phase angle of a transfer function - diyAudio
Go Back   Home > Forums > Amplifiers > Solid State

Solid State Talk all about solid state amplification.

Please consider donating to help us continue to serve you.

Ads on/off / Custom Title / More PMs / More album space / Advanced printing & mass image saving
Reply
 
Thread Tools Search this Thread
Old 15th December 2012, 03:01 PM   #1
diyAudio Member
 
Join Date: Jul 2012
Location: Verona
Default phase angle of a transfer function

I'm trying to find the phase angle of the transfer function of a 2nd order high-pass filter. the phase should vary from 180 at w=0 to 0 at w = infinite
the transfer function with s substituted by jw is:
-w^2/((2*j*w/(C*R2))-w^2+(1/(C^2*R2*R1)))
I set the cut-off frequency at 20 Hz.
the numerator has no complex part so it doesn't introduce a phase shift while in the denominator the phase shift is -arctan(Im/Re) which is the arctan of the ratio of the immaginary part on the real part.
so the phase angle becomes:
-arctan((2*w*C*R1)/(1-(w^2*C^2*R2*R1)))
but if you see the excell file I attached the phase from 0 to 18 Hz goes from 0 to -90 and then it goes from 90 to 0. I think that the problem is that the function arctan is defined between -90 and + 90 so it cannot give higher or lower angles. to solve this problem I summed 180 to the angle of the frequencies lower than 20 Hz and left unchanged the other angles so the plot becomes right. but is this the way to work with phase angles? is my method right?
  Reply With Quote
Old 15th December 2012, 03:56 PM   #2
jcx is online now jcx  United States
diyAudio Member
 
Join Date: Feb 2003
Location: ..
it helps to use tools specific for the application domain - they often have correct assumptions built in

in this case you need to look up "phase wrapping"/"unwrapping" - find a math package that does it right for you - or know when you have to correct by hand http://www.google.com/#hl=en&sugexp=...=1920&bih=1069

even LTspice sometimes makes strange phase plots because it has to assume a starting phase for a circuit - the phase may be asymptotic beyond the frequency range you give it for the analysis - so knowing what to expect, interperting the plot, identifying likely software errors is still required
Attached Images
File Type: png LT_laplace.PNG (67.3 KB, 113 views)

Last edited by jcx; 15th December 2012 at 04:11 PM.
  Reply With Quote
Old 15th December 2012, 07:42 PM   #3
diyAudio Member
 
Join Date: Sep 2004
Location: virginia
"the numerator has no complex part so it doesn't introduce a phase shift"

A high pass filter has a zero in the numerator, so that the output is zero at low frequencies, and the zero does cause phase shift. I don't understand your explanation.

Ray

Last edited by rayfutrell; 15th December 2012 at 07:52 PM. Reason: I mean high pass filter has zero in the numerator
  Reply With Quote
Old 16th December 2012, 10:31 AM   #4
diyAudio Member
 
Join Date: Jul 2012
Location: Verona
yes it has a zero in the numerator because the numerator is s^2/denominator. but to calculate the phase angle s must be substituted with jw, thus s^2 becomes j^2*w^2 but j^2=-1 so the numerator becomes -w^2 which is a real part not imaginary.
  Reply With Quote
Old 16th December 2012, 05:36 PM   #5
diyAudio Member
 
Join Date: Sep 2004
Location: virginia
A two pole high pass filter transfer function has two zeros in the numerator and two poles in the denomonator. As the frequency becomes large, the poles and zeros cancel and the transfer function magnitude becomes unity at infinite frequency. The two zeros are coincident at zero in the complex plane, so you start off with 180 degrees of phase shift from the two zeros. Since the poles are conjugate, their phase contribution cancels at zero frequency because the phases are equal and opposite. As the frequency increases, the phase from the poles starts to subtract from the 180 degrees of phase contributed by the zeros, and as the frequency approaches infinity, the phase approaches 0 degrees. You have 180 degrees of phase from the zeros and -180 degrees of phase from the poles.
  Reply With Quote
Old 17th December 2012, 01:06 PM   #6
diyAudio Member
 
Join Date: Jul 2012
Location: Verona
so is the phase formula or the transfer function wrong?
  Reply With Quote
Old 17th December 2012, 01:43 PM   #7
rephil is offline rephil  Europe
diyAudio Member
 
Join Date: Nov 2004
Location: In Belgium at the French border.
Quote:
Originally Posted by davidel94 View Post
so is the phase formula or the transfer function wrong?
There are two ways in order to calculate the arctg function. From -90 to +90 and from -180 to +180. Look in Wikipedia to the functions atan and atan2.

If you want to get more angle for the phase rotation of the transfer function, you will have to produce your own code in order to have this wanted value of phase rotation. It is not difficult to produce if you think at what occurs with complex numbers in the circle and in which quadrant you are with this phase.

Kind regards

Rephil
  Reply With Quote
Old 17th December 2012, 02:20 PM   #8
jcx is online now jcx  United States
diyAudio Member
 
Join Date: Feb 2003
Location: ..
can't pickup on keywords? try search for: phase unwrapping
  Reply With Quote

Reply


Hide this!Advertise here!
Thread Tools Search this Thread
Search this Thread:

Advanced Search

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off
Trackbacks are Off
Pingbacks are Off
Refbacks are Off


Similar Threads
Thread Thread Starter Forum Replies Last Post
Transfer function. Poles not where expected Raka Multi-Way 35 29th July 2008 01:20 PM
transfer function jenks Solid State 31 24th April 2008 08:28 PM
Question about transfer function magnitude. massappeal129 Subwoofers 4 16th August 2007 10:21 PM
Transfer Function jclouse Multi-Way 22 1st July 2006 01:19 PM
Transfer function of closed box cm961 Multi-Way 1 31st August 2004 06:42 PM


New To Site? Need Help?

All times are GMT. The time now is 05:30 PM.


vBulletin Optimisation provided by vB Optimise (Pro) - vBulletin Mods & Addons Copyright © 2014 DragonByte Technologies Ltd.
Copyright 1999-2014 diyAudio

Content Relevant URLs by vBSEO 3.3.2