Calculate Q from s-parameters (RI Format)

S11 is unequal Z11

FvM said:

S11 is unequal Z11

Click to expand...

Does this mean I should be working Z parameters instead S-Parameters?

Look at the last part.

BigBoss said:

Dr. Mühlhaus Consulting & Software GmbH » Inductor EM simulation: 1-port or 2-port?

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Look at the last part.

Click to expand...

Thanks, but this example uses an stoz() function. Do you know of any arithmetic examples?

Yes, you need to convert to Z-parameters or Y-parameters first.

The next question is what Q you want to calculate:
1) Q into port 1 with port 2 shorted
or
2) Q of the series element between ports 1 and 2 for differential excitation.

The first case is easy: impedance into port 1 with port 2 shorted is 1/Y11.
The second case would be the equation on my appnote linked above, typically used for RFIC inductors with symmetric excitation. For that you convert the 2-port data into the series 1-port between both terminals, and evaluate that differential impedance.

Good luck!
Volker

These are two-port s-parameters

!Murata Part Number: GCH1885C2A101JE01
!These Parameters are Measured in Series Mode Connection
! o--ll--o
!Port1 Port2
! o------o
!Operation Temp=25[degC], DC Bias Voltage=0[V]
!Freq. Start=100[MHz] Stop=8.5[GHz], 401[Steps]
!Data Generated on Jan 10, 2017
# Hz S RI R 50
!Freq.(Hz) S11(Real) S11(Imag) S21(Real) S21(Imag) S12(Real) S12(Imag) S22(Real) S22(Imag)
1.0E8 0.02443218816516882 -0.15136178029257324 0.9755678118348311 0.15136178029257324 0.9755678118348311 0.15136178029257324 0.02443218816516882 -0.15136178029257324

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You can convert S-parameters to series impedance for the shown series connection

Zser = 2 Z0*(1 - S21)/S21

Using Matlab/Octave
>> s21 = 0.9755678118348311+0.15136178029257324i
s21 = 0.97557 + 0.15136i
>> z21 = 2*50*(1-s21)/s21
z21 = 0.094893 - 15.529972i
>> q=abs(imag(z21)/real(z21))
q = 163.66

FvM said:

These are two-port s-parameters


You can convert S-parameters to series impedance for the shown series connection

Zser = 2 Z0*(1 - S21)/S21

--- Updated Apr 22, 2022 ---

Using Matlab/Octave
>> s21 = 0.9755678118348311+0.15136178029257324i
s21 = 0.97557 + 0.15136i
>> z21 = 2*50*(1-s21)/s21
z21 = 0.094893 - 15.529972i
>> q=abs(imag(z21)/real(z21))
q = 163.66

Click to expand...

Verified in MathCad as well. I checked 2 frequency points and the data checks out.
Thank you,