Realisation of a passive RC low pass filter

Question

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?

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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.

Answer 1

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.

Here's the problem: recall that the pole locations occur where the denominator of the transfer function is equal to zero. Therefore, for a particular RC stage, its corresponding pole location is:

$$ s = -\frac{1}{RC} $$

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!