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# Question about active, second-order filter

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#### Michael Craft

##### Newbie level 3
I am looking at someone's design of an active, second-order filter. Here it is:

https://i1103.photobucket.com/albums/g471/ohio_rifleman/2ndorderfilter.jpg

I find this design unusual, in that it is simply two, passive, first-order filters connected in series followed by an op amp buffer. I have never seen this before; in my experience, active, second-order filters always have a Sallen-Key or multiple feedback topology.

Why would someone use this filter in lieu of a Sallen-Key or multiple feedback topology? Are there any advantages to this design? Are there disadvantages to this design? If so, what are they?

Thank you

Hi Michael,

that topology only allows to have two real, not coincident poles. This is a very strong limitation.
Instead, if you want a pair of complex poles (as usaslly one needs), you need an active filter with R and C componentes (Sallen-Key, multiple feedback, variable state) or use of R, C and L.
Regards

Z

Thanks. And sorry for the newbie question, but could you explain why complex poles are better than two, real poles? Will the former have a flatter response in the pass band, for example?

Yes, Michael.
A pair of poles has a parameter: the damping factor ζ.
ζ=1 corresponds to two real, coincident poles.
ζ=1/sqrt(2)=0.707... corresponds to a maximally flat response (Butterworth 2nd order).
0<ζ<0.707 gives a peak in the frequency response (Chebyshev 2nd order f the peak is moderate).
ζ<=0 is an oscillator
The circuit you shown can obtain only ζ>1.
Regards

Z

complex poles give you an extra degree of freedom in shaping the frequency response. You can accentuate certain frequencies, usually around the corner frequency. Eventually the response will roll off with -40db/dec but with sufficient pole Q the initial part of the roll off can be made steeper thus allowing you to gain more attenuation (for ex. in LPF) within a smaller frequency span.

Usually people want to implement filters according to standard filter prototypes like Bessel, Butterworth, Chebyshev etc. All of them have complex poles for order > 1. If you don't rely on a good filter characteristic, you can use the real poles filter anyway. Personally, I won't name it an active filter, because the amplifier is just a buffer to isolate the load, without a meaning for the filter characteristic.

Hello Michael,

there might be a small advantage of the shown passive RC filter if compared with classical active topologies (damping factor less than unity): behaviour in the time domain (step response).
Such an "overdamped" filter exhibits absolutely no "overshoot" if excited with an input step. All filter circuits with a pole Q>0.5 (damping<1) show such an overshoot - even the Bessel response.
The shown passive topology (I agree with FvM, that it shouldn't be called "active") with buffer comes close to the "critically damped" filter response if the following two conditions are met:
* equal time constants for both RC elements (but different impedance niveaus, see below)
* Selection of suitable element values aiming at a negligible loading effect of the 1st stage caused by the input impedance of the 2nd stage (Example: 100ohms*100µF and 100kohms*100nF)

FvM

### FvM

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To implement an exactly critical damped 2nd order filter, a Sallen Key (also called Pos SAB) topology with equal R and C would be the most simple way.

LvW

### LvW

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