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Design >> Analog Design >> complex pole or zero
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Message started by bharat on May 17^th, 2010, 1:43am

Title: complex pole or zero
Post by bharat on May 17^th, 2010, 1:43am

Looking for answer of fundamental question.

If there is complex pole at (say) -3+4j and -3-4j , which means for s plane ( sigma axis, jw axis) and a plane perpendicular to jw axis where the Transfer function will blow to infinity at (-3,4) & (-3,-4) corordinates.
At what corresponding freq in bode's plot will I see the complex pole behaviour. Is it at sqrt(3^2+4^2) ??

Title: Re: complex pole or zero
Post by buddypoor on May 17^th, 2010, 2:56am

Yes, thats right. The mentioned sqare root is the magnitude of the vector directed to the pole position in the s-plane - and it is called "pole frequency".
But be careful, in the BODE diagram this pole frequency is NOT identical to the frequency where the transfer function magnitude has a (possible) peak resp. maximum.
The exact formula is: Fpeak=Fp*sqrt[1-(1/2Qp^2)] ; Qp=pole Q.
As you can see, for large Qp values both frequencies are very close to each other.
I suppose, you know how Qp is defined in the s-plane, don't you?

Nevertheless, you can identify the pole frequency very easily: It is simply the frequency at which the 2nd order transfer function has a phase excursion of exactly 90 deg. This follows directly from the 2nd order transfer function - if expressed using Qp and wp=2*Pi*Fp.

Title: Re: complex pole or zero
Post by raja.cedt on May 17^th, 2010, 8:39am

hi buddy poor,
here Q is very less(around 5/6), so you don't see much peaking here. Max peaking here you can get is 20log(5/3).

hi bharath,
bode plot is only defined for the signal frequencies where damping is zero (means s=0+jw). So blowing(large peak) is only occurs for complex poles. or simple question, for 1/(1+s) have you seen blow at s=1?

Thanks,
Rajasekhar.

Title: Re: complex pole or zero
Post by buddypoor on May 17^th, 2010, 9:08am

Re: complex pole or zero

hi buddy poor,
here Q is very less(around 5/6), so you don't see much peaking here. Max peaking here you can get is 20log(5/3).

I suppose the pole location as given by bharath was only an example.
Nevertheless, for Qp>0.5 there will be always a magnitude peaking !
(Correction: Qp>0.7071; I have mixed it with overshoot in the time domain which exists for Qp>0.5)

hi bharath,
bode plot is only defined for the signal frequencies where damping is zero (means s=0+jw). So blowing(large peak) is only occurs for complex poles. or simple question, for 1/(1+s) have you seen blow at s=1?

I am not sure if bharat will understand this question. Me not!

Regards