# Q value of a passive single stage RC low pass filter

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.

• What do you mean by change the rise time? – Matt Young Feb 12 '13 at 2:22
• 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. – 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.