Calling all Merlinites... Gain of Cathodyne

From Merlin's website ... http://www.valvewizard.co.uk/cathodyne.html ... and the analgous chapter from his hi-fi book, read this ... http://www.valvewizard.co.uk/cathodyne.pdf ... I can't follow the math; maybe you can make more sense of it. FWIW, I've noticed that some of the website content differs slightly from the book (published 2012).

 

Might this make Merlin a mere mortal after all?

I have the both books. I might even be that other person that showed you other info (power tube heater wiring?). But I can't make myself read the hifi book as lots is literally the same as the guitar one. Except for the changes, obviously...

 

It's hard to follow the math when it isn't there.

 

freakin' awesome, thanks! I can follow that.

What throws me off in Merlin's DVPGB book on page 144 ... he says, "But for normal purposes, Rk = Ra. Hence, if we call the load at the anode or cathode R, the gain to either output becomes A = mu(R/(ra+R(mu+2))) ... ignoring minus sign."

I read that, then, as him saying eq 1.5 = eq 6.1 ... substituting in R for Ra and Rk ... but clearly they are not, as the denominators are different.

 

You don't need math to understand that in a balanced cathodyne, the cathode signal swing follows (and is the same amplitude as) the grid signal swing, and so is about unity gain. The plate signal swing is the same amplitude as the cathode signal swing (albeit that's it's 180 degrees out of phase). Therefore, the plate signal swing is also about unity gain.

The effect of 100% cathode current feedback means that there can be no positive gain at the plate. (whereas in a 'conventional' inverting gain stage, the plate load is bigger and the cathode load is a fraction of the plate load)

 

If you like the maths , chew on this;

 

Oh jeeze, Linear Audio... shît just got REAL.

 

Cathodyne PI) The total load resistance is divided into two parts and shared between the anode and the cathode, So from the input perspective the gain is the same to each of the two (anode and cathode) and the gain to each is near unity. The math Ten Over posted works out. The handwritten part is the derivation of the printed equation for gain "A" I don't claim how each of the terms Rp, Rk, Rb, ra, Rt were derived but if he sets Rp=Rk=R and Vk=Vp=Voutput the math is correct, though there are bits he doesn't state which make it a little confusing to follow, like when he shows how he factored out R separately from the rest of the equation seemingly leaving out "ra" and then its there again. But it all works and is correct.