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Design >> Analog Design >> complex poles
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Message started by mvaibhav on Dec 2^nd, 2005, 11:36am

Title: complex poles
Post by mvaibhav on Dec 2^nd, 2005, 11:36am

Hi,
I need an intuitive explanation of how complex poles in the s-plane appear or affect the frequency characteristics of, let's say a low-pass filter. For real poles on the negative real axis, I can simply say that the frequency response will roll off at a slope of -20 dB/decade for every such pole/frequency. How can I map the complex poles on the real frequency axis?? e.g., for Butterworth filter, it has maximally flat passband whereas chebyshev has ripple in the pass band. Why do we use complex poles at all to design filters (apart from a better step response)??

many thanks.

regards,
vaibhav

Title: Re: complex poles
Post by vivkr on Dec 3^rd, 2005, 12:10am

Hi Vaibhav,

I assume that you mean better cutoff rate rather than better step response.

Your question is unclear. What do you mean by mapping complex poles on the
real frequency axis??

Use of complex poles allows one to achieve sharper cutoff between passband and stopband for a lower order filter, which means fewer components and opamps etc. Thus, there is a direct cost/power advantage. Regardless of that, you will still place the poles well inside the left-half s-plane.

I would suggest that you look up a book on basic filter design. Van Valkenburg's text is one possible reference, but there is no dearth of those. You can even use the filter design utility in MATLAB to create filters of different order and type and look at their pole-zero plots to gain some insight. An even better way to gain insight would be to pick up a DSP text and look through the chapter on FIR filter design.

You can also look at a recently posted topic "Effect of zeros on filters".

Regards
Vivek