected to a source with a source impedance of Zref and an open-circuit voltage of V0. A simulation setup that determines the S-parameters of a circuit according to this explanation is shown in http://w7zoi.net/S-param%20extraction.pdf.
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aaron_do
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Re: S parameter fundamental questions, please help.
Reply #4 - Sep 4th, 2009, 8:47am
 
Hi ,

in answer to question (1), Zout is irrelevant. If you excite port 2, then Zout will contribute to the reflection coefficient for port 2. However, If you excite port 1, the power b2 going to ZL will not be reflected, so a2 will be equal to zero.

cheers,
Aaron
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harry_dresden
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Re: S parameter fundamental questions, please help.
Reply #5 - Sep 9th, 2009, 12:11am
 
Hi Frank,

Here, I summarized what I have learned after reading the reference:
It appears that b(Zref) vanished (becomes 0) if Zref=Z0, where b(Zref) is in fact a mathematical artifact that do not exist in physical manisfestation.
So, there is (physically) reflection at the output of the [s], namely between Zout and Z0.

As for S21=2Vout/Vo, i interpret it as S21=Vout/(Vo/2), where Vo/2 is the Vin (voltage across the input of [s]) when the input is match.
So basically S21 gives the gain of [s], assuming input being match and output is equal Zref.

Of course, we can still obtain S21 if the input is not match or output not equal to Zref through S-parameter simulation. For example if the input Zin is high impedance, then S21 will be 6dB larger than voltage gain =Vout/Vin. The extra 6dB here is actually an artifact (which you wouldn't get from transient simulation for example).


Thank you very much for your kind help.

Hi aaron_do,

Could you please explain why there is no reflection at the point where Zout and the transmission line with Z0 intersect, if Zout is not equal to the conjugate of Z0? Thank you very much.

regards,
harry
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Frank Wiedmann
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Re: S parameter fundamental questions, please help.
Reply #6 - Sep 9th, 2009, 1:30am
 
harry_dresden wrote on Sep 9th, 2009, 12:11am:
Of course, we can still obtain S21 if the input is not match or output not equal to Zref through S-parameter simulation. For example if the input Zin is high impedance, then S21 will be 6dB larger than voltage gain =Vout/Vin. The extra 6dB here is actually an artifact (which you wouldn't get from transient simulation for example).

This has nothing to do with the analysis type (S-parameters or transient) but only with the circuit you are using for simulation. If you use a load impedance of Zref and a source with a source impedance of Zref, you will get exactly the same result for both analysis types. Of course you will get a different result if you use a different source impedance (like zero for an ideal voltage source) or a different load. Voltage gain and S21 are simply two different things.
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engrvip
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Re: S parameter fundamental questions, please help.
Reply #7 - Nov 16th, 2018, 3:47am
 
Hi,

I could not find the below reference at given link.

Can anyone please provide me this document to read and understand more on s-parameters and their interpretation.


http://www.mtt.org/measurements/GENERWGCT.PDF

regards
Engrvip
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Frank Wiedmann
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Re: S parameter fundamental questions, please help.
Reply #8 - Nov 19th, 2018, 4:43am
 
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vroy_92
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Re: S parameter fundamental questions, please help.
Reply #9 - Dec 29th, 2018, 4:30pm
 
Whether you have a reflection or not depends on your network. s11 and s22 represent your reflection coefficient only under certain conditions. If you say s11 is -20dB and ask me to judge whether it is a good i/p match or not, I won't be able to say unless you tell me what is the 'reference impedance'. If your reference impedance matches the conjugate of input impedance, well, then s11 is indeed your i/p reflection coefficient. (and a good match for the -20dB)
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Regards,
V Roy
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