RLC

I am trying to find a simple RLC filter, with few components. The component values should be readily available and not too large.

Their are two flavors of the RLC low pass filters. One is where the resistance is in series with the inductor, the other is where the resistance is in parallel with the capacitance. What happens when these two flavors are combined?

The equivalent resistance between R2 and C1 is as follows.

The output is just a voltage divider.

What can I see intuitively from this equation? Well, when s or j omega equals zero, the output is simply the input times a voltage divider. Omega squared is simply the capacitance times the inductance.

Can the equation be simplified? The inductance should be very small, so the middle term should simplify.

I would like the filter to be critically damped. When does that happen?

When the radical equals zero, it is considered to be critically damped, where the system returns to equilibrium as soon as possible, with no ringing or oscillations.

If R2 is much greater than R1, then the radical can be further simplified.

 

The radical must to equals zero.

If the capacitance equals the reciprocal of R1, then the roots are simply this.

But this creates a problem. R1 should be very small. This means that C would need to be relatively large, which we don't want. Thus, I will keep the root as it was.

Because R1 equals 1 kilo Ohm, L equals 0.1 Henry. Even if R1 equals 1 Ohm, the inductance would still be 0.1 mH.

I have come to the conclusion that RLC low pass filtering circuits are best used for attenuating very high frequencies.

It seems my best option is to use an active low pass filtering circuit. This way, the output resistance of the microphone will not effect the filtering equations, I can use much smaller values, and I can make the filter PCB foot print relatively small, even if the part number is relatively large.

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Electrical Engineer, Minneapolis, Minnesota