... Hammond's data on a Marshal replacement transformer, the EDB1750Q, you will find this transformer has primary impedance of 7.4k ...
The primary impedance on its own is 42.5kΩ as I've shown. But Hammond claims 7.371kΩ, so what's up?
They also say the turns ratio is 21.46:1 (this is for 16Ω, as you'll see). I've already linked the discussion with the basic mathematical derivation, so I won't repeat that here. Instead, I'll point out how Hammond's data sheet reiterates the fundamental properties of a transformer.
You mentioned, "What was not explained in this discussion was the voltage outputted at the 8 ohm leads is about 1.414 times higher than that found at 4 ohm leads."
Notice Hammond has a pair of number beside the indicated secondary impedances:
4Ω -> 14.1v, 3.5A = 49.35w
8Ω -> 20v, 2.5A = 50w
16Ω -> 28.3v, 1.8A = 50.94w
For the same power output, if the secondary impedance is lower, the voltage output is lower and the current is higher. Really, their chart should have 50w for each, but the differences are all rounding error (4Ω output voltage is really 20 * √2, or 14.142... v, 16Ω voltage is really 28.284... v).
Look at that other thread I linked earlier; I showed that impedance ratio = turns ratio
2; turns ratio = voltage ratio.
- The voltage of the 4Ω tap for 50w is 14.14v, and the voltage of the 16Ω tap for 50w is 28.28v.
- Voltage ratio = 28.28v / 14.14v = 2:1
- Impedance ratio = 16Ω / 4Ω = 4:1 = (2:1)
2- To have our "constant volts-per-turn" rule hold, the 16Ω tap must have twice the number of tuns as the 4Ω tap.
So how does the voltage of the 8Ω tap wind up 1.414 times higher than the voltage of the 4Ω tap?
- 1.414 roughly equals √2.
- 4Ω has 14.14v for 50w; 8Ω tap has 14.14v * √2 = 19.997v (call it 20v)
- Voltage ratio = √2:1
- Impedance ratio = (turns ratio)
2 = (√2:1)
2 = 2:1
So the rules of voltage and impedance ratios hold whether you're talking about among section of a winding or from one winding to another. The basis is equal volts-per-turn.
Turns ratio is given on the data sheet as 21.46:1, but this is for the whole primary to the whole secondary. I already showed impedance ratio is turns ratio squared, so (21.46:1)
2 = 460.5316:1 (primary to secondary). 460.5316 * 16Ω = 7368.5056Ω, which just means Hammond rounded 21.463632:1 for the sheet.
The data sheet primary impedance was found without reference to any frequency, or with any info of the transformer's inductance, but based solely on knowledge of the turns ratio and fundamental transformer properties.
Therefore, the transformer's primary impedance is based solely on the impedance attached to the secondary, and reflected via the turns ratio to give an apparent primary impedance.So what about that 42.5kΩ we calculated earlier? If that's the reactance due to the open-circuit inductance (end-to-end) of the primary, and the properties of a transformer places a reflected impedance of 7371Ω on the primary (end-to-end), what happens if these values are effectively parallel impedances?
7371Ω || 42.5kΩ = (7371Ω*42587Ω)/(7371Ω+42587Ω) = 6283Ω
What about at the other end of the spectrum, 12kHz? Reactance there is over 10MΩ. 10MΩ || 7371Ω = ~7365Ω
Which is basically no effect. At the treble end, other transformer imperfections limit frequency response.
... Your discussion regarding the output at 80Hz only tells part of the story. There is no discussion the effects of the speaker, where most available speakers have resonance frequency peak in this area of operation. ...
The transformer will still have measurably reduced response at the upper and lower end if you use a power resistor as the load; while a speaker's varying impedance has an impact, it's not the sole cause for everything.
What about a discussion of hearing loss? That has the most impact on the loss of bass, right??? Throw as many complications in as you want, but you just make it an impossible problem to comprehend.
When you reach a point of understanding this stuff, you will find that simplifying assumptions get you the 80-90% solution. After you have that, you can refine with the complications that separate ideal components from real components and get the rest of the way there.
It's taken me more than 10 years to stop making things harder than they are; once I stopped that, electronics became easy to understand.