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Nice experimental work, Nick. It clarifies a number of things about the OT-speaker setup that most people just miss. It's all too easy for folks with not much formal background to get lost in the blizzard of info-oids sprayed on the internet. The real theoretical work on transformers and tube amps is between 75 and 100 years old by now, and is remarkably clear - if not all that accessible. The stuff in RDH4 is particularly good.
I see a lot of resistance (
) to using the classical model of a signal transformer in the niche group of people who want "tone" to be some independent variable in guitar amps. It's very human to want to believe in magic elixirs, but in reality, magic is just any technology that you don't yet understand.
On the first tests, you guys got to the right considerations. To understand speaker inductance- and motion-caused effects, you have to include the connection to the OT. OTs must have primary inductances in the tens to hundreds of henries to preserve low frequency response, and that gets inductances measured from, for instance, an 8-ohm secondary down into the tenths of henries. Speaker inductances are on the order of 2-30 millihenries. Leakage inductances are highly variable and cannot be estimated from the other inductances or loads because they are artifacts of exactly where the wires are inside the transformer coils. The old "Quality Factor" for hifi OTs was the ratio of the primary inductance (which controlled the low frequency response) to the leakage inductance (which controlled high frequency response, mostly). This was between 10,000 and 100,000 for transformers worthy of the "high fidelity" term.
The reason I'm blathering on about inductances is that the same currents flow in the speaker inductance, secondary-referred OT leakage inductance, and secondary winding inductance. The energy in an inductance is E = (1/2)* L*Isquared. Current is identical, so the stored energy is proportional to the inductances. So the speaker inductance is the small dog in the chain here. The big dog is the OT secondary inductance for first order effects. Then the leakage inductance, representing as it does the un-clamped energy that can't be coupled to the primary.
Speaker and secondary inductance energies are linked through the OT to the primary drivers. It's only the leakages that are free to cause havoc. A center tapped primary has the CT tied to B+ and the active side pulled down to as low as about 50-90V depending on the output tube's "saturation" ability. The other half must, by transformer action, rise an equal amount above B+ that the active side drops below B+. So the "off" side must be at a little less than 2*B+. On top of that, you have the effects of leakage inductances. That's the only place you can really get V = L* di/dt spikes.
Spikes from rate-of-change of current are truly unlimited - except by the parasitics of the inductor itself or the other components connected to it. All real inductors have self capacitance, and that is what causes the ringing you see in actual scope traces of inductors loaded and suddenly shut off. Inductive "spikes" are actually a half-sine (if nothing breaks!) and a diminishing ring as the resistance in the inductor eats the inductor's energy down to zero as the energy runs back and forth through the inductor's windings.
Leakage inductances represent a failure of windings to be coupled to one another. There is a leakage inductance on the primary side, and a leakage on the secondary side. The leakage on the primary side creates transients that can puncture primary windings, the secondary endangers secondary windings. To really protect them, each side needs some constant load or a break-over clamp to eat the energy in the leakage inductances when you try to force the current in the leakages to change instantly. Primary side R-Cs work by forming a place to dump the leakage energy quickly (the capacitor) and clamps work by suddenly being a low resistance to clamp the inductive energy.
No magic - but a lot of pick-and-shovel work to undertand.
I see a lot of resistance (
) to using the classical model of a signal transformer in the niche group of people who want "tone" to be some independent variable in guitar amps. It's very human to want to believe in magic elixirs, but in reality, magic is just any technology that you don't yet understand.On the first tests, you guys got to the right considerations. To understand speaker inductance- and motion-caused effects, you have to include the connection to the OT. OTs must have primary inductances in the tens to hundreds of henries to preserve low frequency response, and that gets inductances measured from, for instance, an 8-ohm secondary down into the tenths of henries. Speaker inductances are on the order of 2-30 millihenries. Leakage inductances are highly variable and cannot be estimated from the other inductances or loads because they are artifacts of exactly where the wires are inside the transformer coils. The old "Quality Factor" for hifi OTs was the ratio of the primary inductance (which controlled the low frequency response) to the leakage inductance (which controlled high frequency response, mostly). This was between 10,000 and 100,000 for transformers worthy of the "high fidelity" term.
The reason I'm blathering on about inductances is that the same currents flow in the speaker inductance, secondary-referred OT leakage inductance, and secondary winding inductance. The energy in an inductance is E = (1/2)* L*Isquared. Current is identical, so the stored energy is proportional to the inductances. So the speaker inductance is the small dog in the chain here. The big dog is the OT secondary inductance for first order effects. Then the leakage inductance, representing as it does the un-clamped energy that can't be coupled to the primary.
Speaker and secondary inductance energies are linked through the OT to the primary drivers. It's only the leakages that are free to cause havoc. A center tapped primary has the CT tied to B+ and the active side pulled down to as low as about 50-90V depending on the output tube's "saturation" ability. The other half must, by transformer action, rise an equal amount above B+ that the active side drops below B+. So the "off" side must be at a little less than 2*B+. On top of that, you have the effects of leakage inductances. That's the only place you can really get V = L* di/dt spikes.
Spikes from rate-of-change of current are truly unlimited - except by the parasitics of the inductor itself or the other components connected to it. All real inductors have self capacitance, and that is what causes the ringing you see in actual scope traces of inductors loaded and suddenly shut off. Inductive "spikes" are actually a half-sine (if nothing breaks!) and a diminishing ring as the resistance in the inductor eats the inductor's energy down to zero as the energy runs back and forth through the inductor's windings.
Leakage inductances represent a failure of windings to be coupled to one another. There is a leakage inductance on the primary side, and a leakage on the secondary side. The leakage on the primary side creates transients that can puncture primary windings, the secondary endangers secondary windings. To really protect them, each side needs some constant load or a break-over clamp to eat the energy in the leakage inductances when you try to force the current in the leakages to change instantly. Primary side R-Cs work by forming a place to dump the leakage energy quickly (the capacitor) and clamps work by suddenly being a low resistance to clamp the inductive energy.
No magic - but a lot of pick-and-shovel work to undertand.
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