Output transformer primary inductance - warming, long topic with some simple maths. LOL.
What's the best primary inductance for an output transformer, or even an interstage transformer? Often, we get customers asking for insanely high primary inductance as they read over internet that there should be at least 10H for a 1K primary impedance.
High primary inductance is good but with conditions that the capacitance and the leakage inductance remained the same (which is kind of difficult to achieve since these parameters are conflicting).
Leakage inductance is proportionate to the number of turns (square of it in fact). In order to reduce leakage inductance, one must decrease the number of turns. Then, that reduces the primary inductance! This can be overcome by different winding techniques (interleaving for one, or use different core materials for another, and many more), but those also will introduce different parameters that one need to consider. Yes, it is kind endless - balance is the key.
Let's do a oversimplified calculation for easy understanding.
Required load = 8,000
Primary impedance of SE OPT = 15,000
Primary inductance of SE OPT = 90H
Reactance of primary @ 30Hz = 2piFL = 2 * 3.142 * 30Hz * 90H = 17,000
(30Hz is the reasonable low frequency limit)
Real load with the OPT = reactance of primary // reflected load resistance
Required load = 17,000 // 15,000 = 8K
1K primary impedance needs about 6H in this case.
So, one needs an OPT of 15K primary impedance with 90H primary inductance for very good low frequency response, as required by the driver tube specifications. The stronger the tube (lower Rp - plate resistance), the lesser the requirements on the output transformers.
Now this is not that difficult, isn't it? Of course, if one needs to extend the low frequency to 20Hz, which we think is a bit over, then the primary inductance may need to increase. One simple way of increasing the primary inductance is to increase the primary turns, and/or use a larger core (or core with different electrical parameters - I would not say better here since different core has different intended usages, more may not be the best a lot of the times).
Increase turns, will increase the capacitance and leakage inductance. This will affect the high frequency response since it is sort of like a filter. The more turns, the higher the leakage inductance. Also, the turns number affects the flux density and we do not want to exceed the amount stated for the core size/material. Not forgetting to mention, the transient response of the OPT will need to be taken care off too by controlling the leakage inductance. If you see ringing, that's one of the artifacts of high leakage inductance. It may cause distortion or early overloads if not taken care.
We can use different winding techniques to help with the above but there's just so much those techniques can do before reaching the limits.
Of course, in circuit design, there are other parameters that will come into the picture that will affect the OPT primary inductance requirements, which is out of topic for now. And... there are many more that comes into the picture that we do not have time and space to list out all.
This also shows that universal transformers isn't such a great idea, is it now? Go figure. Go tailor made!