Help with equivalent resistor/capacitor

[Bob D]

I want to simplify a circuit down if possible but I'm struggling to understand the relationship of resistors and capacitors when the caps are bypassing the resistors. Can someone tell me the equivalent resistor/capacitor for the following?

a) a 3k3 resistor with a 1u cap in parallel
b) a 2u2 cap in series with a)
c) in parallel to the 2u2 cap there is the following components:
a 10k resistor in series with a 2k2 resistor.
a 22u cap in parallel with the 2k2 resistor.

know it's hard to describe in words but maybe someone could sketch it out?

Thanks in advance for any help

Bob D

[Jazz P Bass]

The cathode bypass cap is frequency dependant.
It also allows for maximizing the gain of the stage (by minimizing degenerative feedback)
Not being too much into the math, here are a few links.
Cathode Bypass Capacitor Calculator

[Bob D]

Help with equivalent resistor/capacitor

Thanks for taking the time to reply JPB!

I have a basic understanding of the purpose of the bypass cap and how it helps shape the tone of the gain stage.

What I don't understand is how to simplify this circuit into a single resistor and capacitor. Can you or anyone else help with this?

[Jazz P Bass]

I am out of the loop if you are talking 'Spice'.
The key word here may be 'circuit'.
The resistor & the capacitor are part of a circuit.
They do not exist alone.
And the parallel combination has a different response to Vac & Vdc.
Here is some more math.Resistors and Capacitors in Parallel · Teaching Notes · Department of Chemical Engineering and Biotechnology

[Steve Conner]

You can simplify it to a single resistor and capacitor, but it will only be valid at a single spot frequency.

The reason is that a single RC has one break frequency and a 6dB/octave slope, but a more complicated network can have several breakpoints and different slopes than 6dB. The most famous example is the network for converting white noise to pink noise, which uses a half dozen Rs and Cs to approximate a 3dB/octave slope.

[Bruce / Mission Amps]

I want to simplify a circuit down if possible but I'm struggling to understand the relationship of resistors and capacitors when the caps are bypassing the resistors. Can someone tell me the equivalent resistor/capacitor for the following?

a) a 3k3 resistor with a 1u cap in parallel
b) a 2u2 cap in series with a)
c) in parallel to the 2u2 cap there is the following components:
a 10k resistor in series with a 2k2 resistor.
a 22u cap in parallel with the 2k2 resistor.

know it's hard to describe in words but maybe someone could sketch it out?

Thanks in advance for any help

Bob D

It sure would be nice to know what the heck this is for or where it is in relationship to a circuit and high or low impedance sourcing... etc. All those parts seem to be low in frequency response with respect to most guitar playing so here:

-3dB points
3k3||1uF = 48Hz
2k2||1uF = 72Hz
2K2||22uF = 3.3Hz

[Bob D]

Help with equivalent resistor/capacitor

This is a cathode resistor/cap for a guitar amp gain stage.

I was just trying to reduce part count if possible. It sounds like there is no single resistor/cap that will replicate it so I'll leave it as is.

Thanks for the replies!

[Jazz P Bass]

Do you have any more information?
What amplifier, what stage?
This is a strange setup, for sure.

[Bob D]

This is the 2nd gain stage from channel 2, mode "C" of a marshall 6100 amp. I had this amp a while back and I always loved this particular channel so I'm baking it into a homebrew channel switcher. I think the designer did it this way because he had three "modes" on a single channel.

[Jazz P Bass]

Thankyou for that bit of info.
Now it makes sense.
You are correct as to the three nodes using that circuit.

[Dave H]

Thankyou for that bit of info.
Now it makes sense.
You are correct as to the three nodes using that circuit.

You've done it again! I was just about to post that schematic from here

[J M Fahey]

Bruce Mission's comment is the right one: what the h*ck is this used for?
Plus, now I see the actual schematic, your description is incomplete.
And "looking for a 1 cap/1 resistor equivalent" is missing the point.
In a *very* simplified analysis, this setup supplies 2 different gain levels (modes B and C) with very little or unimportant frequency shaping.
To begin with, in both modes the DC value of cathode resistors is the same (2K2+10K+3K3) so bias does not vary.
Now to AC.

Mode B)
R22 and R38 are bypassed at guitar frequencies, one of them at 3.3 Hz so it can be considered a short *always* , and the other at 72 Hz so it *slightly* cuts subsonics. (Thanks Bruce for the Math )
I say slightly because they are in series with much higher R6 (10K) , which ends up being the main influence.
So in Mode B you can consider this a gain stage with 10K cathode resistor.
Did anybody say "JCM800"?

Mode C)
Basically R6 becomes bypassed, gain rises a lot, Fc is very low so we see basically a lot of gain flass across the whole guitar band.
R38 also "gets bypassed" but this is basically irrelevant, since it was already bypassed by C25.
And now C20 becomes somewhat more important.
I would build it as-is and call it a day, but if you are desperately trying to reduce parts count, I'd use the following string:
cathode>4K7 or 5K6 bypassed with .47>10K bypasses(or not, at will) with 22uF.
Would keep the 100K to ground (across the new switch) to avoid thumps and being referenced to ground, my Mod would ease switching, which might be accomplished by a FET, CMOS gate or even a cheap transistor.
But it's up to you.

Or, even simpler, would use a "JCM800 style" unbypassed 10K or 15K cathode resistor , and bypass it with a 22uF or 10uF or 4uF7 capacitor (chosen by best sound to your ear) , always keeping the 100K anti pop across switch.

And next time post a schematic, makes things easier.

[Enzo]

But to answer your original question, think of the caps and resistors separately. Resistor or not, two caps in parallel add up. So a 1u and a 2u2 cap in parallel just makes a 3u2 cap. The resistor doesn;t change that. It has no way to know that your 3u2 capacitance is two caps, one cap, or fifteen caps. Yes, of course changing the part values changes the frequency points, but I didn't see that in your question.

Series resistors just add as well. SO a 10k and a 2k2 resistor in series becomes a 12k2 resistor.

[Bob D]

Help with equivalent resistor/capacitor

Being able to treat the resistors and caps separately was what I was unsure of.

Thanks Enzo.