The Designer's Guide Community Forum

The Designer's Guide Community Forum
https://designers-guide.org/forum/YaBB.pl
Design >> Analog Design >> Poles and zeros in all pass filter.
https://designers-guide.org/forum/YaBB.pl?num=1567691706

Message started by Jacki on Sep 5^th, 2019, 6:55am

Title: Poles and zeros in all pass filter.
Post by Jacki on Sep 5^th, 2019, 6:55am

Hello,

I am a bit confused about the poles and zeros in all-pass filter. As shown in the Figure 8.10 in the document below, it looks like the zeros are in RHP. Shouldn't the zeros also in LHP, and form the pole-zero doublet to achieve the all-pass filter? Anybody can explain why?
https://www.analog.com/media/en/training-seminars/design-handbooks/Basic-Linear-Design/Chapter8.pdf

Title: Re: Poles and zeros in all pass filter.
Post by R.kumar on Sep 5^th, 2019, 11:56pm

The goal here is to have gain cancellation but with phase addition. It happens only when conjugate poles and zeros are on opposite sides of jw axis. The total phase then can be +360 or -360 depending on one of the two combinations of placement.

Title: Re: Poles and zeros in all pass filter.
Post by Jacki on Sep 6^th, 2019, 4:30am

Thank you for your reply. Yes, the gain compensation is good, just wonder why it also requires phase shift. two poles and two zeros in RHP will contribute 360 degree phase shift. As I remember, the phase shift will cover around 100x frequency band based on the pole/zero frequency. As I understand, all-pass filter should have the flat gain and flat phase shift for all of the input signals, and if so, how about the transition frequency band for the phase shift, also how to select the pole/zero frequency in the all-pass filter? Isn't it more convenient to move the zeros to LHP?
Thank you.

Title: Re: Poles and zeros in all pass filter.
Post by R.kumar on Sep 9^th, 2019, 1:36am

2 RHP pole and 2 RHP zeros cannot provide 360 degree phase shift. The only way to get 360 degree phase shift is by placing the poles and zeros on either side of jw axis.

Title: Re: Poles and zeros in all pass filter.
Post by R.kumar on Sep 9^th, 2019, 1:38am

Practically any all pass filter has a bandwidth after which the parasitic poles come into play. So effectively, within a certain bandwidth it behaves as an all pass filter with a flat gain but a phase shift of 0 at DC and 360 degrees at transition frequency. AFAIK an all pass filter with flat gain and no phase shift doesn't serve any real purpose. It is better, in this case, to have no filter at all.

Title: Re: Poles and zeros in all pass filter.
Post by Jacki on Sep 9^th, 2019, 5:47am

Hi R.kumar,

Thank you for your reply. It makes sense.