Configuring Frequency Bandwidth and Input Signal for Bandpass filter circuit

Question

How do I set and configure the frequency bandwidth I want the filter to output to a device?

I am using a physical passive bandpass filter which I intend to take the signal in and filter it and output the result.

So if I have an input signal \$V_{in}\$ which is signal from a .wav file including the frequencies and noise I want to filter. How would I set the circuit or Inductors, Capacitors, and Resistors (because it's an RLC circuit) to output the signal from the frequency from the bandwidth I want. Let's call it \$f: [f_1, f_2]\$. How would I know which ratings of components to have in the circuit in order for it to filter that range of frequencies?

The second question is: How would I exactly input the signal to the circuit from a computer? Should I just connect a 3.5mm jack to \$V_{in}\$ and then play the .wav file?

Thank you.

Answer 1

In general, you'd put a voltage source \$V_{in}\$ across your inputs, and analyze the network until you come to a complex term for the output voltage across \$C_2\$ dependent on the input voltage's (circular) frequency \$\omega\$.

Then you throw in your target filtering behaviour and find optimal solutions for the component values. It's an optimization problem, in the end.

However, in your specific case, I'd first reduce to either the first or the second stage first, and derive the frequency behaviour of that. Or, find it on common RLC literature and online calculators. You normally wouldn't want the R to be between the L and C, because that reduces the quality factor of your filter (your anti-oscillation idea still applies, just not like that).

You'll find that a single stage RLC filter doesn't give you very many degrees of freedom: basically, you can select the center frequency and a passband width, but in rough numbers, the transfer function will always only "decrease" with 20 dB/decade, so with two stages, you'd be very happy to get 40 dB attenuation at ten times the upper corner frequency. In practice, things usually are even worse.

For serious filtering, you'd go for LC-ladder filters (which can become unwieldy for audio frequencies), or for active filters (ask the analog.com website's filter designer tool ;) ). Or, just digitize the audio and do the signal processing in software – audio sampling rates are really no challenge to modern computing hardware, and if latency is not a concern of you, any couple-of-Euros USB sound card with a digitally implemented filter outperforms the frequency behaviour of an analog filter that wasn't designed without a lot of trial, error, improvement and costly revision.

Answer 2

How do I set and configure the frequency bandwidth I want the filter to output to a device?

You have 2 cascaded passive filter stages and, if you don't design them carefully you'll get interaction between stages and, potentially, a disappointing result. For the high-pass stage use a tool like the one below to experiment with values: -

R = 40 ohm, L = 10 mH and C = 1 uF gives a cut-off frequency of about 500 Hz: -

HPF Interactive filter.

As you can see there is a fairly flat frequency response above 500 Hz (the -3 dB point) and very little peaking (about 0.18 dB) and, I see from your comments that you understand about keeping a reasonable value of resistance to prevent excessive ringing. The step response in the lower half of the above picture is also not excessive.

I've chosen particularly "heavy value" components in the above high-pass filter because I want the following low pass filter not to be able to significantly load the HPF. But note this; at resonance, the above circuit will have an input impedance that is purely 40 ohm and, for many, many designs this is too low. For something like a cross over network for a speaker it is fine of course.

The low pass filter (aimed for 10 kHz) is shown below and its values are chosen so as to only lightly load the front-end HPF: -

R = 400 ohm, L = 5 mH and C = 50 nF to give a cut-off frequency of about 10 kHz: -

LPF Interactive filter.

At resonance, the input impedance is about ten times that of the high-pass filter and so loading effects won't be extreme. Play around with the values to suit your required bandwidth requirements but be aware, that as you make your two cut-off frequencies more similar you will get added interactions that are best solved by using a circuit simulator like micro-cap or LTSpice.