Calculation of Q factor

[GGAPBE96]

I got 2port S-parameter of High-Q inductor.
Do you know how to calculate the Q-factor from S-parameter?
At first,I convert S-parameter into Z-parameter and calculate imag(Z11)/real(Z11).
The Q-factor is about 10,probably incorrect...

 

[mdanaie]

You shod devide the imaginary part of Z21 to the real part of Z(21)

 

[RF-OM]

There is old and good practical method. Simulate resonance circuit with your inductor and high Q (at least 10 times higher than expected inductor Q value) capacitor. Plot the S21 and measure 3 dB bandwidth. Then ratio of central frequency to this ratio will give you real loaded Q value of resonant circuit. Because you used capacitor with very high Q this number will reflect actual inductor Q factor. Usually this method is better than X over r ratio because in resonance circuit reactance slopes are mutually compensated, therefore inaccuracy in imaginary part measurement will also compensated. But when you do non-resonant measurements it is not the case and often there may be significant difference. One helpful hint: in simulation chose the same number of points as S-parameter measurements have. In this case you eliminate interpolation and increase accuracy. repeat this procedure for all frequencies of interest. Keep in mind that not all simulators allow numbers of points above 1000, so do not chose 1600 points when measure S-parameters.

Best regards,
RF-OM

 

[GGAPBE96]

To RF-OM,

Thank u for your good method!
I could get Q value of my inductor.

>Usually this method is better than X over r ratio because in resonance circuit
>reactance slopes are mutually compensated, therefore inaccuracy in imaginary
>part measurement will also compensated.

Could you explain "compensate" in more detail?
Does the high Q capacitor absorb the inaccuracy in imag part measurement??

 

[RF-OM]

To GGAPBE96,

1. When Network Analyzer measures the S-parameters it actually measures the voltages. Because imaginary part parameters depend on trigonometry there may be very steep slopes when small changes in argument provide big changes in function result. As close you measure to component’s SRF area as steeper will be the slope of reactance and bigger measuring inaccuracy is possible. Now, suppose you are measuring S-parameters of Murata 0402 inductor on some frequency F. Or you may obtain corresponding S-parameters file from Murata web site, which is preferable because measuring and then de-embed S-parameters is not a trivial task. Now, when you need to simulate resonant circuit with your inductor of interest you need to find suitable capacitor desirable (but not absolutely mandatory from the same manufacturer). In this case both S-parameter files were measured in the same conditions and by the same technology, therefore you may expect roughly equal inaccuracy in measuring process. When you combine these two S-parameters files for L and C in one simulation of resonant (it is very important) circuit, reactance slopes will be equal, but of opposit sign and mutually compensates. Accordingly you may expect a good compensation for measuring inaccuracy of L and C components S-parameters. Finding high Q capacitor usually is not a problem. If you have any difficulties to find a cap, you may chose Q-factor in the simulation program and usually 1000 is a good number for small caps below 10 pF. Practically this method allows determining Q-factors at high frequencies with good accuracy, but if you need to do it for low frequencies, it is probably easier to use X over r ratio.
2. Capacitor as a circuit element do not absorb inaccuracy, the latter just compensated without any physical participation of capacitor. There is much more trigonometry than physics.

Best regards,
RF-OM

 

[GGAPBE96]

To RF-OM,

Thank you.I could understand.