Removing Bass Frequencies

[clyde]

What would be the difference between making the coupling cap smaller or the cathode cap smaller in your typical 12AX7 gain stage for losing some lower frequencies?  Thanks.

[sluckey]

What would be the difference between making the coupling cap smaller or the cathode cap smaller in your typical 12AX7 gain stage for losing some lower frequencies?  Thanks.

They both will lose some lower frequencies, although in different ways. Changing the coupling cap simply changes the RC time constant to affect the frequency response. Changing the cathode bypass cap changes the frequency response of the degenerative feedback such that the tube gain is actually frequency dependant.

[jjasilli]

Point of clarity: the cap attenuates some frequencies; those frequencies are not "lost" in the sense of vanishing completely.

Probably the main issue here is with an overdriven gain stage. Too much bass into the tube will muddy overdrive tone. Overdrive produces lots of harmonic overtones which are higher notes by definition.  So as a general rule of thumb it may be desirable to attenuate lows on the way in, and highs on the way out, of an overdriven gain stage.  There may be multiple cascading gain stages, connected by R-C networks and with cathode bypass caps of different values (whose effects can be reduced with a R under the bypass cap to ground). 

Overdrive tone shaping can be complex.  I'm not sure there is a simple answer to your question. 


However if the coupling cap attenuates lows at 6dB per octave at the crossover point; and the cathode bypass cap boosts lows at 6dB per octave a the same crossover point THEN this is the same as using caps which pass the entire audio spectrum (at least in theory, subject to real world tube performance).


I suspect that a cathode bypass cap is also in the signal path (though in a less obvious way than a coupling cap); so it too may yield a time-constant (phase) issue.  Happily this is not an issue in guitar amps anyway.

[shooter]

changes the frequency response of the degenerative feedback

I'm about to tackle this issue on my last build, except opposite, I have low gain? bass, with some muddiness.

I have the freq roll-off chart showing Ck vs freq, but if I increase Ck, from the reply does that limit the *new* gain to the bass freq's, or does the over all tube gain increase?  (I have way plenty gain - overall)
thx

[jjasilli]

Shooter, I think I understand your question:  You're asking about the effect on frequency response of a cathode bypass cap:  as the valuer of the cap decreases, hi frequencies get boosted more than lows.  For specific results, see your chart.  The following is a general explanation.


Inside the tube there is naturally occurring degenerative feedback which reduces the actual mu of the tube to about 1/2 of its full potential ability to produce gain.  The cathode bypass cap bleeds the offending negative feedback to ground.  For a typical 12ax7 gain stage, a 25uF  cathode bypass cap bleeds the entire spectrum of frequencies of such negative feedback to ground.  Hence the tube's gain is doubled for the entire frequency range. 

If a small value cap is used, then only hi frequency negative feedback bleeds to ground.  Hence, only hi signal frequencies will get boosted within the tube, while lower signal frequencies will get less -to- no additional boost from the bypass cap.

The gain boost might seem to be working "backwards":  By bleeding away hi frequencies we're boosting hi frequencies!!!  That's because the frequencies drained away are negative feedback.  By reducing the negative, we're boosting the positive.

The bypass cap will always boost hi frequencies.  As the value of the cap increases, it boosts lower and lower frequencies along with the hi frequencies.

[sluckey]

Inside the tube there is naturally occurring degenerative feedback which reduces the actual mu of the tube to about 1/2 of its full potential ability to produce gain.  The cathode bypass cap bleeds the offending negative feedback to ground.  For a typical 12ax7 gain stage, a 25uF  cathode bypass cap bleeds the entire spectrum of frequencies of such negative feedback to ground.  Hence the tube's gain is doubled for the entire frequency range. 

That's wild! Where did you hear that?

[jjasilli]

Examples:  "You can double the gain of a cathode stage by adding a Cathode Capacitor. . . If the Cathode Cap is made small . . . low frequency gain will be reduced.  .  . Reducing the low frequency gain is the same as increasing the high frequency gain."  Dave Funk's Tube Amp Workbook, Chapter 13, The Preamp, pp. 96-7.


"Capacitor Ck is used to bypass the cathode resistance to ground for AC signals, which results in a higher gain.  Without Ck, there is negative feedback, or degeneration, which reduces the gain of the stage and increases the output impedance.  If Ck is not large in comparison to Rk, it will affect the frequency response of the stage, by introducing a "shelving" response, where the stage gain is boosted at higher frequencies compared to lower frequencies.  The "breakpoint" of the frequency response is controlled by the value of Ck, in conjunction with the cathode impedance."  http://www.aikenamps.com/index.php/designing-common-cathode-triode-amplifiers

[shooter]

Thx JJ, That's sorta how I *understood* Ck's effect.  Hopefully I get some amp play time this weekend.

[sluckey]

I totally agree with all of that. This is the wild part...

Inside the tube there is naturally occurring degenerative feedback which reduces the actual mu of the tube to about 1/2 of its full potential ability to produce gain.

The degenerative feedback is a result of current flowing thru the unbypassed cathode resistor. When the AC grid signal swings positive the current thru the tube increases causing the voltage drop across the cathode resistor to go positive also (just like in a cathode follower). This positive going signal voltage  on the cathode causes the tube to decrease conduction, counteracting the positive signal on the grid which caused the current to increase in the first place. This action is degenerative feedback. The opposite occurs when the grid signal swings negative. IOW, the signal on the cathode will follow the signal on the grid. Just like the cathode follower, this fight between the grid control and the cathode control will find a happy median. The signal voltage on the cathode will always be slightly less than the signal voltage on the grid, otherwise, if the cathode signal voltage was the same as the signal voltage on the grid, the current thru the tube would never change and there would be zero signal at the plate.

Adding a bypass cap to the cathode changes the degenerative feedback by shunting the AC signal that would otherwise be present on the cathode to ground. Higher frequencies will be attenuated more than low frequencies. But if you make the cap sufficiently large, all frequencies that we can hear will be attenuated so much that none of that signal will have an effect on the cathode bias voltage and you can consider the degenerative feedback to be eliminated. Kinda like the action of a filter cap on the B+ rail.

[jjasilli]

Yes, that's what I thought you were saying in Reply #1.


EDIT:  I.e., I think you (Sluckey) & I are saying the same thing in different ways. More specifically, you focus on current in the cathode resistor.  So what is the source of this current? And what is its complete path of flow?  If its passing through the cathode resistor, then it must be passing through at least some portion of the inside of tube, in order to complete a circuit (a complete circuit is necessary for current to flow).  It must be AC current, because it can flow through a bypass cap which would block DC.  It must be out of phase with the main signal, otherwise it would add to (boost) the main signal, thereby rendering a bypass cap superfluous at best.  Hence this degenerative feedback must be inside the tube, which is what I am saying explicitly, and you seem to be saying by necessary implication.

Another way of putting it may be that the said AC current in the cathode resistor modulates the cathode, and such current is in-phase with the tube's input signal. This in-phase modulation on the cathode subtracts from the tube's output signal which is out-of-phase.  Speaking of this in terms of "negative" and "positive" produces hellish nomenclature issues.  This probably explains why the term "degenerative" feedback is used in this context, to avoid the negative-positive conundrum inherent in this situation.

[sluckey]

Just wanted to clarify... I didn't mean to imply that what you said was wrong or even that I disagreed. Just simply that your statement about "Inside the tube there is naturally occurring degenerative feedback" was an odd way of looking at it. Wild, as in, far out man! (Tommy Chong) I'd never heard that idea before. I was able to grasp what you were saying, but if my mind was a clean slate concerning degenerative feedback, I might have picked up a tube and examined it with a magnifying glass, looking for some fungus like stuff growing on the cathode element.   

[jjasilli]

Whoops, we're posting quickly.       Please see my post above your last one. 


Happy Memorial Day Weekend to all.

[HotBluePlates]

What would be the difference between making the coupling cap smaller or the cathode cap smaller in your typical 12AX7 gain stage for losing some lower frequencies? 

If the input signal to that 12AX7 is big enough, a full-gain 12AX7 might have distortion of those bass frequencies in its output, where a 12AX7 stage with reduced bass-gain due to a smaller cathode bypass cap might not have that same level of bass distortion. To be clear, this might have to be a late-preamp gain stage for this particular impact to occur.

And related, if you've pre-shaped the frequency response to trim bass at the input stage (as Marshall usually does), then the bass is already reduced and less likely to distort in later preamp stages (which is same as saying, "unattenuated mids & highs distort sooner than bass").

Normally, bass is trimmed in an amp that the harmonics (distortion) of bass notes will beat against the fundamental tones of midrange notes when  you play with heavy distortion. "Clean up the mud" as Jjasilli noted in Reply 2.

Other than that, you probably have a wider selection of values in coupling caps, or can more easily adjust bass-cut to taste.

... there is naturally occurring degenerative feedback which reduces the actual mu of the tube to about 1/2 of its full potential ability to produce gain.  The cathode bypass cap [reduces the] negative feedback ...  Hence the tube's gain is doubled for the entire frequency range. ...

The "1/2 shortcut" is close enough & accurate for a 12AX7.

I'm finding out the hard way in a build I'm working on that in tube with lower-Mu and/or higher-Gm, there is not as much signal-gain loss due to local negative feedback and so there's not as much trimming or tone-shaping available by manipulating cathode bypass caps. If there's interest I can post a formula showing it, but I do want to get this build done and hear how it sounds in practice.

The above isn't a new idea; it's found in RDH4 in the chapter on triode voltage amplifiers. But it was a little surprising for me to see it on the drawing board when using a small, medium-Mu (~34-37) but high-Gm triode which might have a cathode resistor only in the 250Ω - 1kΩ range. There's not a lot of feedback across a 250Ω resistor, so not a lot of gain reduction... RDH4 has a formula and table for visualizing gain loss due to local negative feedback across an unbypassed cathode resistor.

[Ed_Chambley]

HBP, I would be very interested in your findings.  I am smack dab in the middle of attempting to understand this topic.  Currently I simply use a Decade box, well not 2 of them since I have found sometimes reducing the bypass cap less and increasing a coupler a little as well gives me what I am looking for.  Sometimes the opposite is true as well.


It seems low wattage amps are much more delicate to tweak since they seem to get mud and with changing one bypass cap it just seems to get harsh, especially working with the 5879 pentode whereas the EF86 seems to be less temperamental and the highs tend to contain more harmonics and produce that glassiness we expect.


I seem to be finding if I reduce the Bypass only I lose fullness or what is referred to by some as swirl or 3D sounding.  Increasing the coupling cap seems to help to bring it back.  Actually Jjasilli explanation made perfect sense to me.


I would love to understand more of this as of right now I simply try and see which works, but I would like to narrow down exterminations as much as possible.

[jjasilli]

Long live Tommy Chong!

[HotBluePlates]

HBP, I would be very interested in your findings. ... with changing one bypass cap it just seems to get harsh, especially working with the 5879 pentode whereas the EF86 seems to be less temperamental ...

Well, you have a screen bypass cap when working with pentodes, along with the normal cathode bypass and coupling caps. That screen bypass can shape bass as well.

But right now I'm doing a PRR 1/3-watt amp, using a 6AK5 preamp and a 6AU6 output tube; however, there is also a 2nd channel with cascaded 6BC4 triodes. All the unusual tube use is about hearing how they sound.

But the 6BC4 has a Mu of 34-37 (depends on the operating point), and its internal plate resistance is down in the 6-8kΩ range (again, depends on the operating point). So it reacts differently than 12A_7 tubes would. And although it imposes a high cost of the B+ current draw, I wanted to see how it (and some other things I'm doing) affect the noise floor of the amp.

[EKDENTON]

What would be the difference between making the coupling cap smaller or the cathode cap smaller in your typical 12AX7 gain stage for losing some lower frequencies?  Thanks.

Sometime in 1968, Marshall went back and completely reworked their Lead/Superlead amp. They separated out the 1st gain stage and gave it its own much small cathode bypass cap. Where it used to share a 330uF (or 220uF) cap with the 2nd gain stage, it was now .68uF. Think of the cathode-bypass cap as a boost for preamp tubes. If you use a large cap, 25uF or larger, you boost the entire guitar signal...but if you move to a smaller cap, you can create a cut-off, below which the signal is not boosted. By moving to a .68uF, it means the 1st gain stage is ONLY boosting the extreme high-end. So, in 1968, Jim Marshall gave his amp's the equivalent of a treble boost hard-wired into the circuit.At the exact same time, they looked at the coupling caps. Removing larger .1uF coupling caps and replacing them with smaller .022uF. These smaller caps filtered out and removed a huge part of the loose, unfocused, boom-y bottom end of the previous amps.

Just found this post on another website.

[tubeswell]

What would be the difference between making the coupling cap smaller or the cathode cap smaller in your typical 12AX7 gain stage for losing some lower frequencies?  Thanks.

In addition to what the others have said about R/C or C/R attenuation (for coupling caps) versus gain boost rolloff (for cathode bypass caps), the two methods employ different circuit resistances to shape the frequency roll-off points.


With a coupling cap, the way the roll-off point is shaped is affected by what precedes and by what follows the coupling cap in terms of AC load. This depends partly on the output impedance of the gain stage that is driving the coupling cap, and partly on the values of any R/C or C/R network (or combination thereof) that follows the coupling cap. A series of equations is necessary to calculate this. Or, you can just experiment randomly with adjusting different values of coupling cap in your particular circuit, in order to arrive at a desirable result.


With a cathode bypass cap, the roll-off point is much more dependant on the tube type (or combination of tubes that the cathode resistor is biasing), and the cathode resistor's resistance value. It is much simpler to calculate the expected frequency roll-off point in this case (than it is for a coupling cap).

[jjasilli]

I submit that it is the same difference: whether a coupling cap or bypass cap, frequency response is the result of an R-C network.  This network may be of more or less complexity, but the knee frequency and curve shape can be calculated in advance. 


The coupling cap circuit is an obvious R-C network. The bypass cap circuit is less obvious but is the same thing.  Instead of thinking of this as dependent upon tube type, you can adopt the frame of reference of the bypass cap.  The bypass cap does not know that it is a bypass cap. It doesn't know or care what tube is present or how the R part of its circuit got its value. It simply sees itself as part of an R-C network.  Though the cap doesn't know or care, we do know how the R got its value: it's the plate impedance of the tube in parallel with the plate resistor. . .  This is more fully explained in gory mathematical detail on the Aiken page I cited in an earlier Reply.

[HotBluePlates]

I submit that it is the same difference: whether a coupling cap or bypass cap, frequency response is the result of an R-C network.  ...

Yes.

You might also note the coupling cap is passive; it is just a frequency-dependent voltage divider. That is how it cuts bass (or treble with a different ordering of R & C).

You might also note that the cathode bypass cap by itself is also passive, but it changes the behavior of an active device. It's a little more complicated to calculate the effect in advance; and because the behavior of the active device is being changed, there are possible 2nd- & 3rd-order effects which follow.

[shooter]

referred to by some as swirl or 3D sounding.

Could I get a little clarification on swirl - 3D, I'm not a player, but I hear *that sound* in my last build and it sounds really sweet to me.  So is it a good sound or bad?

[jjasilli]

Tweed Bassman's have swirl.  There was a recent thread here with youtube soundclips.  Like maybe there's always tremolo on.  I think whether you like it or not is purely subjective.  Money cannot buy happiness -  but it can buy another amp!      Why not have one with swirl?

[2deaf]

However if the coupling cap attenuates lows at 6dB per octave at the crossover point; and the cathode bypass cap boosts lows at 6dB per octave a the same crossover point . . .

Crossover point aside, has anybody actually observed a 6db/octave slope in the wild?  I bought into the 6db thing for RC series filters for a long time, but I never bought it for parallel RC partially-bypassed cathodes.

There are partially-bypassed cathode combinations that will yield a maximum slope of 6db/octave.  But then change the plate resistor and look what happens.  Am I missing something here?

If I put an RC series filter in between two stages of a 12AX7 and note the frequency response coming out of the second stage, I'm not seeing 6db/octave (leastways down to -12db).  If I calculate the expected frequency response, it is incredibly similar to the observed up to the knee (the knee always seems to deviate when comparing calculated and observed gain).  Am I missing something here?   

[2deaf]

I submit that it is the same difference: whether a coupling cap or bypass cap, frequency response is the result of an R-C network.  This network may be of more or less complexity, but the knee frequency and curve shape can be calculated in advance.

No.  The two methods yield wildly different curves as far as knees and slopes are concerned.  The coupling cap method yields a gain vs frequency curve that rises out of the abyss at very low frequencies until it reaches a relatively sharp knee and then it levels out.  The partially-bypassed cathode method starts out with level low gain then goes through a knee and rises until it hits a second knee then levels out again.  This S-shaped curve can be stretched-out vertically or squatted-down by changing the values of the cathode and/or plate resistors.  The perception of the sound of different stretched/squatted shapes causes the same -3db points to sound distinctly different.  The perception of the sound of a coupling-cap curve at -3db is always the same.

I think it has been noted in this thread and I have noticed since the '70's that the two methods do not sound the same.

The general curve shape and slope can easily be calculated in advance, but the knee shape at the higher gain end seems to elude me.   

[PRR]

> "Inside the tube there is naturally occurring degenerative feedback" was an odd way of looking at it.

That's intrinsic to Triode operation. Plate voltage influences effective internal grid field, and (for most audio circuits) the effect is negative feedback.

I do object to simply equating this with Mu. It is more obvious to look at Gm, which is like cathode internal resistance. If you add an external resistance, gain drops. Because rk is often similar to RK, it drops to about half.

A drop-shelf at half level is NOT a strong EQ. Bass below the S-bend is reduced but fully audible. In contrast coupling cap which just falls and falls.
___________________________

> anybody actually observed a 6db/octave slope in the wild?

Yes.

Any deviation, without another element (such as tube internal cathode resistance), would mean it aint working like its supposed to.

The cathode cap begins to cut bass, tending to 6dB/oct, BUT even when the cap is removed the gain only changes 5dB-10dB. So it is two flat gain sections with an S-bend between. The change is not big enough to develop the ultimate 6dB/oct slope. For a typical tube bypass, if you get right in the mid-zone and measure very close, you may find 3dB/oct. In fact this how 3dB/oct (pink) filters are made: a series of 6dB steps spaced correctly.

> I'm not seeing 6db/octave (leastways down to -12db).

Yeah, yeah, 6dB/oct is the limit that it never reaches. It's -3dB at the corner. Plot that point and 6dB/oct beyond. At the next octave the response falls about 1dB shy, or -7dB. Where you figure -12dB would be, it is really -12.5dB. As the corner is really -3dB, you drop 9.5dB in two octaves, and observe 4dB-5dB/oct. Keep going beyond 20dB or 40dB, the shortfall is too small to be sure of without careful calibration

______________________________

> if ...the cathode bypass cap boosts lows at 6dB per octave

Huhh? You got turned around. It doesn't "boost lows".

[HotBluePlates]

Crossover point aside, has anybody actually observed a 6db/octave slope in the wild?  I bought into the 6db thing for RC series filters for a long time, but I never bought it for parallel RC partially-bypassed cathodes. ... I'm not seeing 6db/octave (leastways down to -12db).  ... 

PRR explained it. And thanks to you both for reminding me about the distinction between the S-curve due to the cathode bypass cap vs. the continuous slope of the coupling cap.

Attached are some screen-grabs out of RDH4 to show both of these. First, the distinction between the theoretical limit of 6dB/octave for a coupling cap, and how that's used to plot attenuation. Then a shot of what real attenuation curves looks like, along with RDH4 saying they don't get close to -6dB/octave until you're beyond -10dB.

[HotBluePlates]

The last shot shows the possible S-curves for different triodes (IIRC, usually something between B= 1.5 to 2 is typical for common triode stages). There is reference in red to a previous graph of a 12AU7 stage with different cathode bypass caps stating the maximum slope achieved is 1.4dB/octave, and 3dB/octave is typically a limit. I included the stuff below, which provides a means to evaluate any gain stage, as long as the operating point is known (to derive the other values).

[jjasilli]

Yes, but the S curve was incorporated early in this thread by way of my reference to the Aiken amps webpage.   I specifically stated I was giving a general explanation re RC circuits, which circuits have more or less complexity.  More complex circuits, involving a cap looking at impedance or tube reactance, e.g., require more complex explanations.  Hence the early citation to the Aiken page.  IOW when a short explanation in a forum thread is accompanied by a caveat to read a cited  reference work , it's a good idea to read it.

[2deaf]

Thank you PRR and HBP for those excellent explanations.  Now there is some material that you just don't see on these forums every day.

[2deaf]

I read the previously cited Aiken page . . . can't wait for Appendix C.

At one point in the discussion of the two tone-shaping methods, he wrote:  "When shaping the frequency response of an amplifier, it is important to know which one to use, depending upon the desired result."

[jjasilli]

However if the coupling cap attenuates lows at 6dB per octave at the crossover point; and the cathode bypass cap boosts lows at 6dB per octave a the same crossover point . . .

Crossover point aside, has anybody actually observed a 6db/octave slope in the wild? . . . If I put an RC series filter in between two stages of a 12AX7 and note the frequency response coming out of the second stage, I'm not seeing 6db/octave (leastways down to -12db).  If I calculate the expected frequency response, it is incredibly similar to the observed up to the knee (the knee always seems to deviate when comparing calculated and observed gain).  Am I missing something here?   

I mentioned that 6dB/octave slope purely by way of illustration.  (It's the slope of a sealed speaker enclosure from its F3 which no doubt was on my mind for other reasons). 


Richard Kuehnel gives us a free online calculator for a coupling cap RC circuit:  https://www.ampbooks.com/mobile/amplifier-calculators/coupling-capacitor/calculator/
For a typical Fender circuit, it seems that a .022 cap passes the entire guitar frequency range.  I.e., 82Hz is as many dB down as 1KHz


*  @ 1/10th the value, .002, 82Hz is down about 3dB from 1KHz.  That's about 3.5 octaves, or roughly .87dB per octave.
*  @ half that, .001, we're in the Mesa Boogie cascading gain stage coupling cap value area.  This brings us about 6dB down from 1KHz; or about 1.7dB per octave.


Hotbolue shows that a cathode bypass cap gives similar to slightly better performance, at 1.5 - 2 dB / octave; but in a much smaller, more targeted frequency band.


******************
Again, this is not tube dependent per se.  For a different tube, or the same tube with a different value plate resistor, we "simply" need to specify the new output impedance of the circuit under test.


******************
It should be noted that a doubling of gain for a voltage amplifier (preamp tube) = 2 X voltage output = a gain of 6dB.  http://www.sengpielaudio.com/calculator-levelchange.htm


******************
Back to swirl.  It occurs to me that an amp may have subsonic (below 20Hz) oscillation, perhaps in the region of 5 - 10 Hz. This is like tremolo LFO (low frequency oscillation). Large enough coupling and cathode bypass caps may cause such LFO to be amplified to the point where it can audibly modulate guitar notes, thus producing swirl.

[shooter]

Back to swirl.

I had that on my 2nd last build, It was in that range, riding on ground!  Had to get to 15uF on V1a to kill it, the oddity, it was in the scopes *grass*, and the amp was dead quite, until you played.
This current build, can't find anything and the sound is different, it's like if you sustain a single note, some small time latter, it gets a boost, then decays like normal (haven't scoped it yet).  very subtle, I had a gigging musician play through it to confirm my weak bass, but he never said anything about this odd thing I'm hearing.
It's on hold for now, I'm painting an American flag on my barn!   

[PRR]

> 6dB/octave slope ...  (It's the slope of a sealed speaker enclosure from its F3

Sealed-box speaker ultimately goes 12dB/oct.

6dB/oct bass-loss over most of the range because the cone is smaller than a wavelength.

Another 6dB/oct below bass resonance where stiffness dominates.

[jjasilli]

Whoops, you're right, the sealed box is 12dB/oct. 

[Ed_Chambley]

Well, you have a screen bypass cap when working with pentodes, along with the normal cathode bypass and coupling caps. That screen bypass can shape bass as well.


Do you know of a way to calculate the change in frequency response in the screen cap?  Been reading and not quite getting it.  Is there such an online calculator for such.


Screen grid bias I have had some experience with in old radio and the 5C1 champ and changing them to cathode bias.  Normally I simply use a cap on the screen that was used in another amp.


How does the cap on the screen affect?  Is it basically the same?

[HotBluePlates]

... Do you know of a way to calculate the change in frequency response in the screen cap?  Been reading and not quite getting it.  Is there such an online calculator for such. ...

I'll look it up in RDH4; when I get to my digital copy, I'll grab a shot of the relevant page(s).

How does the cap on the screen affect?  Is it basically the same?

Same but different.

You're already familiar with how a very-large screen resistor on an output tube can compress power output. Normally, preamp pentode screen resistors are quite large values (often several times the size of the plate load resistor). A preamp pentode's screen influences plate current the same way as an output pentode/beam power tube.

The screen bypass is usually made to be a low reactance relative to the value of the screen resistor in order to avoid screen voltage change due to varying screen current. You might only see a 0.1uF cap instead of the 20uF filter cap attached to an output tube's screen because the screen resistance is much higher (and that in turn is because the preamp pentode's screen current is much lower than the output tube's screen current). The 0.1uF may be all it takes to get sufficient filtering.

I'm sure the formula (whatever it is) will include the Mu from G1 to G2, given that's a measure of the screen's effectiveness in controlling plate current.

[2deaf]

Do you know of a way to calculate the change in frequency response in the screen cap?

A screen grid resistor with a capacitor to ground generates an "S" curve for the frequency response as does a partially-bypassed cathode.  The equation for the point where the gain starts to rise from the minimum is the same in both cases.  So for the screen grid, that frequency is the reciprocal of 2*pi*C_S*R_S.

[PRR]

> screen bypass is usually made to be a low reactance relative to the value of the screen resistor

You really want low Z relative to the screen internal resistance.

Which is never on the datasheet.

For quick work, pencil "20K" and move on. 0.1uFd on 20K bypasses to 80Hz which is good enuff for guitar. You find values to 0.5uFd in hi-fi. Film cap is much preferred because the leakage of a bad electrolytic is significant in the large screen resistor. But 0.5u is a big film cap so there is a temptation to go to the 200V types. This may be wrong: at turn-on the cap goes nearer 400V until the tubes start conducting. I've seen enough blown 200V screen caps.

> include the Mu from G1 to G2

That's probably the big factor. Just as the plate resistance of a triode is Mu/Gm, the screen resistance should be about Mu(g2)/Gm. Taking 1/Gm as about 1K for most small tubes, and Mu(g2) about 20 in many (not all) small pentodes, this gets about 20K screen resistance.

And as 2deaf sez: it is an "S" curve from the fully bypassed gain to the un-bypassed gain (which is a little hard to work out on a matchbook).

[HotBluePlates]

Yes, all good points!

As 2deaf says, RDH4 shows the same S-curve for the screen as we had for the cathode cap. The formula for figuring "B" is all that really changed.

> screen bypass is usually made to be a low reactance relative to the value of the screen resistor

You really want low Z relative to the screen internal resistance.

Which is never on the datasheet.

> include the Mu from G1 to G2

That's probably the big factor. Just as the plate resistance of a triode is Mu/Gm, the screen resistance should be about Mu(g2)/Gm. Taking 1/Gm as about 1K for most small tubes, and Mu(g2) about 20 in many (not all) small pentodes, this gets about 20K screen resistance. ...

Right before I saw this I was thinking, "if screen current is usually a fixed % of plate current, wouldn't "screen Gm" likely be the same fixed % of plate Gm?"

Then screen internal resistance should be Mu(g2)/Gm(g2).

Then again, I suspect that screen Gm might hover around 800-1200 micromhos (assuming plate Gm is up around 2500-4000 micromhos), basically the same as the 1k you noted for 1/Gm. Perhaps just worthless accuracy...

[jjasilli]

I submit that it is the same difference: whether a coupling cap or bypass cap, frequency response is the result of an R-C network.  This network may be of more or less complexity, but the knee frequency and curve shape can be calculated in advance.

No.  The two methods yield wildly different curves as far as knees and slopes are concerned.  The coupling cap method yields a gain vs frequency curve that rises out of the abyss at very low frequencies until it reaches a relatively sharp knee and then it levels out.  The partially-bypassed cathode method starts out with level low gain then goes through a knee and rises until it hits a second knee then levels out again.  This S-shaped curve can be stretched-out vertically or squatted-down by changing the values of the cathode and/or plate resistors.  The perception of the sound of different stretched/squatted shapes causes the same -3db points to sound distinctly different.  The perception of the sound of a coupling-cap curve at -3db is always the same.

I think it has been noted in this thread and I have noticed since the '70's that the two methods do not sound the same.

The general curve shape and slope can easily be calculated in advance, but the knee shape at the higher gain end seems to elude me.   

Yes, per Kuehnel's on-line coupling cap calculator (cited above), this curve has essentially no knee in the guitar frequency band (assuming the output impedance of a typical 12ax7) until the coupling cap gets as small as .005uF or less.  OTOH, the by-pass has about the same dB drop, but in a much narrower bandwidth; so there's a steeper slope to the drop-off, and a nicely rounded knee (actually 2 knees at the top & at the bottom of a nicely shaped s-curve), per RDH4, cited above by HotBlue.

[2deaf]

A partially-bypassed screen with the same knee at the low-gain end as a partially-bypassed cathode (with typical R_K values) will sound like it has more bass cut than the partially-bypassed cathode.  This is because the difference in gain between the extremes for the partially-bypassed screen is typically much larger than for the partially-bypassed cathode.  The S-curve is stretched-out vertically for partially-bypassed screens as compared to cathodes.  The same thing happens when you increase the value of R_K for partially-bypassed cathodes.