I'm a student trying to understand filters. I would like to know what the Q value of a series RC low pass filter is. As far as I'm aware, one can't design for it, but I'd still like to know what it is! Surely it must have a Q value!

Also, is it possible to increase the rise time of a critically damped Sallen Key low pass filter? From what I understand, the parameter Q (or \$ \zeta \$) define the rise time. I would've perhaps thought that cascading Sallen Key filters would allow for a sharper rise time.

  • \$\begingroup\$ What do you mean by change the rise time? \$\endgroup\$ – Matt Young Feb 12 '13 at 2:22
  • \$\begingroup\$ I want to improve the step response. I believe an passive single pole RC filter is underdamped. I want it to be either slightly overdamped or critically damped. \$\endgroup\$ – user968243 Feb 12 '13 at 3:02

First, \$\alpha = 2 \zeta\$, \$\alpha\$ (damping constant) is used in filters, and typically \$\zeta\$ is used in controls.

Q is defined as \$ Q = \dfrac {f_o}{\Delta f}\ (= \dfrac{1}{\alpha}) \$. It is a band pass parameter and does not apply to first order filters.

If you want to change the step response, you're going to have to change the damping. In the case of the Sallen-Key, that involves changing the gain of the amplifier. This is where you have to start being careful. Damping is set based off the approximation you chose. As an example, for a Butterworth approximation \$\alpha = 1.414\$. If you want a faster rise time, you'll want a lower damping constant. Look at the Chebyshev =approximations. You do need to be aware that there will be overshoot with those approximations.

Cascading filters does not have the effect you think it does. For example, simply cascading two second order Butterworth low pass filters for example, does not equal a fourth order Butterworth low pass. There are tables of common approximations and the appropriate correction factors that need to be considered when cascading filters.

  • \$\begingroup\$ Okay, thanks for the explanation. I'm stil la little confused as to what the first order passive RC filter actually is. Is it considered a Butterworth filter? Also, if I want to improve the rise time of my Sallen-Key filter, can't I just decrease the Q? Have a look at the picture with the different step responses and Q values in the following article: sensorsmag.com/da-control/… \$\endgroup\$ – user968243 Feb 12 '13 at 3:36
  • \$\begingroup\$ First order filters just roll off at 20 dB/decade, I don't know that I've ever seen them given an actual approximation. I edited my post to show the connection between the damping factor and Q. If you want a faster rise time you need to decrease the damping factor, which increases Q. It is an inverse relationship. \$\endgroup\$ – Matt Young Feb 12 '13 at 4:46
  • \$\begingroup\$ Okay thanks! Basically, I'm trying to improve a simple passive RC low pass filter that I have... It is at the end of a precision full wave rectifier and it is making the full wave rectified signal a constant DC signal. The problem is, there is too much ripple. To reduce the ripple though, I need to increase either R or C and increasing either of them cause me problems because I need a good rise and fall time. So I thought I could give designing an active RC Sallen-Key filter a go, but it is proving harder than I thought to design for the rise time of the filter. Thanks for your answers! \$\endgroup\$ – user968243 Feb 12 '13 at 6:33

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