Is there a formula...

[12AX7]

that will tell you when you change the cathode's R value on a gain stage what you should do with the cap to maintain the same tonal balance? for example, i had a 1.5k/.68mf on V1 and changed the resistor to a 2.2k. So now it's a bit thinner sounding due to the resistor value allowing for a larger balance of the cap's effect in the tone.  Is there a formula for what cap to use that would bring the same tonal balance back as before? Or would it be best to just dial it in by putting a trimmer inline with the cap ?

[jazbo8]

Check out Fred's blog here, I think he wrote something on it.

[12AX7]

Thanks, but i think that may be in a different article because he says this right at the start...

The values of both the anode resistor and the cathode resistor will be left alone for the moment for they will be addressed in a later post

[jazbo8]

I could swear he wrote it up, may be it was just on AX84, anyway, head on over to Merlin's page and download the chapter on triode amplification (see p.26). But it's just f=1/6.28xRkxCk and I am pretty sure it is hard to tell the difference between 1.5K and 2.2K if you leave the Ck the same.

[12AX7]

yeah, it's not a big change but i can telll it sounds a bit thinner, and if i raise 2 stages the same it becomes real obvious.

[sluckey]

for example, i had a 1.5k/.68mf on V1 and changed the resistor to a 2.2k.... Is there a formula for what cap to use that would bring the same tonal balance back as before?

R1 x C1 = R2 x C2
C2 = R1 x C1 / R2
C2 = 1.5 x .68 / 2.2
C2 = 0.4636363636363636

[HotBluePlates]

Use what Sluckey wrote.

Or, use the formula jazbo posted, and find "f" for your original setup. Now take the formula, transpose the location of "f" and "Ck" and solve for Ck's value.

... i had a 1.5k/.68mf on V1 and changed the resistor to a 2.2k. So now it's a bit thinner sounding ...

Which you'll find from the math doesn't compute, because if either C or (in your case) R gets bigger, the roll-off frequency moves lower.

So fastest way for you to figure what you'll like is to try a different (bigger) cap in the circuit and decide what sound you like best.

[PRR]

Bigger resistor, smaller capacitor.

For hi-fi bass in an 8 ohm speaker you find 1,000uFd.

Hi-fi bass into a 1Meg grid resistor you find 0.01uFd.

Resistance goes up 1Meg/8 = 100,000 times, capacitor goes down 1,0000/0.01 = 100,000 times.

For your small 2.2/1.5 difference, you want a number like 0.46uFd.

[12AX7]

Odd. Seems my hearing is opposite of what i'm supposed to hear ! I swear it sounds thinner, and i thought it was because the .68 cap's influence on brightening that stage would be more so if the resistor were bigger. Just like that thread i started about using pf values from one PI plate to the other and parallel gain stage plates. They remove high end, yet i always hear what sounds like a thinner sound ! Weird. Well, in any case thanks, i will try a .47uf.

Actually, now that i think about it, it makes sense. A .47uf will cut off the frequencies it allows to pass higher up, so less high end gain overall. Thinking about it, this may just do something i've been trying to accomplish, and i've tried a lot of bypass values up to 22uf, but i never thought to go below .68uf.

[HotBluePlates]

.... A .47uf will cut off the frequencies it allows to pass higher up, so less high end gain overall. ...

No, that's backwards. Smaller cap = more low end stripped out. Highs remain unaffected, but because more low/low-mid is removed, highs seem boosted by comparison.

Do what jazbo said and look at p.26 of the download at Merlin's site. The graph is for a single cathode resistor value (and actual gain number refer to the specific stage he has pictured beside the graph). If you increase the cathode resistor, all of those curves are shifted to the left, and roll off at lower frequency. So while smaller caps still result in rolling off more bass, the specific frequency is changed if you change the cathode resistor value; it's interactive because both things impact frequency.

I have no explanation for why you're hearing what you're hearing. Maybe you're hearing the brightness of the amp in a new light as a result of the changes.

[12AX7]

Well, thats basically what i'm saying. You're talking about rolling off low end up to a certain frequency. Basically i'm talking about the volume relationship between the highs and lows regardless of how it's accomplished, be it raising certain frequencies or lowering the other. For example, if you took 1/2 the sliders on a EQ from the middle up and raised them 3 DB, it would be the same if you instead lowered the other side 3DB then adjusted the master volume to compensate. So i'm talking about the tonal balance and by going to a .47uf you would just see less of the high frequency range being louder from the rest of the range. The cutoff would just be higher up the range than a .68uf. I get that. And i think going to a even smaller cap than a .47ufmay accomplish something else i have thought about and i will try it tonite. It may fail my expectations miserably, but i'll give it a go.

[HotBluePlates]

Odd. Seems my hearing is opposite of what i'm supposed to hear ! I swear it sounds thinner ...

I've got the answer.

Notice that when you look at Merlin's graph, the roll-off due to the bypass cap is not like that in a coupling cap. Rather than a roll-off that continues down to nothing, the slope goes from full (bypassed) gain to a lower (unbypassed) gain. The lower gain limit is due to feedback from an unbypassed cathode resistor, which is the case at a low enough frequency that the cap looks like a large impedance compared to the resistor.

Two things happen when you rasie the cathode resistor's value, while making no other changes:
- The roll-off frequency shifts lower due to the larger resistance (which has the effect of passing somewhat more low end)
- The lower gain limit due to feedback shifts downward (due to more feedback across the now-larger cathode resistor)

This is equivalent to a shelving-type EQ, where all bass was reduced. Even though the bypass cap now roll-off at a lower frequency and thus passes more low end, all remaining low end is reduced in relative volume. The net result is that the treble seems boosted by comparison, because the level difference between the bypassed and unbypassed gains is greater.

So you're not hearing things, even though the math when focused just on the cathode resistor and cap would suggest you should hear more bass. The near-doubling of the cathode resistor resulted in more feedback, reducing the bass compared to the treble being bypassed by the existing bypass cap.

[12AX7]

So, I haven't lost my mind after all?!

[tonewood]

So, I haven't lost my mind after all?!

Not sure about that but...
Some people say warmer bias = fatter sound. The larger Rk means cooler bias, could that contribute to a thinner sound?

[HotBluePlates]

Some people say ...

Beware of sweeping generalizations. It's very easy to find examples that don't fit with what "some people say"... 

Larger Rk, by itself, doesn't tell you anything about how the stage is working. You need more information to try to characterize, or you need more experimentation with a pot in place of Rk to determine a favored value.