Calculating NFB (Open Loop Gain and Closed Loop Gain)

[Littlewyan]

I've been tweaking my amp recently and one part I've been playing with particulary is the Negative Feedback. I settled on 47K on the 8Ohm tap, which is great, but I've been trying to work out why that sounds good. I look at other amps and I see a whole variation of values, i.e. Friedman BE100 47K on 4Ohm, SLO100 39K on 4Ohm, Marshall 100K on 4Ohm etc. So I follow the equations in Merlin's book to see how much feedback these values equate to in the different amps and the maths doesn't seem to add up when compared to other methods. I've come across three different ways of calculating NFB and they don't seem to add up. Aiken's site, Ampbooks.com and Merlin's book.

So, lets start with the basics. How do you calculate Open Loop Gain?

https://ampbooks.com/mobile/amplifier-c ... alculator/

The calculator here seems to do that for you by taking the Input Voltage, PI Gain, Wattage and Speaker Tap. However, the input voltage on an EL34 Power Section doesn't seem to really vary if I change the OT Impedance from 3.5K to 6.6K going by the datasheet, which means the Open Loop Gain is the same for either Impedance. Yet, when I follow the maths in Merlin's book it changes a lot (Goes from 21.6 to 28.3). So what's right and what's wrong? Am I missing something?

[Ten Over]

However, the input voltage on an EL34 Power Section doesn't seem to really vary if I change the OT Impedance from 3.5K to 6.6K going by the datasheet, which means the Open Loop Gain is the same for either Impedance.

I'm not following you. If you put the same input voltage on the EL34's, the 3.5K OT will put out a a larger signal than the 6.6K OT on the same output tap. That means that the open loop gain is larger for the 3.5K OT, doesn't it?

[Littlewyan]

If you follow the maths in Merlin’s book, then it’s the opposite. The 6.6K impedance has a higher gain.

[pdf64]

...If you put the same input voltage on the EL34's, the 3.5K OT will put out a a larger signal than the 6.6K OT on the same output tap. That means that the open loop gain is larger for the 3.5K OT, doesn't it?

I think you've got that mixed up.
Consider that for the same signal ac plate current, the larger the load impedance, the larger the signal voltage across the load.
Of course the plate resistance is in parallel with the load impedance (OT primary), so as the load impedance value increases, the effect will lessen as its value becomes equivalent to the plate resistance.
The max voltage (ie power output) may differ, but that's another matter.

[Ten Over]

I think you've got that mixed up.

Yes, you are correct, I do have that mixed-up.

[Littlewyan]

Any ideas on how you calculate the Open Loop Voltage Gain of a power section?

[martin manning]

You can estimate power amp open and closed loop gain like this:

The voltage at the OT primary Vpri = Vg * Gm * Ntubes/2 * Zload,
where Vg is the power tube control grid signal, Gm is the transconductance, and Ntubes/2 and Zload
are the number of tubes and the load impedance on each side of the power stage respectively.
Note that the effective Gm will vary with the operating point and the signal level.

Across the OT: Vsec/Vpri = (Zsec/Zload)^0.5
where Vsec is the voltage across the OT secondary.

Combining and simplifying the above:
Vsec/Vg = Gm * Ntubes/2 * Zload^0.5 * Zsec^0.5

Zload (Class B) is Zpri/4, where Zpri is the a-a impedance of the OT.

Across the PI, Vg/Vin = Api, where Vin is the PI input voltage, and Api is the PI voltage gain.

So, all together the power amp open loop gain Aopen (Vsec/Vin) is:
Aopen = Api * Gm * Ntubes/2 * (Zpri/4)^0.5 * Zsec^0.5

The feedback voltage ratio Vfb/Vsec = (Zsec_fb/Zsec)^0.5 * R2/(R1 + R2)
where Zsec_fb is the secondary impedance tap used for the feedback voltage, and R1 and R2 are the feedback voltage divider.

Closed loop gain (ignoring Zo sec) is then: Aclosed = Aopen/(1 + Vfb/Vsec * Aopen)

[Littlewyan]

Brilliant, thank you Martin! But how do you know the Gm or Vg if you've not followed a spec on the datasheet? For instance, I'm running EL34s at 470V with a 6.6K OT.

[martin manning]

Vg is just the grid signal voltage, so it's arbitrary. The Gm is strongly driven by the screen voltage, so you need to correct data sheet values for that. What is your screen voltage?

[Littlewyan]

Ah, so basically the bias voltage?
Screen voltage is roughly 460-465V

[martin manning]

You really need a load line, but looking at the curves in the 1964 Mullard data sheet, for 400V Va and Vs, it looks like 0.01 would be a reasonable estimate for Gm.

[martin manning]

With that 0.01 assumption for Gm, the 6k6 Zpri you mentioned, Api of 25, and an 8Ω speaker, I get Aopen about 29.

[Littlewyan]

Brilliant, thank you Martin!

[martin manning]

One more small edit above to cover the case where the FB is taken from an OT secondary tap other than the one the speaker is connected to.