How to calculate mic input xfmr ratio for tube circuit

PRR

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> historical types that I measure at roughly 1:22 ratio which IMO also measure fine for practical response

The real limit is not ratio but secondary impedance. And what you call treble.

As you aim for higher impedance, inductance and leakage-inductance both rise, but capacitance hardly changes. The leakage-inductance against the capacitance forms a 2nd order high-cut. The frequency of this high-cut moves as square-root of the impedance you want.

High-Mu core allows a smaller winding for the same L and Ll and therefore less C and a higher resonance. "Pie" winding can drop C but tends to increase Ll- this needs a sharp pencil and a painstaking winder.

For "broadcast" response 5K is easy, 22K is harder.

For "AM radio" response (>3KHz generally bad) you can wind higher secondary impedance.

Referenced to common 150r sources and music treble,  1:7 to 1:12 are typical "best" ratios for economical winding.

_IF_ the source (microphone) impedance is lower you can get the same response from a higher ratio. A 1.5 Ohm mike could drive a 1:100 transformer just fine, *except* more than a few feet of mike cable starts adding Ohms to the mike, reduces level and treble at the primary. The 37 Ohms once common at RCA suggest ratios about 2X higher than we now use for 150r nominal impedance.
 

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