Gain calculation of tube class AB output stage

[yungman]

Hi

I don't know if anyone here design tube power amps. I am calculating the gain of the class AB output stage of push pull tubes and output transformer. Class AB by definition has a small signal region that both tubes are working and is operating in pure class A. Only when input signal is large to a certain point when one or the other tube is turned off and the stage goes into class B region.

I have trouble proofing the gain of the class A region is the same as class B region in the output stage. That would not be good as the gain changes from small signal to large signal. Here is my derivation of gain of both class A and class B. The article I use is:https://pearl-hifi.com/06_Lit_Archive/07_Misc_Downloads/Push_Pull_Theory_MIT.pdf Fig.33b. for class A calculation. For class B, one tube is off, so the one tube that is working sees the primary impedance of R_pp/4. I showed the calculation of both and you can see the equation do not match. I would like someone with this knowledge to take a look.

Thanks

 

[NFuller]

I'm not sure what some of the subscripts here mean so it is a bit difficult to follow your math. The gain of a push pull stage is difficult to calculate in full generality since the load line is not a smooth function when transitioning from class A to class B. So I am suspicious whether or not the formulas you have describe AB operation.

In my experience, calculating the exact gain is not feasible anyways because both tubes and transformers have strong non-ideal behavior. I usually just try to find a rough estimate of the gain. For a power output stage, I usually expect a gain of around 6 or so.

Since I'm not a fan of drawing composite curves, I tend to follow the method suggested here for calculating the gain http://www.valvewizard.co.uk/pp.html. This is certainly not exact, but it is simple and will give you a reasonable estimate of the gain of a push pull stage.

 

[yungman]

Yes, I have not found any article talking about this at all. That's why I took on the task to get down to the bottom of this. Tube articles are very incomplete, nothing like for transistors where you can get all the information in the world.

I read the article from Valve Wizard many times and I drew the load line for my design using their technique of drawing the class A and class B load line. But that's not exact. ( I know nothing is exact in tubes, but the gain has to be the same before or after the transition from class A to B, or else, the distortion will be substantial.) I just cannot see the gain is different between class A and B. But I worked on this for a while already. I am just hoping someone have better insight than me.

Actually my derivation is very much follow the Valve Wizard article, that separate the class A from class B like the two load lines drawn. ( the composite load line is just the class B load line where the primary impedance of the output transformer is R_pp/4... or in the Valve Wizard Z_a/4)

I think this field is so small that nobody cares to research into this. Not like the SS output stage, the crossover distortion and gain is well studied already. I never even see any article addresses the crossover distortion in tubes. And believe me, I read a lot of articles. I am pretty sure I download and read most of the articles I can find by Google. Actually the Valve Wizard article you named is one of the very best, I think it's written in the modern days. I did not see any old books or articles that address the transition that well already. But still it's not getting to the bottom.

 

[yungman]

I just dug up the composite load lines I drew for KT88 with 3.3K and 4.5K primary using the method shown by the Valve Wizard. You see the complete composite load lines is on two plate cureves drawing back to back so you see both the +ve and -ve half. The top and bottom composite load lines are jointed together to form a straight line. the joining line is approximately the two class A load lines combined together:

The Valve Wizard article is very good. It's the only article that kind of explains SUMMING the two class A load lines to give the line joining the two composite load lines ( top and bottom) to become one straight line.

My question is how perfect is this approximation.

 

[NFuller]

My question is how perfect is this approximation.

During class A operation is where there will likely be some deviations. Notice how the composite curves in class A don't intersect. I don't expect the deviation to be large from class A to B, but it is there. During class B operation, the gain should be close to what you have drawn, since only one valve is turned on.

If you are building a push-pull output stage, my best advice is to follow these composite curves that you have drawn. Once the circuit is built, you can use an oscilloscope to fine tune the bias of the output stage to minimize crossover distortion.

 

[yungman]

I know about approximation and tweaking, what I am trying to do here is trying to analyze what's going on.

I since did the calculation using current source and voltage source to replace the tube, the gains are not equal between class A and class B region. I am just surprised.

 

[LvW]

Yungman - while speaking about "gain" I suppose you mean "voltage gain" - correct?
At first you have to face the definition of voltage gain: Output-to-input ratio of the amplitudes or the corresponding mean values.
However, this definition applies to equal signal forms only (sinusoidal), which is identical to require a linear transfer characteristics.
But his is not the case for class-B operation.
Hence, it is not possible to apply the term "voltage gain" to class-B operation. It makes no sense to calculate the ratio of two different waveform shapes.
For example, we are often using the term "power amplifier" - but the main purpose of such an amplifier is to PROVIDE the desired ouput power.
Mostly, the power gain is of secondary interest only.

 

[jim hardy]

I was taught to do it graphically as in your post 4.
Those nonllinear characteristics make the algebra explode on you and an approximation is the best you can do.

Degree of precision depends on how much effort you're willing to invest interpolating and extrapolating.
And how close your individual tubes match their datasheets.

 

[Tom.G]

Aww heck... just make sure you have extra gain in the system then supply negative feedback from the output transformer secondary. Works wonders, also reduces the amplifier output impedance for a higher damping factor.

 

[yungman]

I since looked deeper, I wrote out equations for 3 cases, 1) plate resistance equal very high, 2) plate resistance equal 0, 3) plate resistance equal Rpp/2

You can see the gain of class A and B match if r_p=0.

I understand that tubes are no linear, gm increase with higher current, the real change is gradual, not abrupt. I just want to examine how the circuit behaves. NFB will help, but it's not a good practice to use NFB to hide problems, NFB is more like the final touch when the circuit is already optimized before the NFB.

At this point, I think I got the answer to my original question using the 3 cases of rp. Part of the problem is also the output transformer acts as autotransformer in class A. Primary resistance change from Rpp/2 in class A for each tube to Rpp/4 when one tube turns off.

Thanks for your time.

 

[jim hardy]

Part of the problem is also the output transformer acts as autotransformer in class A.

That's an interesting observation. We end to forget it's inductive...