[Question]Second-order low pass filter

[GDF]

If we want to implement a second order low pass filter, why we use
complex conjugate poles rather than two real poles? For instance, cascade
two RC filters with different time constants.

Thanks,

 

[zhi_yi]

what is the complex conjugate poles, and what is the two real poles?

thank you

 

[Kral]

GDF,

You can cascade 2 RC filters to yield a 2 pole filter.
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The filter characteristics depend on the pole locations. In general, the higher the "Q" (ratio of imaginary to real components of the pole), the sharper the transition region (region between the pass band and stop band) will be, and the higher the overshoot to a step input will be.
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As an example, the Butterworth filter is optimal in the sense that of all filters with monotonic (constant sign of the slope) passband and stopband responses, the Butterworth filter has the flattest passband (lowest value of attenuation in the passband). Its, frequency response is far superior to that of a cascaded RC filter with the same passband and stopband specifications. The poles of a Butterworth filter are equally spaced on a circle in the complex plane. So the Butterworth poles for a 1radian/second cutoff frequency are at .707 +/- j.707.
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Pick up any book on analog filter design for more details.
Regards,
Kral

 

[ptmsl]

Conjugate numbers are used in order to implement a known transfer function.In the general form all lowpass filters have a transfer function that is an expression in the s plane. Building a second order filter using two RC filters in series can be done but some form of isolation (buffer) between them must be provided so that there will be no interaction between them.
Building a second order active filter is relatively easy and there are many programs (freeware) that will do the calculations for you so that you will not have to deal with conjugate numbers. (try FilterPro from Texas Instruments)
Using an opamp biquad is the best option if you are not designing with frequencies more than 10MHz

 

[Iouri]

now there is no problem of putting to RC network series, but how you control (or mutch the input and output impidance) which is OPAMP does perefctly
next: OP AMP are not designed to use in the 10MHZ circuit.

also How you will control phase shifting of the two series network filter
Everything has a reason....