# bode plot phase

Discussion in 'The Projects Forum' started by suzuki, May 4, 2012.

1. ### suzuki Thread Starter Member

Aug 10, 2011
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0
Hi,
not sure if this is correct place to put this but here goes.

I was having a discussion about bode plots and it was stated that you cannot estimate the phase plot using the magnitude plot. For example, say you only have information about the magnitude, you can't tell what the phase is.

IMO, this should not be true, as I would suspect that the phase should follow the magnitude plot. For example, if you had a pole on your magnitude plot, I don't think there would be a case where the phase increases 90 degrees (as opposed to decreasing 90 degrees).

Who is correct? I'm fairly certain that with just magnitude information, you can at least get a good estimation of the phase plot. Am I missing something here?

tia

2. ### wayneh Expert

Sep 9, 2010
16,011
6,101
Yeah, I think you're in the wrong forum. The General Electronics or Homework forums might get you a better response.

3. ### crutschow Expert

Mar 14, 2008
21,728
6,267
Depending upon the location of the poles and zeros of a system the phase can significantly change with little change in the gain, so it's true, the magnitude plot can not be used to give an estimate of the phase plot (and vice versa).

For example, an all-pass filter can have a phase change of as much as 180° with frequency with no appreciable gain change.

4. ### suzuki Thread Starter Member

Aug 10, 2011
119
0
hmm my apologies, if mods want to move this, please do.

crutshow,
Your point about the allpass filter is actually very interesting, I didn't realise that. However, it seems to me this is sort of just a special case where the pole and zero are reflected, and you get a negative sign?

Can we at least say that with the magnitude plot, we can get a good estimate of the phase in most cases?

5. ### crutschow Expert

Mar 14, 2008
21,728
6,267
If the system has a simple one or two pole rolloff then perhaps you can make a reasonable estimate of the phase as an academic exercise. But in a typical real world complex feedback system where you are concerned about stability, you need to measure both to reliably determine the system stability from the Bode plot. The difference in the gain plots between a stable and unstable system can be quite small for many such systems.

6. ### The Electrician AAC Fanatic!

Oct 9, 2007
2,666
473
For a given magnitude plot, there is an associated phase plot that is the minimum phase that that magnitude characteristic can have. However, there can be more phase shift than that minimum.

Have a look at:

http://www.atp.ruhr-uni-bochum.de/rt1/syscontrol/node34.html

And also the general topic of minimum phase.

This was all explained by Hendrik Bode long ago:

http://en.wikipedia.org/wiki/Hendrik_Bode

On page 3 of this pdf:

http://trs-new.jpl.nasa.gov/dspace/bitstream/2014/19495/1/98-0905.pdf

second column, near the bottom is described "the third Bode integral formula". This formula allows you to calculate the minimum phase response of any given magnitude response. You can then add any number of all pass functions to get a larger phase shift, but Bode's formula shows that any magnitude function has a specific minimum phase response. It's not just an estimate; it's the exact (minimum) phase response.

Last edited: May 6, 2012