Low-pass filter with C but no R

[carbonzit]

This is something that's bugged me for some time now.

I hasten to point out that IANAEE (I am not an electronics expert); I know enough to get into trouble, and maybe a little more. Hence my puzzlement on this point.

In another thread there's a discussion of why, when a guy added a series resistor to the input of an amplifier, it degraded the sound quality by what sounded like attenuating high frequencies, the classic effect of a low-pass filter. The theory advanced was that by adding the series resistor, it formed a low-pass filter with an already-existing capacitor at the input of the amp.

This does not make sense to me. Let me explain why.

This shows the classic low-pass filter with both a C and R, but also simply a C:

We know the C-R network forms a low-pass filter. But doesn't a C by itself also form one? It's simply the degenerate case where R=0, right? It will still function to attenuate high frequencies. Look at power supplies that have filter capacitors but no series resistors (some have them, some don't). There's your R-less LPF.

Just to be clear, I am not suggesting that one doesn't ever need an R to make a LPF; it's certainly needed to create the proper response curve, rolloff and cutoff frequency. But if that amplifier already had a C across its input, I don't see how adding an R would suddenly create a LPF where none existed before. It would certainly change the response of the filter, but my guess is that it would have less effect, overall, than the C already has.

So what am I missing here? I'll let the experts here respond.

 

[crutschow]

So what am I missing here?

To create a low-pass filter there is always some R, even if it's not explicitly shown.
If R were truly zero than the LP rolloff frequency would be infinity--clearly not a real-world possibility.
So a real signal source will always have some finite impedance, even if it is small.

A power supply likely will have a low output impedance at low frequencies, but the impedance generally goes up with frequency.
The output capacitance then keep the impedance low at the higher frequencies.

 

[Nigel Goodwin]

The 'r' is the source impedance, so the configurations are identical.

 

[carbonzit]

The 'r' is the source impedance, so the configurations are identical.

So are you saying that even if you omit the R, it'll still be present as whatever the source impedance (output impedance of the source) is? That makes sense; there's always some R, even if not explicitly placed as part of the LPF.

To create a low-pass filter there is always some R, even if it's not explicitly shown.
If R were truly zero than the LP rolloff frequency would be infinity--clearly not a real-world possibility.

So even in a power supply with filter capacitors but no resistors, there's some R (the resistance of wires, diodes, etc.).

So what I showed as "C" with no "R" is a valid LPF, yes?

Would this be a fair representation of a LPF with C but no R?

 

[ronsimpson]

The R might be just the wire going to the cap.

 

[carbonzit]

OK, so this discussion has gone pretty much the way I thought it might. But something still bothers me:

When we draw a schematic for a circuit, we generally don't show things like the resistance of wires, or the mutual capacitance of adjacent conductors or the self-inductance of wires, right? (To be clear, I'm not talking RF here! Those things become actual components at those frequencies.) Even though we recognize that every component has some L, C and R in it.

So when I show a LPF with just C and no R, that's exactly what I mean: whatever R there is in wires or other components should be completely swamped by the other components, since R is essentially zero, correct? So in other words, we can have a LPF that has (virtually) no R.

If we had to show all those existing but usually ignored things, our schematics would look like hell and be pretty indecipherable.

 

[Papabravo]

In simulations it is not uncommon to add parasitic components to achieve results that more closely resemble reality. If the purpose of the schematic is to layout a PCB then the parasitics are not represented, but that does not mean they are not there.