# LC Topology for band-pass filters

I, as a beginner, am looking to design a passive band-pass filter for a crossover speaker system.

This project that I am doing has the following specifications:

1. The filter should be a Butterworth filter, i.e. $$\\zeta=0.707\$$.
2. The filter should consume as little power as possible so that the maximum power is transferred to the transducer
3. The filter should act as a band pass filter in the frequency range: $$\150 Hz - 1.5 kHz\$$
4. The roll off should be as large as possible for the filter
5. The filter load impedance is known and is assumed to be constant

In order to satisfy the first two points an RC filter would not be suitable as I cannot achieve a Buttersworth filter and the resistors in the filter dissipate energy. Similarly I disregard series RLC circuits as they also include a resistor.

So, in the end, I arrive at LC filters. They are also the best as they satisfy the fourth requirement best, since they are an order higher than RC filters.

Having looked at online literature, I have encountered two different LC topologies:

1. A constant K band pass filter
2. A band pass filter as a combination of two inductors and two capacitors (low and high pass filters put together)

Is there some sort of way to decide which of the two topologies are best suited assuming that resources are no limitation?

NB: I am aware that for low frequency applications, large inductor values are needed. I am making the assumption that when I need to construct the filter I have any needed inductance (and capacitance).

• Best way, in my opinion is use a simulation tool. Commented Nov 25, 2021 at 21:55
• There's a lot to deal with in what you write; plus some conflicts. It may also be that your bandpass carries enough of the midband that you may need a Zobel or else there may be no point in bothering with the bandpass. In any case, there's too much to consider and correct in writing an answer. So I'm passing on the idea for now.
– jonk
Commented Nov 26, 2021 at 5:37
• @jonk Thank you for your response. I understand that I am asking a lot, but you have mentioned that there is a lot to correct from the things I have written. Is there some sort of mistake in the things I wrote? I would really appreciate knowing what I am doing wrong.3 Commented Nov 26, 2021 at 6:51
• @Steven How much power do you expect to lose, in the optimal case? (re: #2) You should know. But do you? What does "roll off should be as large as possible" mean? (There's no limit to how far you can go, though adjusting things can be quite complex. Later you talk about a certain number of devices. But I'm not sure if that's defining or just a discussion.) In some ways I think you are talking about 4th order and Butterworth. But I'm not sure. In any case, any particular order of Butterworth is easy to compute and easy to find in tables. Have you looked? There's much to discuss.
– jonk
Commented Nov 26, 2021 at 6:57
• Since your purpose is building these, I'll have to warn you that whatever nice formulas and graphs you may see, they will all go poof when you'll have to use real life capacitors with their impossible tolerances and, perhaps worse, when you'll have to build or buy the bulky inductors. Skipping that, any 4th order LC bandpass filter (all pole, not pole-zero) will have 2xL+2xC -- it's their values that make the transfer function. That constant-K is a 6th order (3xL+3xC), and it has the same topology as a 6th order Butterworth, Chebyshev, Papoulis, etc; values differ. Commented Nov 26, 2021 at 7:52