Math behind OT impedance rules-of-thumb?

[R.G.]

Since impedance doesn't apply to DC

I know what you're saying, but this is sure to confuse him if he goes on and learns more. Impedance in general as a concept applies to all frequencies, including DC; it's just that at DC inductive impedance goes to zero and capacitive impedance goes to infinity, leaving on the resistive parts to consider at DC. Then as you note:

and transformers cannot pass DC, the speaker on the secondary draws nothing from the primary when there is just static DC on the primary.

which is exactly correct.

As the signal is swinging positive/negative, plate current is swinging above and below that static DC bias current.

... in a class A amplifier where the bias is such that the plate current in either output tube never goes to zero. In a Class AB amp, the plate current swings lower until it hits zero, while the opposite tube is conducting more current.

You now have an alternating DC current (I say "alternating DC" because while it is an "alternating current" in the sense that it is constantly alternating in value, it's still positive going current in terms of flow direction so the direction of flow is not "alternating" like it would be in pure AC) through the primary, which the transformer does pass, thus the speaker draws from that and the valves now see the reflected impedance of the transformer that is provided by its impedance ratio.

Yes. The transformer combines alternating DC pulses on opposite sides of its primary into an alternating AC current, which can then be transformed. Any DC offset is lost as far as transforming through to the secondary.

[Steve Conner]

What are you guys talking about! Now my head is hurting.

The important thing is that Ra of a pentode or beam tetrode is very high and more or less meaningless. You can't use it to calculate the optimum load impedance. You have to take a large-signal approach that looks at the maximum current you can shove through the tube, the maximum voltage, power dissipation and so on. There is a lot of latitude: depending on the supply voltage and load impedance, a pair of EL34s can produce 20w of luscious Class-A cathode biased power, or 100W of harsh, horrid Class-B mush.

The physics behind Ra of a triode: The plate voltage influences plate current in just the same way as the control grid voltage. You can prove that for maximum power output the load impedance should be equal to Ra.

But in a tetrode or pentode, this effect is stopped by the screen grid, which launches electrons towards the plate almost irrespective of its voltage. Ra is almost infinite compared to a triode.

[elushi]

This means that when the valves are in a quiescent state (i.e. idle, or "zero signal conditions"), the valves do not see the reflected impedance from the secondary load and only see the "DC resistance" of the primary coil itself, which has nothing to do with the transformer's impedance ratio.

well, they reflect impedance as long as it stay close to an ideal transformer...It's less confusing to me to think that it transform voltage, and with the speaker connected, it induces a current that can drive it (which is large because the speaker has a very low impedance)...Am I right? well...in fact V, I and R will all three make a "balance" according to Ohm's law.

"Bias" only applies to the static DC current which flows through the transformer under zero signal conditions

It just came to my mind that impedance question because I thought that, with signal of frequency f Hz applied to grid, inductive impedance of OT would be 2.pi.f.L and capacitive impedance of the tube would be 1/2.pi.f.C (with C the tube internal capacitance) and so the impedance load would also change and this in turn would made the tube instable. but I was just raving.

[elushi]

What are you guys talking about! Now my head is hurting.

Hi Steve! my bad! I'm afraid I change myself the subject of the thread...

You can't use it to calculate the optimum load impedance.

In fact, I started the thread because I thought it was some kind of formula with Ra and Rl in parallel...

The physics behind Ra of a triode: The plate voltage influences plate current in just the same way as the control grid voltage. You can prove that for maximum power output the load impedance should be equal to Ra.

So it means that with the same impedance load that you use with a pentode (i.e. the same OT) when you switch the tube to a triode (for example, with a switch that connects screen grid to OT) you are not driving full power any more (because the tube sees 1/4 of the primary and this is usually far less than Ra), right?

[Wilder Amplification]

well, they reflect impedance as long as it stay close to an ideal transformer...It's less confusing to me to think that it transform voltage, and with the speaker connected, it induces a current that can drive it (which is large because the speaker has a very low impedance)...Am I right? well...in fact V, I and R will all three make a "balance" according to Ohm's law.

That is precisely how one should think about it! One thing that most people have the misconception of is that OTs somehow are different from a power transformer. But in reality, an OT is just a power transformer that operates at audio frequencies. It transforms high voltage/low current to low voltage/high current just like a step down power transformer does. Impedance is just a figure that is calculated off of these two things.

Amplifiers are just modulated DC power supplies...an AC power inverter if you will. As Steve Connor once mentioned, a push pull output section is basically just a full wave center tap rectifier circuit flipped upside down and backwards.

It just came to my mind that impedance question because I thought that, with signal of frequency f Hz applied to grid, inductive impedance of OT would be 2.pi.f.L and capacitive impedance of the tube would be 1/2.pi.f.C (with C the tube internal capacitance) and so the impedance load would also change and this in turn would made the tube instable. but I was just raving.

One thing one must remember is that idle bias current only exists when the amp is in a quiescent state. Once there's a signal present, plate current and plate voltage fluctuate with the input signal as well as with the impedance of the transformer so the "static bias current" no longer applies except to mark where the "zero crossing" point of the output signal will be on the primary side of the OT.

[elushi]

As Steve Connor once mentioned, a push pull output section is basically just a full wave center tap rectifier circuit flipped upside down and backwards.

Yes! Totally! I didn't noticed that!

Once there's a signal present, plate current and plate voltage fluctuate with the input signal as well as with the impedance of the transformer so the "static bias current" no longer applies except to mark where the "zero crossing" point of the output signal will be on the primary side of the OT.

Thank you! very helpful! and your first reply about loadlines was very helpful too

[elushi]

a pair of EL34s can produce 20w of luscious Class-A cathode biased power, or 100W of harsh, horrid Class-B mush.

Well I've read about load lines...but just to get this straight:
The 25W max plate dissipation that shouldn't be exceded is Vp * Ip, with Vp=Vpp-Vk the voltage drop of the tube, right?

Output power is Ip^2*Rl with Rl = Zout/4 (for push pull OT center-tapped at B+) and also can be calculated as Vpp-Vp * Ip, right?

I'm confused because if I plot a load line for a EL34 tube with 450V B+ supply and 5k p-p load and the line exceeds the 25W limit curve almost all the time.
Just to got an idea of the slope, these are two points:
First point of the line: 450V @ 0A (that's not the bias point), second point of the load line 0V @ 450V/1250 = 0.36A

[Steve Conner]

Well, the 25W figure is an average. Unlike puny transistors that can be damaged by high power peaks, the plate of a tube takes several seconds to heat up.

In particular, it's a push-pull amp so the tube is only conducting half the time, therefore the average dissipation is half what the diagram implies. Actually a little more than half, to the extent that the amp runs in Class-AB rather than pure B.