# Interstage Filtering Question

Discussion in 'Shock Brother's DIY Amps' started by cometazzi, Sep 26, 2021.

1. ### cometazziTele-AfflictedSilver Supporter

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Today's \$14 Question: How does one calculate a frequency limiter of inter-stage capacitors and resistors in parallel?

I know the formula for calculating frequency knee/rolloff with a regular R/C filter where one goes to ground, like this low-pass filter:

But I don't know one if they are in parallel. I.e., the front end of the Heavy Watter:

There's the usual (a la Fender) .022uF capacitor that takes the signal off the plates and sends it on to the next stage. Here, they're followed by a 470K/3n3 and 470K/470p arrangement in the first and second stage, respectively. As I interpret that, the 470k resistor on the first one attenuates some signal coming from the coupling cap, and the 3n3 allows a set of higher frequencies to pass around it (mostly) unaffected. Same for the 470p on the next stage.

The net effect is emphasis on higher frequencies, since a 'brighter' sound through a high-gain circuit (like this one) avoids farting later. That latter combination of 470k/470p is all over the triode coupling caps in the JCM800 preamp, an amplifier renowned in the Bad Ole Days for staying 'tight' when overdriven hard.

Also to note, the cathode bypass cap on the first stage is smaller than typical. Again, my SWAG is that it's designed to emphasize upper frequencies. The following two gain stages have typical (read: Fender) values on all the caps thenceforth.

I've been gargling the Googlemachine for some time now, but I'm striking out when it comes to a formula for calculating a frequency rolloff for resistor/cap in parallel. Also, I don't know if I would have to factor in the .022uF in series with the whole shebang either. Also suspect that the interstage calculation will probably be similar but different from the cathode bypass calculation.

Is anyone willing to spin me round and point me in the right direction?

THANK!

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2. ### James KnoxTele-Afflicted

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I’m in for the info! Good question, can’t wait to hear some answers...

3. ### Tom KamphuysTele-Holic

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4. ### guitar_paul1Tele-Holic

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I would approach it graphically using excel. Visual stuff always works better for me. Just an idea.

Make a column of reactance vs frequency on the cap.
Xc=1/(2*pi*F*C) where C is in Farads.
Then, using the parallel formula for the reactance and the resistance (R*Xc/(R+Xc) get a column of total impedance vs frequency.
Then make a scatter (x y) graph of that impedance and frequency.
I wouldn't think of it as rolloff, but it should give you a picture of what it is doing.
You can see at 1 Hz the cap does nothing, and you can see at 10KHz, the lower reactance of the cap dominates.
I think the frequency of that inflection point (around 2KHz) is probably what the designer was going for.
Knowing the impedance you can check to see how it interacts with the other circuit elements.
Oops forgot to label the far left column as frequency in Hz. Starting at 1 is a lazy way to avoid a divide by zero error in excel.
Phase will change with frequency, but since you have a single signal path you can ignore that.
This graph is for the 470 pF cap:

Last edited: Sep 26, 2021
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5. ### guitar_paul1Tele-Holic

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Here's the same chart (slightly cleaned up) but with the 3n3 capacitor in it instead.

6. ### guitar_paul1Tele-Holic

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Here are the charts for the cathode bypass caps. I would bet these cap values were experimentally determined as the amp was being prototyped.

Last edited: Sep 26, 2021
7. ### andrewRneumannTele-Afflicted

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I think the reason you haven’t found anything on google is that a resistor and capacitor in parallel doesn’t create a filter. It just sinks current.

Yes, if you want to get a handle on the total effect of everything from previous stage anode to next stage grid.

Since I made the leap into designing my own circuits I’ve realized that every value is subject to experiment. Substitution boxes are our friends. I’ve been turned off to trying to pin down every value exactly before the amp is built. Even Merlin suggests starting off with 1n coupling caps and clipping in additional capacitance from there. The theory is all good and you all know I love a good theoretical conversation, but my experience is that my ears don’t always agree with the theory when I finally build something.

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8. ### Tom KamphuysTele-Holic

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For now let's assume the coupling cap lets all frequencies pass. Then we have a voltage divider. This divider has two extremes, one for DC and one for very high frequencies. For DC one can ignore the capacitor, for very high frequencies one can ignore the (top) resistor and the capacitor is a short. It that case the full input is at the output.
The output is 'halfway' these extremes at the frequency where the impedance of the capacitor is equal to the top resistor and their equivalent resistor is half their individual values.
This is called a shelf filter.

9. ### guitar_paul1Tele-Holic

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It's interesting the cathode bypass and the parallel combination off the plate on the first stage have the same corner frequency.

10. ### cometazziTele-AfflictedSilver Supporter

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Me too!

Thanks for that first link, it was exactly what I was looking for. I haven't had a chance to read the second one yet, but I will. Is all of Merlin's book online, or just select chapters? Every time I see a reference to his site a little voice tells me I should buy his book and read it 1472 times. It gets louder each time.

This is pretty clever, and I too do better with graphical stuff like this. I'm not quite skilled enough in Excel to reproduce that, but I bet I could figure it out over time. Thanks for building this, though. It shows the answer for this question, and gives me something to work towards.

Could be. Ace Pepper builds all kinds of custom amps, but I don't know much about them.

Same here. When I was experimenting with stompbox circuits, I would build something on a breadboard, get an earful of what it did, then start tweaking. I played with every single component. I never got any sub boxes as a result, as on breadboard it's pretty easy (and safe) to just pull a cap out of a live 9V-18V circuit and plug another one in its place. For resistors, I'd often just use a linear pot- tune it by ear, then measure the resistance. I had a great time sticking parts and snippets of various circuits together and I made a lot of neat stuff (and some real turds, too). I learned a lot doing this, but it was lots of 'rule of thumb' kind of stuff. That's all plenty useful, but I feel like I'm just a hack. I'd like to know more of the theoretical stuff as well

Would you be willing to recommend a brand or type of substitution box for resistors and caps for use in tube amplifiers? I mostly just see new Elenco kits and expensive vintage stuff (that probably needs all the passives replaced). I could build one from scratch out of my parts bins but I bet a kit is cheaper/nicer in the end.

Thanks again, Tom. The description was helpful, plus "shelf filter" and "shelving filter" have given me new leads on things to look up.

Yes indeed. Happy accident from experimentation, or planned design? This could sound like a religious debate!

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11. ### guitar_paul1Tele-Holic

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As far as cap sub box, I have had one of these for about 15 years and it's very useful for guitar and other audio stuff:
https://www.amazon.com/dp/B0002KX776/?tag=tdpri-20

I suggest the assembled one unless you really want practice on kit assembly.

There isn't any magic on the excel sheet I put up. No macros or anything. Only if you put a reference to a particular cell
you make it "sticky" by using the dollar sign. Like =\$B\$3 will always point to that cell for your constants.
It makes iterating on component values really fast.

12. ### andrewRneumannTele-Afflicted

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I’m in the same boat. I have an Elenco 1W resistor box and a home built capacitance box using a rotary 12 way selector switch. I also have an old Eico that is in the process of being rebuilt, but it’s a pain collecting all the values. If the those can’t do the job, I tack solder and clip in values—but a substitution box is far superior for AB comparison.

13. ### cometazziTele-AfflictedSilver Supporter

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Elenco 1W, like this?

These are the kits I was talking about:

Pretty cool but I would sub 1/2W (at least) metal film for all the resistors, as they look like a mix of 1/4W metal and carbon film. Can't see the V rating on the caps, and it tops out at 0.1uF.

Last edited: Sep 27, 2021
14. ### andrewRneumannTele-Afflicted

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Yeah I have the first box you posted. It works fine. I like that it's 1 W.

I don't have one of those other ones. If you can't determine the rating of the caps, it's useless.

Using substitution boxes is inherently noisy. Don't sweat about having the right type of resistor in there--as long as it can handle the current and voltage it's fine.

15. ### cometazziTele-AfflictedSilver Supporter

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Yours may be different, but the manual for the RS-500 suggests that 100K and up is only 1/2W. That's probably still good enough, but just an FYI:

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16. ### Tom KamphuysTele-Holic

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Buy it. It's the best 40 bucks you'll ever spend on anything tube related. Only the triode gain stage and grounding chapters are freely available online.

http://valvewizard.co.uk/Book1.html

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17. ### LowerleftcoastFriend of Leo's

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I have no clue if I am correct but here is my \$.02 observation to your \$14 Question. Our ears tell us the .022uF coupling cap does not work in series with the .0033uF bright cap. The resulting capacitance would result in a high pass filter which would cut off too much of the low frequencies. We don't hear a large reduction of lows with similar bright cap circuits.

Amp Books handles it as separate calculations.

https://www.ampbooks.com/mobile/amplifier-calculators/bright-boost/

The Amp Books calculators only addresses the issue with the statement, "It does not account for coupling capacitor bass attenuation."

I question if there may be some interaction with the two. Possibly partially making a second order filter of sorts.

It will be interesting to read what the number crunching shock brothers come up with to answer your \$14 question.

18. ### andrewRneumannTele-Afflicted

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19. ### LowerleftcoastFriend of Leo's

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So this simulator treats it much like the Amp Books calculator. They are pretty much separate filters. They do not form any kind of 2nd order RC filter.

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20. ### andrewRneumannTele-Afflicted

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