# S parameters: BW and Fc

Discussion in 'General Electronics Chat' started by Management, Jul 17, 2008.

1. ### Management Thread Starter Active Member

Sep 18, 2007
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How do you calculate center frequency and bandwidth from a set of s parameters? Actually I know the center frequency but how do you get bandwidth? Can you get the from 1 port s-parameters (S11 only)? Especially if you have S11 over a range of frequencies.

So i just ran off. But any help would be appreciated.

Last edited: Jul 21, 2008
2. ### theamber AAC Fanatic!

Jun 13, 2008
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If you know the center frequency and know the higher freq. cut off or lower freq. cut off then you can calculate the bandwidth by doubling it from the width at -3dB from the peak of the center freq or .707 of the signal amplitude.
No S11 is a measure coefficient of reflected power and mismatch loss over a specified range of frequencies. They are analogous to frequency response. S- Parameters are voltage ratios of the waves. But S parameters can be actually converted to impedance.

3. ### roddefig Active Member

Apr 29, 2008
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The S parameters are the reflection and transmission coefficients. I'm pretty sure there is a way to calculate the frequency response from those, but it's been a while since I had electromagnetics. You should be able to find something in a textbook.

4. ### SgtWookie Expert

Jul 17, 2007
22,201
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Well, the band edge is generally the -3dB point on S21 or S12. If you can find the two frequencies that are nearest -3db, you could interpolate between those points and the next nearest point. (That's relative; -3dB from the highest measurement. The highest measurement is insertion loss.)

S11 is forward reflection, S21 is forward transmission.
S22 is reverse reflection, S12 is reverse transmission.

As far as filters go, S11 was the preferred parameter to look at for tuning purposes; but I'd generally look at S11, S22 and S21 simultaneously if the network analyzer supported it. If you were better than -20db down, you were getting it pretty well tuned. So, depending upon your device and what your S11 ranges are, if you're below around -15dB, you're inside the passband. If you have a collection of S11 data over frequency, just look for the highest and lowest frequencies below -15dB, and that'll be your band edges. From there, figuring Fc is a snap.

Last edited: Jul 17, 2008
5. ### Management Thread Starter Active Member

Sep 18, 2007
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I have another question. If I have a signal with a frquency response of a "notch" and looks like this.

Is it possible to get a 3 dB bandwidth since it desn't even go down to/past 3 dB?

I am using ADS btw and it has a function "bandwidth_func()" to help find the 3 dB bandwidth but i am getting some funny and mixed results.

Any help would be appreciated.

6. ### SgtWookie Expert

Jul 17, 2007
22,201
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Looks like the output from a Gaussian bandpass filter with a center of 62MHz. What was the scale used when recording it?

7. ### Management Thread Starter Active Member

Sep 18, 2007
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Its not a bandpass filter but a S11 of a coil tuned to 62-63 MHz. What i want to see is that notch at 62-63 MHz.

What do you mean by scale?

And could you answer this one for me? Is it possible to get a 3 dB bandwidth since it desn't even go down to/past 3 dB?

If no would I have to look at teh magnitude plot of this, go half way down and basically do it by hand to get the bandwidth?

Thank you.

8. ### JoeJester AAC Fanatic!

Apr 26, 2005
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No. Since your reference is already 0, you can't possibly get three dB cutoff. That notch has an insignificant nadir to be considered useful.

However ...

Half-power of that notch using the method described by Management is valid. You can even call it the 3 dB point. It would be a valid 3 dB point if the frequency of interest was as weak as that notch ...

e.g. If my signal was 1 uV, that would be a good notch and have the -3 dB points at 700 nV. If my signal was 1000 uV, the nadir on that notch would reduce the signal to 912 uV. Not exactly -3 dB. It's all relative.

Last edited: Jul 22, 2008
9. ### theamber AAC Fanatic!

Jun 13, 2008
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At what point on the dB axis you want to get the bandwidth range of that notch filter?
The 3-dB bandwidth of the filter, is the frequency range for which the filter attenuates the signal energy by a factor of two or more.