Second design - SE EL84, cascode pre

[Joe P]

Hi,
Posted my first amp design a while back, https://el34world.com/Forum/index.php?topic=24808.0, and decided to follow the many advices to start simpler - so here's what I've come up with. Two-tube amp, single ended, EL84 output with a cascode frontend, James tonestack in the middle.
If my calculations are correct, plate voltage on the 12AU7 is too low to come close to its full gain potential, but I could sub a 12AY7 for a lot more gain if needed, i'd just change Ra to 47k.
Before anyone in the US wonders about the fuses on both hot and neutral, we have symmetrical plugs where I'm at.

Thoughts?

Edit: bypass and coupling caps are a bit large because I want to see if this is could be useable for bass as well.

[shooter]

close to its full gain potential

never used the cascade setup, the 84 drives easy, with your 330 cathode R, I suspect you'll only need ~~ 5-7Vac at G1 to drive it to compression, maybe clipping.
G2 could probably be dropped to 470 - 1k, but the 1.5k won't hurt anything for getting it up and running.
enjoy the process, go slow, focus on clean, you'll have plenty of time to jam after 

[jjasilli]

Lack of substantive response tends to indicate that you're still in the deep end of the pool, with no lifeguards on duty.  My advice continues to be: build a proven design (cascode OK); produce a working amp; then mod it systematically.

Relatively few people have cascode experience. 

Here's an except from Merlin:  http://www.valvewizard.co.uk/cascode.html 

N.B.:  Your supply voltage is low.  Note that for a typical gain stage, low supply voltage tends toward dark tone.  Baxandall is dark tone (no mid dip). 

What are your tube curves?  What is your cascode's output impedance?  What is the input impedance of the tonestack?  How do the two balance?


What is the signal voltage into the EL84?

[kagliostro]

Here on the forum, if I remember correctly, there was a guy that build a small amp with a cascode arrangement

may be someone can remember more than I and post a link to the thread

EDIT: I remembered the member (jbfumo) and think this is the thread

http://el34world.com/Forum/index.php?topic=14793.msg217649#msg217649



Franco

[shooter]

I'll agree with JJ here on B+ somewhat low.  The 84 - modern, will do fine at 300 plate, so aim for 320 at 1st tap since you're gonna loose some to the cathode and G2.
Also agree on a deep read for the cascode, pretty sure on a conventional configuration, 1/2 tube before TS, 1/2 tube after you can hit a target of ~~ 7Vac to the 84's G1.
I personally like to take my SE PA tube B+ from the 2nd PS tap using FWB and ~ 100uf 470ohm pi filter before feeding the PA tube.  There is no inherent hum cancelling like you get in PP design

[2deaf]

Your PT is rated for 190V at 75mA and your rig looks like it isn't going to use much more than 49mA, so I am going to use a conservative value of 260V for your B+.  7mA of screen current and 5mA of cascode current both go through the 470r dropping resistor.  By Ohm's law, 12mA times 470 Ohms is 5.64V, so the second node will be about 6 Volts less than the first node.  Only the 5mA of cascode current goes through the 2K2 dropping resistor for a voltage drop of 11 Volts, so the third node will be about 243V.

The gain of the cascode is about the same at most supply voltages, so 200V (or 243V) will allow it to come close to its full gain potential.  Headroom will decrease with decreasing supply voltage, but this cascode is the first stage so that headroom is not a consideration.  A 12AY7 cascode with the same components as a 12AU7 cascode is likely to yield similar gain.

As far as bass is concerned, C5 needs to be changed to 22uF and C7 needs to be changed to 100nF.  The existing 1uF/560r cathode combination has a cutoff frequency of 284Hz, so there is significant bass rolloff.  C7 at 10nF will also contribute a little to bass rolloff.

The gain of the cascode with a 10K plate resistor is probably around 18.  If you put a 100mV_p guitar signal into it, you will only get 1.8V_p out of it and that is at higher frequencies.  Even without the tone-stack loss, this isn't enough to drive the EL84.  Changing the plate resistor to 47K will probably give you a gain of 60 for an output of 6V_p, still too small after the tone-stack loss.  A 100K plate resistor might give you, who knows, a gain of 90?  Still might not be enough to drive the EL84 after tone-stack loss.       

[Tony Bones]

Hi,
Posted my first amp design a while back, https://el34world.com/Forum/index.php?topic=24808.0, and decided to follow the many advices to start simpler - so here's what I've come up with.

And it is simpler! That's good, but I'm going to suggest that you also think flexibler.

I'll spell it out: Buy a chassis and power supply for a Marshall 1974 (a.k.a. "18 Watt".) Both are overkill for an SE EL84 build, but they'll provide room to grow. Here in the US we might find an amp from an old Hammond organ for cheap, or even a whole organ for free. I don't know how common organs are where you live, but you might be able to find something. Or just buy the 18 Watt chassis and transformer.

Then build this, more or less exactly as drawn (except for the rectifier.): http://mercurymagnetics.com/images/pdf/schematics/wiring/E-VJ-schem1a.pdf

It should take very little time, but I guarantee that if this is your first build, then you will learn a ton. But, It'll be a lot easier troubleshoot because you'll know what to expect from the circuit. Or, if you don't then everyone here will and it'll be easy to get help.

Once you have that working, then go nuts trying different tubes, cascodes, whatever... There're enough tube sockets that you can have multiple preamps at once. Eventually you can try PP if you want. You'll just need to find another output transformer. All with that chassis and power transformer.

[PRR]

> If my calculations are correct, plate voltage on the 12AU7 is too low to come close to its full gain potential,

How are you calculating??

SPICE figures your plan has gain of about 6 (yes, six!) and eats near 5mA current.

If 10k is changed to 100k gain rises to 11 and current falls to 1.5mA.

A single section of 12AU7 can give gain of 16. Two in cascAde gives gain over 200. At total current near 3mA. And much lower impedances.

The usual rule-of-thumb for a guitar amp is two high-Mu stages cascade; maybe more if there is a tone-stack.

Yes, cascOde 12AU7 has Mu like 20*20=400, but (like pentodes) you can not get a load impedance high enough to use all this. (Even so, 6 seems absurd.)

As a general rule, a Power Tube needs a fairly direct feed from a driver. You drive through the quite lossy James tonestack. Even with a super-hot guitar to cover the low gain, it is likely the pre-tone stage will distort before the power stage makes its big 4 Watts.

Gain does not vary a lot with plate voltage, only slowly with supply voltage. Overload does vary pretty directly with these voltages of course.

[tubeswell]

Some more cascode stage examples attached FWIW. (The one on the R.H. side in the Weber schematic is not a cascode, but is a totem pole SRPP with the upper triode acting as a current source in place of a load resistance, so another interesting variant on totem pole designs)


These would all benefit from moderate (30V - 40V) heater elevation, especially the AU7 examples


Another good triode to use for a cascode would be a 12WD7, with the AU triode as the input triode, and the AX7 as the grounded-grid (upper) triode. This should enable good gm for the input triode and reasonable output signal swing on the output triode.

[DummyLoad]

12WD7

no such tube. 12DW7/7247 - is that the tube you're thinking of?

--pete

[tubeswell]

12WD7

no such tube. 12DW7/7247 - is that the tube you're thinking of?

--pete

WD40 = engine oil and I've just been putting some in the car before I posted this duh.

[Joe P]

Thanks for the replies!

It's evident that my calculations on that cascode are completely wrong. It's Merlin's guide I've been using. I'm going to figure out where I went wrong, and then go with Tony's suggestion to start with a Valve jr and a 1974 psu.
No cheap Hammonds here, but I have a couple old transistor amps that I can butcher.

[PRR]

> calculations on that cascode are completely wrong. It's Merlin's guide I've been using. I'm going to figure out where I went wrong

One error found. Upper grid-cap is actually a cathode cap. I though that was odd, but didn't get-it until I put your plan against Merlin's.

With that grid just following cathode this is not a cascode but an idle resistor in the plate circuit.

[PRR]

With the correct grid connection, gain rises from ~~6 to like 18. Your undersized capacitors (all around) give a major bass-loss.

[PRR]

With fully ample caps and 47k load, gain soars to near 60 and full bass. (You may want less bass for guitar, but let's see full response before we start carving.)

This uses a whole bottle to do what a half a bottle of 12AX7 would do, and about twice the current of a single 12AX7 stage.

[2deaf]

One error found. Upper grid-cap is actually a cathode cap. I though that was odd, but didn't get-it until I put your plan against Merlin's.

Ahhh, I totally missed that.  I was wondering how you got a gain of 6 while I got a gain of 18.

[PRR]

The ultimate voltage gain of a cascode should be Mu*Mu. We never get there (in audio) because of loading and DC-feed impedances.

Curious, I tried two way-out extremes. A 1,000H choke (you can't buy one cheap or full audio band); and a huge resistor with a huger supply voltage, both with impossibly large loads.

The big choke with 250Meg load does come very close to Mu*Mu. And it promises a voltage swing like 140V. Which makes the input overload near 140V/400= 0.35V, marginal for e-guitar. Of course the choke is nearly unobtainium, and the "250Meg" AC load needs buffering. Since two-half 12AX7 makes gain over 2,000 and can drive 200k comfortably, why?

Resistor loaded 1Meg with 1KV supply doesn't get halfway there. According to G.E., Gm of 12AU7 at 100V 1mA is like 600uMho, or 1/1700 Ohms. Mu here has fallen to 13. So "plate resistance" of the cascode is near 280k, and "Mu" is 169. Which does not quite match what the Koren model tells me. But IAC the phantom of high gain is clouded by uselessly high output impedance.

[Joe P]

> calculations on that cascode are completely wrong. It's Merlin's guide I've been using. I'm going to figure out where I went wrong

One error found. Upper grid-cap is actually a cathode cap. I though that was odd, but didn't get-it until I put your plan against Merlin's.

With that grid just following cathode this is not a cascode but an idle resistor in the plate circuit.

Ah, yeah, and it's the correct circuit that I've made calculations on.

With the correct grid connection, gain rises from ~~6 to like 18. Your undersized capacitors (all around) give a major bass-loss.

I must have made a calculator typo on the cathode cap. For Ck on the EL84, if that's too low my definition of "roll off" can't be the same as Merlin's.

Ahhh, I totally missed that.  I was wondering how you got a gain of 6 while I got a gain of 18.

I got 26, so there's something else I've been doing wrong.

Getting as much gain as possible wasn't really my goal here, I wanted the pentode sound without the microphony. I've only heard pentode preamps, not played one, so I'm curious.

[shooter]

as much gain as possible wasn't really my goal here

agreed, what you need is enough to overcome the circuit n TS loss (I don't do math:), and have enough to at least bend the 84.  Most don't really care for 84's that are screaming, but bent is goooood 

from what 2Deaf came up with and my ballpark, I'd aim for 8VACp-p on G1

[tubeswell]

The 12DW7 variant I mentioned earlier - should be good for driving a TMB tone stack as well as having a decent amount of gain. To make it gnarlier, change to grid-leak bias (using 1M) on the AX triode (or experiment with reducing the upper triode grid bypass cap size, or increasing the load resistor (slightly) for the upper triode).


Wait til you get it installed, then decide whether it needs heater elevation or not. It shouldn't need any but you could always give it a little boost by running the heater 'ground reference' to the cathode of your cathode biased output tube.

[shooter]

I re-did my ballpark with #'s from datasheet.

If their correct, you might need more drive than ~~8vac.
I use the cathode volts DC as a guide for Vac  on G1. so closer to 20vac to get the tube bent hard 

[2deaf]

The 12DW7 variant I mentioned earlier - should be good for driving a TMB tone stack as well as having a decent amount of gain.

I can't see how you are going to get much more than unity gain out of that rig.  Also, I'm not catching on to the advantage of using a 12AX7 for the upper triode.

[PRR]

...upper triode grid bypass cap...

And yet, again, the cap is connected to cathode not grid. The upper tube is an inert resistor.

I also too have doubt that a high-Mu upper tube really wrings any more gain out of a cascode.

Moreover for same current, a 12AX7 has more Gm than a 12AU7.

[DummyLoad]

The 12DW7 variant I mentioned earlier - should be good for driving a TMB tone stack as well as having a decent amount of gain. To make it gnarlier, change to grid-leak bias (using 1M) on the AX triode (or experiment with reducing the upper triode grid bypass cap size, or increasing the load resistor (slightly) for the upper triode).


Wait til you get it installed, then decide whether it needs heater elevation or not. It shouldn't need any but you could always give it a little boost by running the heater 'ground reference' to the cathode of your cathode biased output tube.

cap connects as shown in attached.


--pete

[Joe P]

How about a regular gain stage on the input and a cathode follower after the cascode to drive the TS?

[2deaf]

cap connects as shown in attached.

That certainly makes a lot more sense, but why 470nF?  Looks like it will take a long time to charge when B+ is first applied during which time the gain will be reduced due to the lower "screen" voltage.  It seems to me that 10nF would be plenty for a flat response. 

[shooter]

How about a regular gain stage

wait, the numbers are still coming in 
the bottom-line, determining enough signal to drive the PA, and whatever "tone" flavor you want to add before that.
Me, I'd stick with your idea but expect, work out, a 2nd pre tube in your design, just in case you need more gain or impedance matching (CF)

[jjasilli]

FWIW:  https://sites.google.com/site/stringsandfrets/Home/deluxe-plus


Contains an interesting article by Aiken.


Note that the cascode drives a cathode follower > tonestack.  Followed by a cascode tone recovery stage driving another cathode follower!   

[shooter]

but we all agreed to KISS 
I do think a 2nd tube might be needed, a 3rd for an SE EL84 is overkill by alot

[jjasilli]

KISS!?! I thought the design might turn Joe P ON. But seriously, folks, if you want to KISS, the design suggests the desirability of a CF after the cascode to deal with the cascode's hi output impedance; along with the "need" for tone recovery stage.  (Not to mention Aiken's insights). 


Also, if Joe P wants an example of a proven, complex cascode design, there it is, with soundtracks.  (Not that I recommend it as a first tube build.)


Not to mention that if a cascode design complies with KISS, then we must already be on our 3rd date.  Someday, we may even give birth to an actual design.

[DummyLoad]

cap connects as shown in attached.

That certainly makes a lot more sense, but why 470nF?  Looks like it will take a long time to charge when B+ is first applied during which time the gain will be reduced due to the lower "screen" voltage.  It seems to me that 10nF would be plenty for a flat response.

i didn't choose that value - 47nF could be overkill and is 10n enough though? personally i'd use 100nF just because john broskie does. :p 


--pete

[2deaf]

i didn't choose that value - 47nF could be overkill and is 10n enough though? personally i'd use 100nF just because john broskie does. :p 

I'm sorry, I knew you didn't choose 470nF and I wrote it wrong so that it implied that you did.

With the usual equation for cut-off frequency, 1M and 10nF would yield 16Hz.  But I'm not well enough versed on tube cascodes to state that the upper grid leak resistor and bypass cap will act like that.  The charge/discharge path for the 1M grid leak makes me suspect that it will appear to be larger than 1M for cut-off frequency purposes.  Really going out on a limb with that one.   

[PRR]

The cap that clamps the "idle" grid in a LTP or a Cascode has to be larger than you think.

A coupling cap we hardly notice 29% loss (-3dB).

These "idle" grids have to be IDLE. Even a few-percent wobble degrades expected performance.

You often see, on LTPs, 0.01u on one grid and 0.1u on the other. This 10X difference is a good rule of thumb.

Somewhere in this thread (probably a link) someone used 1uFd. Yes, a 1 Second time constant just to get to 67% of final value. It isn't far off from the 10k+40uFd (0.4sec) found in B+ decoupling networks. This is probably moot in light of 11 seconds for heater warm-up and 234 seconds to adjust your shorts, find your pick, adjust your strap......

[Joe P]

I would not want to troubleshoot that DR...
But as you say, it is a proven cascode circuit. Now, I am going to KISS at first, but it feels good to have a plan for the future!
My thinking is, first get the Valve jr/1974 up and running, then mess around with tonestack and other tweaks, and then maybe insert the cascode.

Regarding the double cascode/CF, he's driving a PP pair of 6V6s with NFB, I'm only driving a SE EL84 - so my remaining half 12AX7 could be more than enough, right? Question is whether to have it as a recovery stage or as an input stage to overdrive the cascode.

[shooter]

fwiw
I use this circuit as a "standard"
http://www.valvewizard.co.uk/dccf.html
with small bottle PA I like to put it pre TS, ala Marshall, with big bottle I use it after TS as recovery/drive for PA
pre gets to crunch nicely, less "annoying" pre-amp distortion, post keeps the signal "original" enough with the extra demands of a large PA tube

[jjasilli]

I would not want to troubleshoot that DR...
But as you say, it is a proven cascode circuit. Now, I am going to KISS at first, but it feels good to have a plan for the future!
My thinking is, first get the Valve jr/1974 up and running, then mess around with tonestack and other tweaks, and then maybe insert the cascode.

Regarding the double cascode/CF, he's driving a PP pair of 6V6s with NFB, I'm only driving a SE EL84 - so my remaining half 12AX7 could be more than enough, right? Question is whether to have it as a recovery stage or as an input stage to overdrive the cascode.

The beauty of that amp is not to miss the trees for the forest!  I.e., the over-complicated forest of that amp contains some really useful, simple clusters of trees.  These can be effectively plagiarized.


1.  A working Cascode-CF input section. 


2.  The CF drives, in essence, a Fender TMB tonestack.  (Like the old Bassman circuit)

3.  A working Cascode-CF tone recovery stage.

So, there's the option to use just one, or both, cascode circuits.

From the tube charts:  At 360 Plate volts a pair of 6V6s in PP needs -22.5 fixed bias volts, or +22.5 cathode bias volts.  @ 250 Plate volts, an SE EL84 needs 7.5V bias.  You can plagiarize the cathode bias voltage from a known SE EL84 amp @ your plate voltage; and feed signal voltage accordingly. 

See, e.g., Epiphone Valve Jr., which I think was suggested earlier, as the basis for your project.


This has Dummyload's breadboard written all over it!

[Joe P]

See, e.g., Epiphone Valve Jr., which I think was suggested earlier, as the basis for your project.

Yup, that's my starting point - though I've started contemplating maybe just using the PA and taking the pre from some version of Champ. Nicer sound to start with...

This has Dummyload's breadboard written all over it!

Can't find it with a quick search... I've been planning on whipping something up with screw terminals, I'll be sure to dig through the threads I did find for further layout ideas

[DummyLoad]

another approach - in theory it should work... maybe split the second cascode into cascaded stages? please comment liberally as i am new to cascodes as well. i used joe_p's presented plan as the basis for this design, except i used higher B+ and EL34 because i don't like EL84 amp and ~10W of power for some added clean headroom.   

just my opinion, but 12AU7s aren't of much use in guitar amps (flame away h8rs)*, except for use in high power amps that require low Z drivers, and the odd-ball amps that use it for a reverb driver, etc.. they are rarely used as the main gain stages of a guitar amp. could the cascode change things? maybe.   

i have not built, nor have i breadboard the circuit presented, just throwing out other options for those that may want to experiment with low mu tubes and the tonal characteristics that are a result of cascode gain stage(s).

regards,

--pete

if you wish to add NFB, then add a 100R under R12 and C9 then connect a 10K from the 8 ohm tap to the junction of R12 C9 and the 100R - the 10K is a value that you would use your own ears to choose. 1K to 10K is a suitable range to start with. use the princeton reverb schematic for NFB insertion as a reference if the preceding is unclear.

* if i'm looking to use the 12AU7 in any application, i almost always turn to 6CG7 or the 12BH7. IMO, a much better tubes + i have a box full.

[Joe P]

just my opinion, but 12AU7s aren't of much use in guitar amps

My main reason for using the 12AU7 here was that that's what Merlin suggests for use in a cascode - now I'm thinking I'm just going to go with a 6922 for simplicity - I can just copy the cascode stages from that DR from hell and tweak from there.

[shooter]

h8ter alert 

i have a box full.

my 1st reason for using AU7
my 2nd, I am blissfully ignorant of some tube math, so I just plug it in an observe.  What I find for "V1", because it's a low gainer, signal only gets a smallish boost, but way more than the noise floor, so it leaves more hissey/hummy out of the signal path.
In a DCCF it seems to be harder to slap around, thus adding less sour taste to the signal
I wouldn't try and use those arguments as an answer to your EE tube Final exam 

[2deaf]

I had some time today so I built a cascode stage and ran some frequency response trials with various capacitors in the C_g2 and C_K positions.  Attached are the test setups that I used. 

I set C_k at 220uF for the C_g2 tests so that the cathode would be fully bypassed and not a factor in the frequency response.  I found that the cut-off frequencies at the output closely followed 1/(2*pi*R*C).

I set C_g2 to 0.22uF for the C_k tests so that the "screen" had a flat response.  I found that the cathode bypass capacitor has a much more potent effect in a cascode than in a standard gain stage -- like twice as much.  So the cut-off frequencies at the output more closely follow 1/(pi*R*C).

That's what I got, anyways.  Maybe somebody can see if they can replicate my results.

[Joe P]

I had some time today so I built a cascode stage and ran some frequency response trials with various capacitors in the C_g2 and C_K positions.  Attached are the test setups that I used. 

I set C_k at 220uF for the C_g2 tests so that the cathode would be fully bypassed and not a factor in the frequency response.  I found that the cut-off frequencies at the output closely followed 1/(2*pi*R*C).

I set C_g2 to 0.22uF for the C_k tests so that the "screen" had a flat response.  I found that the cathode bypass capacitor has a much more potent effect in a cascode than in a standard gain stage -- like twice as much.  So the cut-off frequencies at the output more closely follow 1/(pi*R*C).

That's what I got, anyways.  Maybe somebody can see if they can replicate my results.

Very interesting! Merlin Blencowe (where I've gotten much of my information) says:

For most purposes it is sufficient to choose the cathode bypass capacitor according to:
Ck = 1/ (2 . pi . f . Rk)

So now we have empirical evidence that says otherwise.

[PRR]

> I found that the cathode bypass capacitor has a much more potent effect in a cascode than in a standard gain stage -- like twice as much.  So the cut-off frequencies at the output more closely follow 1/(pi*R*C).

The cathode node impedance is not just the 1K resistor, but also the internal cathode impedance. Which is frequently very similar to the bias resistance. So not 1k but 500r. Which is about your lost factor of 2.

[2deaf]

Very interesting! Merlin Blencowe (where I've gotten much of my information) says:

For most purposes it is sufficient to choose the cathode bypass capacitor according to:
Ck = 1/ (2 . pi . f . Rk)

So now we have empirical evidence that says otherwise.

Merlin never said that his equation is for a frequency that gives a gain that is 3dB below fully-bypassed gain, but mine is. 

In general, if you come up with something that doesn't agree with what Merlin said, then you are either in error or you misinterpreted what he said.

[tubeswell]

Merlin Blencowe discusses cascode design in a couple of his books (as well as small signal pentodes).


The extent to which the screen (in pentodes) and the upper triode grid (in cascodes) is bypassed, has a significant impact on bandwidth. If the upper triode grid is ‘fully’ bypassed, the lower triode acts purely as a transconductance triode - because the effect of ‘fixing’ the upper triode’s grid voltage (at ‘all’ frequencies) is analogous to the way operation of a screen (in pentodes) shields the input (signal) grid from changes in output voltage at the plate. Therefore, bypassing the lower triode’s cathode resistor does not have as much of an effect on bandwidth, as fully bypassing the upper triode’s grid does. The reason I used 470nF in my earlier example, is because this works better than 100nF in this regard. (However, if you want maximum gain, then you should bypass the cathode resistor for the lower triode as well).


If you want maximum current, then use grid leak biasing on the upper triode.

[2deaf]

The cathode node impedance is not just the 1K resistor, but also the internal cathode impedance. Which is frequently very similar to the bias resistance. So not 1k but 500r. Which is about your lost factor of 2.

There is no lost factor of 2, but there is a lost interpretation of the data.

1/(pi*R*C) only works for the Test Setup with a 1K cathode resistor.  If you change the cathode resistor to 2K, then 1/(0.6*pi*R*C) is a better estimate for the cut-off frequency.  If you change the cathode resistor to 560, then 1/(2*pi*R*C) is a pretty good estimate.

For a partially bypassed cathode, the frequency at 1/(2*pi*R*C) is where the gain has risen a certain amount above the unbypassed gain.  If you choose 3dB for that certain amount above minimum gain and there is a 6dB difference between unbypassed and fully bypassed gain, then the -3dB cut-off frequency is the same as the +3dB above minimum gain frequency.  With a 560r cathode resistor in the Test Setup, the gain spread is right in there at 6dB and that is why 1/(2*pi*R*C) works for the -3dB cut-off frequency.

If you change the cathode resistor to 2K, the difference in gain between unbypassed and fully bypassed is more like 10dB.  Now the +3dB above minimum gain frequency is not the same as the -3dB cut-off frequency.  There is a 6dB/octave section in the S-Curve plot for the frequency response between the two 3dB points.  So the -3dB cut-off frequency occurs at a higher frequency than the +3dB above minimum gain frequency.  The denominator in the cut-off frequency equation needs to be reduced to account for the difference in 3dB points.

[2deaf]

Therefore, bypassing the lower triode’s cathode resistor does not have as much of an effect on bandwidth, as fully bypassing the upper triode’s grid does.

Can you re-word that?  I can't make any sense out of it as it stands.

[2deaf]

another approach - in theory it should work... maybe split the second cascode into cascaded stages? please comment liberally . . .

The 1.2K/10uF cathode combination looks like it might have a cut-off frequency around 13Hz, but it probably has around a 30Hz cut-off frequency with this cascode.  You may have already known that because 30Hz sounds pretty good to me for a guitar amp.

The Miller effect has been nearly eliminated because the bottom triode has very little gain (this is about the only reason I can see to use a cascode with tube triodes).  If I generously give the bottom triode a gain of 1.5, then the input impedance will be 1.5pF times the 1.5 gain plus the grid-to-cathode capacitance of 1.5pF.  Call it 4pF.  So an 820K grid stopper will give about the same high-frequency cut-off as 33K with a standard 12AX7 gain stage.

[shooter]

If you change the cathode resistor to 2K, then 1/(0.6*pi*R*C)

I can't make any sense out of it as it stands.

not looking for a deep dive, simple bellyflop works 
the 2K, isn't that the "R" in the equation?
If so, why .6
If not the R, why

thanks
dave

[2deaf]

the 2K, isn't that the "R" in the equation?
If so, why .6
If not the R, why

Yes, 2K is the "R" in the cut-off frequency equation.  0.6 comes from observed frequencies when the the output voltage was down 3dB from the maximum voltage.  I just re-arranged the original equation to solve for the factor that R*C had to be multiplied by to get those frequencies.  Then I wrote that factor as 0.6*pi instead of just 1.9 for dramatic effect.  For example:  I observed a -3dB voltage at 26Hz with a 2K/10uF cathode combination.  The factor I am looking for is 1/(26Hz*2K*10uF) which is 1.9 and that converts to 0.6*pi.

You get 8Hz if you plug the same numbers into 1/(2*pi*R*C).  This is not the -3dB cut-off frequency, but rather the point when the gain is up somewhat from the un-bypassed gain.  The frequency difference between the two points depends on the value of the cathode resistor, all other things being equal.