Selection of values for Underdamped Second order low pass filter

Hello everyone

I want to design a second order low pass filter, but I need to select values of resistances and capacitances so I get underdamped oscillation for a step input.

I have read that this can be done using RLC circuit, but I want to design it using two cascaded RC first order filters, but i could not manage to do this. As I understand, the matter is just a selection of parameters for having damping ratio < 1 , but I could not get any values that achieve the goal.

I wonder, is it possible to design a second order filter using two RC circuits while making the system underdamped??

This are two cascaded first order filters which have real poles and can't show an oscillating step response by nature. Instead you'll want a second order filter with a complex pole pair. It can be implemented either as LC filter or as active filter with feedback. Some references are here https://en.wikipedia.org/wiki/Active_filter

You'll decide for a specific cutoff frequency, filter Q and a circuit topology, then use any of the filter design tools on the internet to calculate the R and C values.

hmmm yes, now I got it . the transfer function of a cascaded RC second order Low pass filter is by nature 1/((T1S+1)(T2S+2))
so it can be either over damped or critically damped, but it will never oscillates because these 2 poles are always real.

mamech said:

hmmm yes, now I got it . the transfer function of a cascaded RC second order Low pass filter is by nature 1/((T1S+1)(T2S+2))
so it can be either over damped or critically damped, but it will never oscillates because these 2 poles are always real.

Click to expand...

Yes - correct.
But with the componenets you have used in your circuit you can realize a second-order RC filter in Sallen-Key configuration (search for "unity-gain Sallen-Key").
All you need is some feedback. So you can implement pole damping (Q values) as you like.

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If you want (or can afford) to use two buffers (by the way: Two buffers in series are meaningless) do the following:
* Place one of the buffers at the output of the 2nd RC section ;
* Connect the output of this buffer to the first capacitor (instead of grounding it) thus realizing signal feedback.
* Then, the following formulas apply for two equal capacitors C1=C2=C and R2=k*R1 (R1 is the resistor of the first RC section):

Pole frequency wp=1/[R1*C*sqrt(k)]
Pole quality factor Qp=sqrt(1/k)
Qp=1/(2*d) with d=damping factor.

Note: Using this two-opamp topology you have simplified formulas if compared with the single-OP Sallen-Key structure.

A Sallen-Key filter with equal resistor and capacitor values will have a Butterworth response when its gain is 1.586 and will oscillate when its gain is about 2.0 and higher. Try it with a gain of 1.8 times.

Audioguru said:

A Sallen-Key filter with equal resistor and capacitor values will have a Butterworth response when its gain is 1.586 and will oscillate when its gain is about 2.0 and higher. .

Click to expand...

For this single-opamp unity gain Sallen-Key filter the Pole Q is Qp=1/(3-Acl) with the closed-loop gain Acl.
That means: For a gain of Acl=2 we have Qp=1. Hence, the circuit is stable and will not oscillate (oscillation condition: Qp=infinity for Acl=3).