Bass attenuation with bypass caps vs coupling caps in cascading gain stages

[elipsey]

If a pre-amp has two gain stages in series, should I expect a difference in sound between a configuration with a smaller first stage bypass cap and larger first coupling cap, versus an alternative configuration with a larger first stage bypass cap, and smaller first coupling cap, given that the frequency response of the combined stages is held constant?

For example, case one might use a 1uf bypass, and 22nf coupling cap into the second stage, whereas case two might use a 25uf bypass, and 1nf coupling cap into the second stage. I suppose that this is not enough information to actually determine that the two configurations will have the same frequency response in the given example, but I stipulate that they do so that we can discuss whether there will be any other effects from the change. If it matters, this is a high gain amp and the second stage is a cold cathode clipping stage.

I'm principally concerned with whether there is a difference in tone (subjective, I know), but also interested in other practical considerations.

Cheers

[uneumann]

If a pre-amp has two gain stages in series, should I expect a difference in sound between a configuration with a smaller first stage bypass cap and larger first coupling cap, versus an alternative configuration with a larger first stage bypass cap, and smaller first coupling cap, given that the frequency response of the combined stages is held constant?

For example, case one might use a 1uf bypass, and 22nf coupling cap into the second stage, whereas case two might use a 25uf bypass, and 1nf coupling cap into the second stage. I suppose that this is not enough information to actually determine that the two configurations will have the same frequency response in the given example, but I stipulate that they do so that we can discuss whether there will be any other effects from the change. If it matters, this is a high gain amp and the second stage is a cold cathode clipping stage.

I'm principally concerned with whether there is a difference in tone (subjective, I know), but also interested in other practical considerations.

Cheers

If I understand you correctly... two diffs I can see...

Smaller bypass cap lowers stage gain, which means more headroom for the first stage for LF notes.
Also 1st stage distortion is lower since bass effectively has nfb.

[R.G.]

I think you mean "cathode bypass cap" where you say "bypass cap". Is this right? I'm going to assume it is until you tell me different. I think of the electrolytics in the power supply string as bypass caps as well.

The two versions of high pass filtering have different results. The cathode bypass cap is a shelving lowpass. At frequencies below the RC turnover, gain is just the DC and very-low-frequency gain, set by the plate resistor, cathode resistor, tube mu, and loading. At frequencies above the RC combination on the cathode, gain rises at 6db/octave until it reaches the gain of the fully-bypassed cathode resistor/cap. Then gain levels off and stays there until other (irrelevant to this discussion) effect affect high frequency gain.

The coupling cap lowpass has no lower "shelf". It has truly zero gain at DC, and this rises at 6db/octave until it reaches the frequency where the capacitive reactance is equal to the combined loading. Above that frequency, the coupling cap does not restrict the stage gain.

Exactly how these two stages interact depends on where the relative turnover points are, and what the fully-bypassed stage gain is. It's possible to make the coupling cap rolloff so low that the frequency response in audio is completely determined by the cathode rolloff. It's possible to put the coupling cap rolloff so high compared to the cathode bypass rolloff that the cathode rolloff has little or no effect. And there is a wealth of ways to make them interact by moving the rolloff points near one another.

In fact, it would be difficult to make the "frequency response of the combined stages [be] held constant" because of the interactions of the two -6db slopes unless you deliberately made one so low or so high that it did not interfere with the other.

I know, I ought to draw some pictures. I'm lazy tonight.

uneumann is right - lower gain in the first stage will reduce clipping for those frequencies in the clipper. And another side effect is that once you remove signal, it's hard to get it back. If you cut signal with a coupling cap, you can't necessarily just raise the gain in those frequencies in a following stage and make it look like the signal wasn't lost to start with. Where in a signal chain signal is lost (or made too small to take part in things) matters.

[elipsey]

I think you mean "cathode bypass cap" where you say "bypass cap". Is this right?

Yep, that's what meant. I probably should have said so in the first place.

In fact, it would be difficult to make the "frequency response of the combined stages [be] held constant" because of the interactions of the two -6db slopes unless you deliberately made one so low or so high that it did not interfere with the other.

It occurred to me that my hypothetical might be impractical or even demonstrably impossible, but I was having trouble thinking of another way to ask the right question.

I know, I ought to draw some pictures. I'm lazy tonight.

Well, I probably should have too, but I was also lazy. Anyway, I think that actually makes lots of sense as is. If I were to plot the two curves of attenuation vs. frequency, I think the plot for the coupling cap would be linear, in the sense of having a non-zero but constant slope, on the interval from 0hz to the frequency above which the coupling cap does not restrict stage gain, while the plot for the cathode bypassed stage would have a lower shelf. Is that sort of right?

uneumann is right - lower gain in the first stage will reduce clipping for those frequencies in the clipper. And another side effect is that once you remove signal, it's hard to get it back. If you cut signal with a coupling cap, you can't necessarily just raise the gain in those frequencies in a following stage and make it look like the signal wasn't lost to start with. Where in a signal chain signal is lost (or made too small to take part in things) matters.

Thanks for clearing this up, I think I'm at least starting to see what's going on here. Pretty soon I will draw a couple of schematics of how I actually tested this out in real life and explain why and what happened, if anyone cares. I just wanted to ask about the theory before I muddied the waters with details or had to draw the schematics.

Thanks, Chris

[R.G.]

If I were to plot the two curves of attenuation vs. frequency, I think the plot for the coupling cap would be linear, in the sense of having a non-zero but constant slope, on the interval from 0hz to the frequency above which the coupling cap does not restrict stage gain, while the plot for the cathode bypassed stage would have a lower shelf. Is that sort of right?

Yes, that's right. For the cathode cap curve, the lower shelf is the unbypassed cathode gain, the upper gain is the fully bypassed cathode gain, and the slope between the two is one RC-filter slope. For the coupling cap, the gain at high frequencies is whatever it's fed from the plate, and it starts sloping down at the coupling cap/load impedance point with one RC slope down all the way to DC. The various combinations of the time constants can make places with a two-RC slope if the coupling cap and cathode cap slopes overlay one another.

Thanks for clearing this up, I think I'm at least starting to see what's going on here. Pretty soon I will draw a couple of schematics of how I actually tested this out in real life and explain why and what happened, if anyone cares. I just wanted to ask about the theory before I muddied the waters with details or had to draw the schematics.

You're welcome for anything I added. Go for it!

[pdf64]

With ac heaters, I think early stages benefit from better hum rejection if their cathodes are fully bypassed, ie at line frequency.
My finding is that if a stage is being heavily overdriven (unlikely for early stages), the overdrive tone is much smoother / controlled if its cathode is unbypassed, such that the bypassed / unbypassed difference seems rather larger when overdriven than when not, though it's not easy to quantify; maybe some sort of spectral analysis for harmonic content would help?

[R.G.]

With ac heaters, I think early stages benefit from better hum rejection if their cathodes are fully bypassed, ie at line frequency.

Hmmmm. Nice observation! It makes sense that if the heater is boiling off electrons in some way, whether from contamination with stuff boiled off the emitting cathode or whatever, a cap shunting this to ground would make things hum less. I'd love to see a spectrum of signal with two different bypass caps, one above 2x line frequency, and one well below 1x line frequency. Signal should be at midrange, 500-1Khz sine. The telltale would be a spike at 1x or 2x line.

My finding is that if a stage is being heavily overdriven (unlikely for early stages), the overdrive tone is much smoother / controlled if its cathode is unbypassed, such that the bypassed / unbypassed difference seems rather larger when overdriven than when not, though it's not easy to quantify; maybe some sort of spectral analysis for harmonic content would help?

Also a good point - it would be nice to see that. I suspect that the three different distortions - gate positive, plate cutoff, and "saturation" will be different, perhaps.

Nice observation!

[J M Fahey]

I distinctly remember reading old datasheets, where the hum spec was accompanied by a foot note, which read something like : "cathode bypassed by 25uF " (or was it 100 uf? ) , the point was absolutely unrelated to audio frequency response but to turning the cathode structure into a grounded shield around filament.

To boot, way back then it was common practice to ground a filament end, so measures like this definitely helped.

[Dave H]

I think of the electrolytics in the power supply string as bypass caps as well.

They are not bypass caps. They are filter caps.

[Dave H]

If I were to plot the two curves of attenuation vs. frequency, I think the plot for the coupling cap would be linear, in the sense of having a non-zero but constant slope, on the interval from 0hz to the frequency above which the coupling cap does not restrict stage gain, while the plot for the cathode bypassed stage would have a lower shelf.

The upper plot below is the coupling cap. The lower plot is the bypass cap.





Edit:
Sorry for the faint plots. They looked fine before they were uploaded.

[Chuck H]

They are not bypass caps. They are filter caps.

Enzo is one person here that has commonly referred to their function at the preamp end of the string as "decoupling" caps. It's a very useful perspective. And also lends to R.G. position. There isn't much filtering necessary at that end, but you sure as hell do need to get any signal AC off the power supply there. Of course they do the same thing as the main filter too. Serving double duty.

[Dave H]

Enzo is one person here that has commonly referred to their function at the preamp end of the string as "decoupling" caps.

And paradoxically they "decouple" by coupling the power rail to ground to AC.

[Chuck H]

And paradoxically they "decouple" by coupling the power rail to ground to AC.

Right! Just like a "cathode bypass cap" does. It's easy to see R.G.'s position is you imagine a tubes internal resistance and it's cathode resistance analogous to power supply rail resistors. If a tube cathode is AC bypassed there is no AC interaction (local negative feedback) at the cathode "node" and if an HV rail resistor is AC "bypassed" there is no AC interaction at that node. Same thing really

[Dave H]

I wasn't really being serious. I was just thinking it would be less confusing if all these capacitors had unique names. For example we could call the first capacitor after the rectifier a 'filter cap', capacitors between power supply nodes 'decoupling caps', signal capacitors between stages 'coupling caps' and capacitors across cathode resistors 'bypass caps'.

[pdf64]

we could call the first capacitor after the rectifier a 'filter cap'

I've often seen that referred to as the 'Reservoir' (and used the term myself without being queried)?