Choosing cathode bypass values

[Rhodesplyr]

When it comes to choosing a cathode bypass capacitor value for a typical guitar input stage, what tests/experiments do you run? What is your decision-making process?

I'm working on ~1957 single 6V6 amp with a 12" speaker, treble cut control only, no bass tone control, that was pretty obviously put together with whatever they had on-hand. The cathode resistor is 1.5k with a 6SN7 input tube, and you hear differences moving from 3.3uF up to 10uF. Once you're over 10uF, you're at the point of diminishing returns. Schematic value was 20uF. The actual original cap was 50uF.

Still, it seems to be a matter of taste, and it's hard to decide between having a full sound and too much muddiness. Owner may use it for lap steel.

[R.G.]

The hard part is deciding what frequencies you want to emphasize and de-emphasize.

After that it's C = 1/ (2*pi*F*R); C is capacitance in farads, F is the "corner frequency" where the rolloff is 6db down, and R is the resistor associated with the cap.

A cap in a cathode gives full gain at all frequencies well above F = 1/(2*pi*R*C) for a cathode resistor R. Below that frequency, the gain is determined by the ratio of Rplate and Rcathode. Above it, the cap makes the cathode resistor disappear to the AC signal, so the triode runs its fully bypassed cathode gain.

[Chuck H]

For anything with AC filaments it's good to operate the first gain stage fully bypassed (22u or better) for the best hum prevention. That doesn't mean I always do it or that it always mitigates significant hum. But pay attention for any hum level difference between the partial any fully bypassed. If you find you want to keep the first cathode fully bypassed there are other ways to shape the signal.

[Rhodesplyr]

For anything with AC filaments it's good to operate the first gain stage fully bypassed (22u or better) for the best hum prevention. That doesn't mean I always do it or that it always mitigates significant hum. But pay attention for any hum level difference between the partial any fully bypassed. If you find you want to keep the first cathode fully bypassed there are other ways to shape the signal.

Interestingly, in this amp, a Lectrolab R400, complete bypassing with 22uF actually increases hum compared to 4.7uF, which is what I ended up using.

I do understand the usefulness of AC-grounding the cathode to reduce heater hum, but, in this case, dealing with a very cheaply-built amp with a grounding scheme designed to save money, it doesn't work that way.

The amp uses a thick copper wire buss that runs through all the control pot grounds and hooks to the input jack grounds. Then, they hung grid-leak and cathode resistors off this copper buss wire. It uses the chassis as part of the ground path. It was obviously designed to be thrown together in a few minutes with a minimum of parts and effort...

[Justin Thomas]

And this is why I follow the "rules" as best I can, as PRINCIPLES, not Laws. It's good to know the theory and why of doing things a certain way, but sometimes...

I was rebuilding a Gibson Thor, and after a few years of trying to get rid of a horrible hum, I was about to give up. Then I heard about someone having a particularly noisy transformer. I ran some long clip leads all over the place inside & outside the chassis, and ended up changing one ground wire out for about 12" of solid-core wire, and ran it all over the chassis and through a couple holes. That long wore routed in such a convoluted way killed nearly 90% of the PT radiated hum. Yes, it broke all the "rules" of grounding, but it had to be done.

My only electrical "law" is Ohm's Law.

Justin

[Justin Thomas]

It was obviously designed to be thrown together in a few minutes with a minimum of parts and effort...

Is the cabinet laminated corrugated cardboard, too? Like the one Lectrolab R600-B I worked on?

Justin

[Rhodesplyr]

Is the cabinet laminated corrugated cardboard, too? Like the one Lectrolab R600-B I worked on?

No, this one actually has a pretty decent cabinet covered in two-tone leatherette. Not sure if it's plywood or solid wood.

This amp uses two 6SN7s, one 6V6, and one 5Y3.

[Gnobuddy]

After that it's C = 1/ (2*pi*F*R); C is capacitance in farads, F is the "corner frequency" where the rolloff is 6db down, and R is the resistor associated with the cap.

A cap in a cathode gives full gain at all frequencies well above F = 1/(2*pi*R*C) for a cathode resistor R.

That should be (3 dB) down, not 6 dB. That was probably just a minor typo.

However, the formula itself, while very popular, is actually wrong. The "R" that matters isn't the external cathode resistor. It's the invisible "internal" cathode resistor, which has a value of (1/gm).

More accurately, the proper resistance to use is the internal (1/gm) resistance in parallel with the external cathode resistance Rk. Usually (but not always!), the parallel combination is dominated by the (1/gm) term, as Rk is usually much larger than (1/gm). So usually we can ignore Rk, and just use (1/gm).

The simplest way to see that the F = 1/(2*pi*Rk*C) formula is wrong is to do a simple thought experiment. Replace Rk with an ideal current source, so Rk is tending to infinity as far as AC is concerned. The formula now predicts that C should tend to zero for full bypassing. Which is obviously nonsense, in fact, voltage gain will be essentially zero in this situation! We have an attenuator, not an amplifier!

If, on the other hand, you use F = 1/{2*pi*(1/gm)*C}, which simplifies to F = gm/(2*pi*C), then you get the correct answer. C isn't zero, it's given by C = gm/(2*pi*f).

If you don't like algebra, the next easiest way to confirm the original formula is wrong, is to run a simulation in LTSpice or similar. Use a big 10k cathode resistor on a 12AX7 SPICE model with a transconductance of 1600 micro Siemens, bias the grid up to +8.5V or so to get a milliamp of cathode current through that 10k cathode resistor, use a 0.1592 uF cathode bypass capacitor. The (wrong) formula F = 1/(2*pi*R*C) says you'll get a 100 Hz as your (-3dB) frequency. But that's not anywhere close to what you'll see in the simulated results!

Now if you use the correct formula C = gm/(2*pi*f), and plug in 100 Hz and 1600 u Siemens, you find that you should be using a 2.55 uF capacitor, not the 0.1592 uF value given by the wrong formula. So edit your LTSpice schematic and change the cathode bypass cap to 2.55 uF; run the frequency response plot again, and this time you'll get the proper (-3 dB) response at 100 Hz.

The most significant takeaway from all this is that the optimum cathode bypass capacitor value varies with the gm of the tube being used. Use a 6AG5 in a preamp stage instead of half a 12AX7, and you need about triple the cathode bypass capacitance to produce the same low-frequency response curve (the 6AG5 has a gm around 5000, compared to around 1600 for the 12AX7). I have indeed used a 6AG5 small-signal gain stage, and I did indeed need triple the cathode bypass capacitance compared to a 12AX7.

Incidentally, I have seen the exact same wrong formula very frequently in the analysis of common-emitter BJT transistor stages, too. Many textbooks give the F=1/(2*pi*Re*C) formula, which is quite wrong. As before, Re should be replaced with the internal dynamic emitter resistance of the transistor.

For a BJT, the internal small-signal AC emitter resistance is about (0.026/Ie) ohms, where Ie is in amps. Substituting that into the formula and rounding off a little for convenience gives us f = 40*Ic/(2*pi*C).

As long as Rk is much bigger than (1/gm), the correct formula for the lower cutoff frequency actually does not contain Rk at all. This may be what confuses people into using the wrong formula - how can it be that the cathode resistor apparently doesn't matter? The answer is, it does matter a little bit, but what matters much more is the invisible cathode resistor inside the tube, with a value of (1/gm).

Note once again, that there are some cases where the value of the external Rk does matter, namely, whenever it is close to (1/gm) in value, so that the parallel combination of Rk and (1/gm) is significantly smaller than (1/gm) alone. To use the 12AX7 as an example, (1/gm) is about 600 to 700 ohms, depending on bias point. If you're using an external Rk of, say, 820 ohms, then that is comparable to the internal (1/gm) value, and in this case, you should calculate (Rk in parallel with 1/gm), and use that value in the formula, rather than just (1/gm) alone.

The funny thing is that there is never a situation, however, where the proper resistor to use is actually only the external one, Rk. The most commonly offered formula is always wrong when it comes to calculating the (-3 dB) frequency!

One final thing to add, for those who like an extra serving of theory: a valve with a bypassed external cathode resistor actually acts like a shelving filter, and not a simple high-pass filter. There are *two* break points in the frequency response. The formula R = 1/(2*pi*Rk*C) is wrong for calculating the (-3 dB) frequency - but it is correct for calculating the (usually irrelevant) lower shelving frequency. The formula I gave - C = gm/(2*pi*f) - is the one to use to calculate the -3 dB frequency, which is what we usually care about.

-Gnobuddy

[Gnobuddy]

The cathode resistor is 1.5k with a 6SN7 input tube, and you hear differences moving from 3.3uF up to 10uF. Once you're over 10uF, you're at the point of diminishing returns.

Out of curiosity, I did a few calculations using the correct bypass cap formula (which I just posted).

From the datasheet, gm is about 3000 uS for the 6SN7. That means (1/gm) is roughly 333 ohms.

The external Rk is 1500 ohms. Put that in parallel with (1/gm), that's now 1500 ohms in parallel with 333 ohms. That works out to about 273 ohms.

The lowest note on a six-string guitar in standard tuning has a frequency of about 82 Hz. Plug 82 Hz and 273 ohms into the usual RC filter formula, and you get:
C = 1/(2*pi*273*82) = 7.1 uF.

So using the proper equation, we find that a 7 uF cap will give you a response that's 3 dB down at the very lowest note a guitar can play. Three decibels down is an audible change, but quite a small one. So we can expect that using any capactor bigger than 7 uF will give us increasingly diminishing returns.

Given the inexactness of everything we're working with - the value of gm, the tolerances in capacitor values, the inexactness of the human ear - I would say this calculated prediction agrees extremely well with your observation that 10 uF was the point of diminishing returns.

-Gnobuddy

[Rhodesplyr]

This online cathode bypass calculator suggests that at 7.1uF, you're only down 0.22dB at 82Hz with this circuit:

Tube = 6SN7
Rg = 500k
Rl = 47k
Rk = 1.5k

https://www.ampbooks.com/mobile/ampl...ode-capacitor/

Cathode bypass capacitor calculations are actually pretty complicated when you look at the whole circuit. It's why many people do it by ear and experimentation based on experience with standard values.

[Gnobuddy]

This online cathode bypass calculator suggests that at 7.1uF, you're only down 0.22dB at 82Hz with this circuit:

Tube = 6SN7
Rg = 500k
Rl = 47k
Rk = 1.5k

https://www.ampbooks.com/mobile/ampl...ode-capacitor/

That most probably means the online calculator also contains the wrong formula. As I mentioned, the wrong formula is very widely used - this is a pervasive mistake. That (wrong) formula "thinks" that the resistance to be bypassed is 1.5k. In reality, it should be 273 ohms.

Try raising Rk to 15k in the online calculator. Does it tell you that 0.129 uF (that's 129 nF) now gets you -3 dB at 82 Hz? If so, that proves the online calculator is using the wrong equation. ( The fact that the online calc isn't asking you for the valve's gm is another tip-off that the calculator is doing the wrong thing. )

Real simulation software (like SPICE and its derivatives) do not contain this sort of mistake. That's why if you run an LTSpice sim, you'll get the correct answer, assuming you have a good model for the valve/tube in question.

-Gnobuddy

[Chuck H]

One thing about cathode bypass caps in typical guitar amp circuits is that the actual gain increase will only be 5 to 6dB. The typical 3dB criteria gets lost a little IMHE regarding listening tests That is, the +3db point doesn't sound like the audible knee (maybe because it's 50 ish % of the total change?), the +5 or 6dB point does. And that could be why a 1uf cap across a 1.5k cathode resistor on a 12ax7 has a +3dB around 150Hz but audibly it predominantly accentuates the upper mids and HF. You can tell me what the numbers say all day, and I'll listen too. But this is what my ears tell me. And I can tell by values chosen is many designs that my ears aren't the only ones hearing it this way. That should be a significant consideration to the discussion.

[Rhodesplyr]

I chose a 5uF bypass because I actually wanted a little bass cut. It's been my experience with some 50s guitar amps that have only a Treble tone control can sound bloated in the bass if there's not some sort of high-pass filter. Some of the best-sounding small amps of this type I've heard have high-pass filters right at the input.

[Chuck H]

I chose a 5uF bypass because I actually wanted a little bass cut. It's been my experience with some 50s guitar amps that have only a Treble tone control can sound bloated in the bass if there's not some sort of high-pass filter. Some of the best-sounding small amps of this type I've heard have high-pass filters right at the input.

See, now, that's my point in post 13. According to a calculator a 5uf bypass cap is less than half dB lower in gain at 82Hz than at 10k!?! Gnobuddy might have more sensible numbers that differ from the on line calculations too, but if you're hearing a bass cut over fully bypassed then you're hearing it. In fact, considering what I hear when compared to any figures calculated, by a calculator or an individual, it always seems to me that the perceived tonal change with partial bypass sounds like a higher frequency than the numbers give.

[Gnobuddy]

One thing about cathode bypass caps in typical guitar amp circuits is that the actual gain increase will only be 5 to 6dB.

That certainly seems to be the case for 12AX7s, with their rather low gm. So the cathode bypass cap isn't a very powerful way to shape the frequency response with these low gm triodes. Which happen to be the most widely used preamp valves of all!

I have been tinkering with some valves from the $1 lists, some of which are high gm triodes or pentodes originally used in TVs. With those, the two corners of the shelving filter response tend to be further apart, 10 dB or more depending on the bias point and Rk.

Even so, the input coupling capacitor seems to be a much more powerful way to shape triode frequency response. And the screen grid bypass cap seems to work very well for pentodes, but the proper value is hard to estimate theoretically, so I do it empirically, by measurement.

-Gnobuddy