# Realisation of a passive RC low pass filter

I have an unusual low-pass filter problem that I would like to realise with a passive RC network (Note 1).

It's easy enough to find prototype filters for passive RLC networks, or for the various active RC filters.

I am having difficulty finding prototype filters for the classic filter types (e.g. Butterworth, Chebychev, Elliptic) that are implemented using such a network. The closest I have managed to find is this which recommends equal R and C values for each passive in the network:

Hence, I would like to ask

• Is there a good reference that covers this sort of design?
• Are there any "tricks" or "gotchas" for this design?
• What is the design procedure to implement one of the classic filters?

Note 1 - Context:

The design is for a second-order low-pass anti-aliasing filter. A first order doesn't attenuate an annoying periodic glitch enough - and I may yet need a higher-order filter. Board space is very limited and the ADC has a built-in buffer that I would like to make use of. The attenuation is desirable - the signal is larger than the ADC would normally accept. Inductors are completely undesirable for the application.

• If this is something you're doing purely in the analogue domain then the question would probably be better suited to electronics.stackexchange.com – Paul R Dec 11 '13 at 12:10
• @PaulR, Yes, it is a pure analogue problem. I was tossing up whether to post this question here or there. – Damien Dec 11 '13 at 12:18
• I expect some of the DSP people here are good with analogue too, but there are some very good people on electronics.SE who can probably help you with this. I'd expect more responses on electronics.SE, and the question would be more on-topic there too. – Paul R Dec 11 '13 at 16:04

Note that your desired passive RC network is really just the cascade of multiple first-order RC filters, each of which have the transfer function $\frac{1}{1+RCs}$. By choosing the R and C values to use in each stage, you can place pole locations where you want them in the $s$-plane.
$$s = -\frac{1}{RC}$$
Note that this value is purely real. This makes such a topology infeasible for implementing a prototype such as the Butterworth filter. Its poles are located in a semicircle in the left half of the (complex) $s$-plane. Since you can only place poles on the real axis using your RC stage topology, you cannot implement a Butterworth network. You end up having the same problems with other types like Chebyshev or elliptic structures.
The solution is to use additional elements like inductors or amplifiers; these provide more degrees of freedom in the resulting transfer function to place poles at other places in the $s$-plane. That's why all the references you can find use them!