# Calculate Q from s-parameters (RI Format)

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#### chiques

##### Full Member level 3
Following up on the solution recommended by post 59511(https://www.edaboard.com/threads/how-to-calculate-the-q-factor-from-the-s-parameters.59511/).

I noticed they are already in R+jw format (according to the header)

Taking S11 at 100MHz I see:

1.0E8 0.02443218816516882 -0.15136178029257324 Therefore: If I look at Murata’s SimSurf, the Q @ 100MHz should be 163.7. Anybody know what I’m missing here?

S11 is unequal Z11

S11 is unequal Z11
Does this mean I should be working Z parameters instead S-Parameters?

Look at the last part.

Look at the last part.
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

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

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

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

Last edited:
• chiques

### chiques

Points: 2
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 ---

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