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Graphing S21 Phase after removing best fit linear?

Question asked by RZEITLER on Jul 18, 2007
Latest reply on Aug 3, 2007 by RZEITLER

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I'd like to graph S21 phase in degrees after doing a linear analysis, but I'd like to subtract out a linear best fit to show deviation from linear phase.

For bonus points, I'd like the best fit to be performed on a subset of the frequency span. So if my total analysis is from 40MHz to 80MHz, the fit should be done from 52MHz to 68MHz.

This is similar to adjusting the electrical delay reference on the HP8753ES while displaying phase.

I imagine there's an equation involved, but I can't figure it out. And nothing obvious is popping out at me. I'm surprised this isn't a FAQ.

TIA

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RANDY_RHEA Jul 18, 2007 12:25 PM
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This is very easy and doesn't even involve equations. Simply add a negative length of transmission line in series with your network or data. The characteristic impedance of the line should equal the reference resistance such as 50 ohms. Then you may simply tune or optimize the negative line length to rotate out as much linear phase as you wish.

Youy will find tuning the length is easy. But optimization of the line length may be combined with other optimization goals and the frequency limits within the optimization goals window may be used to your hearts content.

It is fun to watch what happens as the negative line length is tuned to rotate out the excess phase.

Clear skies and high Q
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RZEITLER Jul 19, 2007 2:47 AM
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Thanks for responding, Randy.

I think a transmission line will distort the return loss phase, kind of like using a network analyzer that's calibrated for 2 foot cables with 1 foot cables instead. I suppose over such a narrow band it might not be much of an issue. And I can set the length to zero when I'm ready to export the result.

All the best!

"

This is very easy and doesn't even involve equations. Simply add a negative length of transmission line in series with your network or data.

"
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MZachmann Aug 2, 2007 8:23 AM
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Conversely, if you'd rather do this with equations, you can (although Randy's way is pretty simple). The equation is a typical best fit linear regression. Let me know if you'd like an example.

Regards,
Mark
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RZEITLER Aug 2, 2007 8:56 AM
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Hi Mark:

I'd be interested in seeing this.

I had tried plotting =dev_lin_phase(F,ang(S21)) (or something like that) but the simulator hung. I wonder if I had the syntax wrong, or if dev_lin_phase is entirely the wrong function to use for this. Or maybe I was working over too large a span and the out-of-band phase was messing up the routine.

Anyway, thanks for offering to show this. I'd like to try it.

"

Conversely, if you'd rather do this with equations, you can (although Randy's way is pretty simple). The equation is a typical best fit linear regression. Let me know if you'd like an example.

Regards,
Mark

"
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dansavio Aug 3, 2007 3:33 AM
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Hi,

dev_lin_phase is actually the correct function to use. You just switched the order of the parameters. According to the help for dev_lin_phase, the syntax is:

dev_lin_phase( Dependent, Independent)

So ang(S21) is your dependent, while F is your Independent. If you switch the order of arguments you get what you're looking for.

Now, to answer your question about using only a subset of your data, the key to this is to use range indexing. In your example, you want to only use the data from 52 to 68 MHz. The syntax F@[52,68] returns the INDICES of the F variable that contain the values between 52 and 68 MHz. So we want to index into F at these indices like so:

indices = F@[52,68]
F_subset = F[indices]

Of course you could have done it in one line without using "indices", but since we also want to extract ang(S21) at those same indices, we might as well keep the indices around. So, the following equations would use only 52 to 68 MHz to compute the deviation from linear phase:

indices = F@[52,68]
F_subset = F[indices]
angS21_subset = ang( S[indices,2,1] )
deviation = dev_lin_phase( angS21_subset, F_subset)

Best Regards,
Dan Savio
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RZEITLER Aug 3, 2007 6:19 AM
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Thanks, Dan. This is just what I was looking for!

"
[snip]

indices = F@[52,68]
F_subset = F[indices]
angS21_subset = ang( S[indices,2,1] )
deviation = dev_lin_phase( angS21_subset, F_subset)

Best Regards,
Dan Savio

"
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Graphing S21 Phase after removing best fit linear?

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