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    Building, troubleshooting and testing of these amplifiers should only be
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6E5P Microphony

You use the "wrong" output of cascode CCS.
The "low Z" output of CCS guaranteed much lower output impedance. It's most "immune" to the cathode resistance changing.

Ah, I disagree with this one! Taking the mu-out fundamentally changes the circuit from a common cathode parafeed amp to a hybrid mu-follower. Gary Pimm wrote a great whitepaper (here) on the topic.

The cascode CCS stage does not require regulated power supply, the only criterion is the appropriate headroom (at least 30V greater B+, than output swing upper corner).

The shunt reg's main purpose was to ensure that the minimum current draw was being met from the moment the amp is powered on. This way, there's no risk of B+ overshooting while waiting for the tubes to warm up.

If you use CCS loaded stage, the LED is prefect in the cathode. If you want higher bias, series connected (if the current is high, paralleled series strings) LEDs even gives lower dynamic impedance, than BJT.

It depends on the LED. Here are some measurements. Let's assume an LED has an impedance of 2 ohms, noting the HLPM-6000 is a particularly good example. With the BJT biased to 30mA, Vt/Ic = 0.86 ohms. I've built both with different tubes and found that they give very similar results, but opted for the BJT circuit here because 30-40mA closer to the HLMP-6000's 50mA maximum rating than I would prefer.

BTW 6E5P cathode pins 4,9 must to connect together with wire (as short as possible) under the socket, instead of 10R resistors.
These pins are the inner screen too, so AC grounding IMO is necessary.
Use AC blocking paralleled with cathode biasing part (100nF//100pF).

I tried this with 10nF a few posts earlier, but replaced it with 100n//100pF just now per your suggestion, directly from the pins to ground. Still no luck. :(

I still wonder if its external to your amp.

If not than maybe you have built a VHF squegging oscillator.

Good question. I ran two more measurements. The uppermost trace is with the amp turned off and the cable plugged in (i.e. probe leads across the transformer secondary). The bottommost trace is with the audio analyzer cable plugged in, but disconnected from the amp, to measure any noise being picked up by the cable.

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I'm not too sure what to think of the 1K and harmonics, but the rise in the noise floor around 7k is very much still there even with the amp off! I redid the measurement with the power cable and input cables disconnected and got a similar result. I repeated the measurement once more with the OPT disconnected (measuring on either side of the parafeed cap), and still saw it. The only way I was able to eliminate the blip was by shorting the probe leads during a measurement.

My gut feeling is that the output transformer is acting up. Just for debugging, can you disconnect the transformer, replace it with a load resistor, and measure again?

Good idea-- here we go. Note that this is a relative level measurement, so even though we don't have the voltage step down of the OPT, the level can be directly compared to that of prior measurements, and doesn't really seem to have moved.

I'm relieve the OPT is not to blame, but it really looks like there's something sneaking in through the ground, or some oscillation I still haven't figured out. I know you are uniquely qualified to say that 6E5Ps should not be particularly microphonic. :)

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We all know there must be a solution the blip problem a5 3.7k kHz... this is quite an interesting puzzle to work out!

...to say that 6E5Ps should not be particularly microphonic.
If it were microphonics, it would be some acoustic/mechanical feedback. I don't think that's the case here, but you can always test microphonics like I did in the OSDEHA thread. Just hook up the anode of the tube to a scope and then smack the tube with a stick. Don't break it (the tube). If you see an oscillation at 3.7 kHz, that might ring a bell (no pun intended).

Before further debugging, I'd convince myself 200% that the measurements are correct. I'd make sure there is no ground loop or similar in my measurement gear (I have been bitten by this more than once). Also, I'd confirm the blip to be absent at the input of the tube (grid pin) with the amp fully powered on.

My approach to debug this would be to run the tube in the most simple anode-follower circuit one can think of, using different supplies for B+ and the heaters. Can you replace the active loads with some resistors (both on the anode and the cathode)? Do you have another B+ supply you could use for testing? Run the heaters off a battery or some other PSU? Once you replaced all the circuitry around the tube I'd expect the blip to be gone. If so, it's "only" a matter of putting things back step-by-step and see if/when the blip comes back.
 
I have a bit of an update, but unfortunately not a very exciting one.

I took @mbrennwa's advice and rebuilt the amp as a very simple common cathode stage: RC circuit in cathode, resistor load, no volume pot, unregulated suply. It still rang when certain notes played. I replaced the OPT with RC coupling to measure, and still saw the squiggle on the FR.

So, I gave up on the 6E5P and rolled in another high gm triode strapped pentode, changing out the socket for a teflon socket of slightly different design to rule out any mechanical issues. It also rang with some music, and showed the same squiggle in the FR at a slightly higher frequency. I applied the usual measures to reduce oscillation-- adjust stoppers, reduce bias/gm, etc. It sounded great. I then added the regulator and other bells and whistles back, took the output off of the mu-output, and gave it a listen. Even better.

To anyone reading this thread in 2030, I think the takeaway is that a breakout board with small SMD stoppers and all the usual mitigation strategies for oscillation won't make up for a sprawling layout in a big chassis.

The one thing that I still haven't figured out is the noise floor. When I meansure the amp noise floor with the amp turned off, and the IEC power cable disconnected, the 7kHz hump is not there. If I connect the power cable, the hump appears, even with the amp off. If the power cable stays plugged in, but I sever the connection between IEC earth the circuit while maintaining the connection to the power toroid's shield and amp chassis, the hump disappears again. My usual connection point is the star ground, which is situated at the final B+ cap's ground. Any idea why this might be?
 
External ground loops are always present.
The frequencies, amplitude, etc. vary.

Once you fix those, it is time for the amplifier power supply, and then for the amplifier circuit.

The first capacitor of the B+ filter, always has the most hum and ripple current (to create microvolts or millivolts across milli Ohms of return/ground wire).
Capacitor input filters have the largest and most transient current, and the fastest rise current, with lots of hum harmonics.

Choke input filters have lower, smoother, lower rise time currents, with very few harmonics.

Pick the one that is easier to tame,
Or,
Pick the one you have to do everything right, to keep the hum and hum harmonics out of the amplifier.
This is an art and a science.

Next, attack the input connector and input tube circuit. Any ground loop here is amplified by the gain.