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Question regarding half-μ (actively loaded triode) stage

Hi,

The stage is sometimes referred to as SRPP, totem-pole or whatever.
I'm no expert on the matter so I'll just refer to it with the name I read in Merlin Blencowe article, 'half-μ stage'.

Here is a picture of the actual stage, from his article:
1737316458155.png


Nomenclature aside, I'm interested in using this topology (instead of a usual SRPP), to amplify voltage coming out an AD1865 DAC with resistor I/V.
I'll be using 6Η23Π (soviet equivalent to ECC88/6922) with B+ around 200VDC.

So, my simple question is regarding the Rk1/2 values.
What are suggested values for them resistors??

In SRPP applications using the same tube I have seen values as low as 75Ω and as high as 820 with most common values being around 150-200Ω.
But this is different to an SRPP and I have no idea on how to calculate the right value for them.

By the way, I want to avoid bypassing the resistors.
I have no need for the lower impedance.
Following stage will be high enough (47kΩ minimum).

Any suggestions would be appreciated.

Thanks!
 
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First, you have to make sure that the cathode resistors are big enough for your valves to survive.

Then I guess you will want to bias the valves for minimal noise, as noise is critical in the first stage after a DAC with a small resistor used for current-to-voltage conversion.

When you choose Rk1 = Rk2 = Rk too small, you get little white noise but more excess noise than needed.

When you choose Rk1 = Rk2 = Rk too large, you get little excess noise but more white noise than needed.

Somewhere in between there is a point where it works best, but the data in the datasheet are normally insufficient to find out where.

There are two ways to do that:

1. Try a couple of values and measure or listen what works best
2. See if someone has characterized the noise of your valve type in such a way that you can calculate the noise minimum from that. Merlin Blencowe has done that for the ECC88, but I don't know if his measurements apply to the Russian equivalent.
 
Regarding keeping the valves alive, 68 ohm would be about the bare minimum to stay below the ratings. Taking some safety margin, I would not go below 100 ohm.

That is, in

https://tube-data.com/sheets/112/6/6N23P.pdf

the maximum anode dissipation is specified as 1.8 W and the maximum average cathode current as 20 mA. Your 200 V supply should divide equally between the upper and the lower part, so each part gets 100 V. That means the current actually has to be restricted to 18 mA because of the dissipation limit.

Looking at this graph,

Screenshot_20250119-215136.png


and interpolating between the 90 V and 120 V graphs, you see that you need about -1.2 V of negative grid voltage to stay below 18 mA.

1.2 V/18 mA = 66.6666... ohm, nearest E12 value 68 ohm - but that is very much on the edge.
 
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To get an idea where the noise optimum is, I've tried to calculate it based on Blencowe's ECC88 data, taking into account that the cathode resistor will not be decoupled and assuming flat weighting from 200 Hz to 20 kHz, which is equivalent to optimizing the noise density around 4.3 kHz.

It's remarkably close to Rayma's and euro21's recommendations. I end up at 6 mA and 390 ohm.
 
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How much does the noise change for your 6mA case when both Rk are decoupled?

See the graph, which shows the calculated power spectral density of the input-referred noise voltage (that is, the number of V2/Hz) around 4.3 kHz, which is the same as the average power spectral density from 200 Hz to 20 kHz, as a function of the anode DC current. (Regarding that 4.3 kHz: doing a similar calculation using A-weighting, you would probably end up somewhere around 3 kHz, and using ITU-R 468 weighting, somewhere near 6 kHz. It doesn't matter much because of the shallow optimum.)

halfmunoisedensity4kHz3.png


The optimum has shifted from yesterday's 6 mA to 8 mA because I used Child's law to extrapolate the transconductance yesterday and just looked at an old E88CC transconductance graph today. With decoupling, the white noise is smaller, shifting the optimum to somewhat smaller currents.

Noise power spectral density at 4.3 kHz split up into parts, factor of two missing because this is just for one degenerated common-cathode stage instead of a half-mu stage:

halfmunoise_parts.png
 

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