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I'm trying to figure out how to construct a filter with the following constraints. If it isn't possible, this would also be acceptable, albeit disappointing (and I would hope for some kind of proof). The important feature is that filter would only have one capacitor, but multiple characteristic frequencies, which both depend on the capacitor.

For instance, a normal bandpass filter has two frequencies \$f_L\$ and \$f_H\$ which can be easily identified, but they each depend on a different capacitor. Similarly, there is a filter to remove just one frequency (and narrow surroundings) from a signal, by attaching a resonant load across the circuit, but this has only one characteristic frequency -- the resonant frequency.

I would like to build something like that has two frequencies that it resonates at, or where the lower and upper boundaries of the bandpass filter are both derived from one common capacitor, but I can't find any simple way of doing this. I suspect that any answer will require a fairly nontrivial topology (eg. a lattice filter where all components are different). The circuit must also consist only of passive components.

Thank you for any help!

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This circuit has two resonances, both of which depend on the value of C1:

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One resonance produces a peak in the transfer function and the other produces a null.

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