Electronic – What’s the difference between filters with the same cutoff frequency, but different component values

audiofilter

I've heard mention of this topic, and it seems pretty useful, as I'd like to design high-quality audio equipment & synthesizers. But I've never heard it explained, only mentioning that it "changes the sound".

Say I want a low pass filter with a cutoff of 1 kHz. There's a (theoretically infinite) number of component values I can choose. Two examples:

  1. 15 Ω resistor, 10.61 µF capacitor.
  2. 47 kΩ, 3.39 nF cap.

I heard it mentioned from an EE guru that this changes the sound of the filter. I even found the paper he mentioned of how it changes, but I couldn't make head or tails of it as it was heavily centered around math instead of sound. I'll try to find it again so ya'll can take a look at it.

If anyone can explain it — especially in terms of what value it would have for the sound of something — it would be fantastic.

Best Answer

The original question misses two important points that affect the choice. A passive R-C filter is usually situated between two active circuits - a driver, and a reciever. A driver practically has certain output impedance, and the receiving stage has finite input impedance as well. These two factors are missing from the question, and the result depends on the value of these impedances.

If you have an ideal driver with zero output impedance, and ideal receiver with infinite input impedance, then the choice doesn't matter, any pair of R-C will behave identically, and the "sound" will sound exactly the same assuming that R and C don't have significant voltage dependence. The only difference is that the first circuit will draw quite a bit of more power than the second one.

However, if your driver and receiver do have finite impedance as any real circuits do, these impedances effectively change the cut-off frequency, which does have an effect on how this entire circuit will sound.

For example, if you have a driver with output impedance of 50 Ohms and choose the circuit #1, this will lower the cut-off frequency of this filter by a factor of 4, because the filter RC will effectively have the R as 50+15 Ohms. Which might have a serious effect on sound.

If your input stage has, say, an impedance of 20 kOhms, and you select the circuit #2, the low-frequency gain will be 1/3 of the initial one, which again will sound differently.

In summary, values of a passive filter (its "characteristic impedances") should be selected in accord with impedances of the stages it is connected in between. Generally the input filter impedance should be much higher than the driver's impedance, and the input impedance of receiver stage should be much higher than the filter's output impedance, all impedances should be estimated at the cut-off frequency.

Alternatively, you can run simple SPICE simulations of the filter including correct models of outputs and inputs, and adjust passive RC values to get the best desired result.