martin manning wrote: ↑Fri Jul 05, 2024 4:44 pm
The hard part as I see it is getting values to use in the non-ideal model. Some manufacturers provide some of it, for example Hammond includes DCR, primary inductance, and no-load voltages on their data sheets; capacitances and leakage inductance are most likely going to come from measurements. I don't think those details are critical unless one is trying to get an accurate frequency response.
Mostly frequency response, but the leakages come in really handy if you're messing with transients, such as a speaker lead going open.
For the OT model I used to produce the plot above, there is a coupling factor of 0.995, which I didn't mention. It's a guess, and probably on the low side. It might be as high as 0.999, but I don't have one to measure. Any idea of what that value might be for a typical good quality guitar amp OT? No capacitances were included, but I don't believe they are very important for estimating mid-band output power.
It varies hugely, primarily (?!) with the windings' layer interleaving. Leakage inductances can be used in calculating the coefficient "k". Here's a reasonable sendup on measuring the k and M factors:
https://www.onallbands.com/audio-transf ... -modeling/
It's common for a guitar amp manufacturer to change the vendor and possibly interleaving on their OTs, so things change. Both leakage inductance and mutual coupling are slightly different views of the same thing - magnetic field leaking out of windings and not going through the coils of the other winding(s).
I think that leakage inductance may be something you need. Falling back on the ideal-transformer-plus-lumped-parts-model; the power through the transformer does not depend strongly on k being 0.95 or 0.99, exactly. My personal view of how a transformer works, and this is how I started the stuff I may post, is that the core has to be charged up with enough magnetic "zoots". A "zoot" is an imaginary unit of magnetic muchness. For a given voltage-frequency in the frequency domain and a given volt-time integral in the time domain, the core gets charged up to some level. This forms a "bridge" over which the secondaries can suck power from the core, but this is instantly replaced by power from the primary. The core is not really a player in power transfer, with only a couple of exceptions.
The exceptions are that the core sucks in magnetizing current to feed the field up to the desired level. Simple modelling says this is linear, more complex modelling says that magnetizing current is nonlinear, depending on the B-H curve it pumps. The area integral of the BH curve traversed is the energy lost to core loss, and it is nonlinear too, but modellable.
Hang on, I'm getting to it.
Core losses are pretty much fixed at some level of volt-time or volt-frequency drive. This is easy to figure out for power transformers, harder for audio transformers. Leakage inductance limits power through the transformer by lowering the voltage drive to the ideal transformer inside, much like primary resistance does. This is probably the biggest contributor to power loss. Leakage inductance losses go up as frequency increases. Use of "mid band" means by definition that you're far away from where leakage losses are overwhelming other losses, so if you''re measuring at "mid band" you're probably in a region where the coupling coefficient k and its evil secret identity leakage are not big contributors.
Audio output transformers done for fidelity are usually wound to a much lower flux density than power transformers. This is to both get the primary inductance to be larger and more constant, without the fall off in incremental inductance as the BH curve starts its gradual rolloff. Guitar OTs??? Who knows?? Is there an MBA in the company? That will definitely make for smaller cores, higher Bmax, and higher losses.
There's another subtle effect getting you. Remember that volt-time and volt-frequency stuff? Bmax in a transformer is heavily, heavily dependent on frequency. It's the volt-second integral that drives Bmax; so a transformer driven with 200Hz has only half the Bmax it would if driven with the same voltage at 100Hz. Qualitatively, transformer power handling goes up with increasing frequency, until the frequency gets high enough that the losses in primary and secondary voltages due to leakage inductance start being significant. By saying "mid band" you have set the frequencies to where magnetizing losses are not severe, primary inductance losses are not big, and losses to k/leakage are not severe. I would expect not much change in power losses anywhere in the mid band that are not accounted for very closely by winding resistance.
To be fair, I'm typing this from general principles, so if you're trying to find sub-2% issues, things might be more critical.
"It's not what we don't know that gets us in trouble. It's what we know for sure that just ain't so"
Mark Twain
