> capacitor mics, I found that there are a large number of mics that exhibit extemely low source impedance
Right. For one tube or one FET, your only hope is to match the plate resistance or FET drain resistor, and they generally aim square for like 150.
But when you get to many-transistor mikes like my AKG414 w/transformer, even some of the push-pull emitter followers, you end up with feedback techniques and near-zero output impedance. Some designers think this is a good thing, others feel that a hundred ohms does no harm and may be better for loads that expect some source impedance (transformer high-end can be optimized either way, but a winding optimized for ~200Ω source may ring like a bell with zero-ohm source).
> we know that TX's have no given impedance, ... to figure that out, we would have to now know what load is being connected to the secondary no?
In this case: no and yes.
Think this way: there are "two kinds" of transformers. Power transformers, and voltage transformers. They may actually be the same transformer: the difference is how we use them and what we expect from them.
There is a power transformer on the pole in front of your house. 95% of the power that goes into it comes out of it. Impedance is reflected almost exactly: you turn on more lights, the primary acts like a lower impedance. Audio loudspeaker transformers, and 600Ω line transformers, are also power transformers, and reflect impedance.
But what is the impedance of a vacuum tube or FET grid? A 1Meg resistor was mentioned but we often don't need one. For bass and midrange, the input of a tube or FET is about as close to infinite as we can find. (It gets significant at the top of the audio band....) A tube/FET eats only voltage, no current, no power.
So what is the impedance into a 1:10 transformer loaded with infinity? ∞/(10^2) == ∞. That seems to defy some law of nature. Even if we pencil 200Meg, it leads to absurd results. If we actually try it, we never really get ∞ or even 2meg. In fact we see about the same thing at the primary whether or not there is a tube on the other side. It appears that the transformer is eating more power or energy than the tube grid, and this is true. Considered as a power transformer, it is crappy. But since the power required in the tube grid is very near zero, we don't care about power efficiency. We only care that the transformer does not load the mike excessively. So we design the transfo without regard for the grid load.
But wait: if the grid load does not matter, why not wind 1:20 or 1:100 and get free gain? Aside from the fact that this leads to wire too fine to wind, there is a place where an audio voltage transformer does handle power:
The input capacitance of a tube is like 250pFd. The capacitance of a transformer winding is about 250pFd. That gives 500pFd at the secondary. This reflects back to the primary as 250pFd*10^2= 50,000pFd. The reactance of 50,000pFd at 20KHz is 159 ohms. This means the 150Ω mike is significantly loaded and the transformer has to pass energy efficiently at 20KHz.
You can fiddle the numbers a bit. PA transformers often did not aim for 20KHz. FETs have lower capacitance. Winding capacitance can be reduced (though not without other compromise). But basically you can't get 20KHz response if you try to wind the secondary for reflected source impedance higher than about 15K-30K. The ratio isn't really an issue, but once you pick a source impedance like 150Ω or 200Ω you have pretty well capped your turns ratio. In effect, you raise the ratio (free gain) until the tube and winding capacitance load the source at the top of whatever you consider the audio band. And then at the top of the band the input impedance will BE your minimum designed load on the source.
> I'd take issue with Hugh Robjohns' implied assertion that microphones were originally ribbon and moving coil, with condensers arriving a good deal later.
I mumbled on that but let it lay as historical trivia. All mike types have deep history, often running back before there were amplifiers to make them practical. Each type went in and out of fashion in different countries at different times.
There is a deeper issue: power and impedance.
The condenser is actually the weakest commonly used mike type. It can be designed for nice high voltage, but the output impedance is like 50pFd, too weak to drive a yard of cable well, or even to drive some tube grids. So a condenser HAS to have an amplifier AT the element (or very close), which may be awkward. However, once you get over the awkwardness, you can have an output as strong as you want. Line-level output condenser mikes have been made, were apparently common in a sector of German PA.
The crystal is superficially a condenser but with solid-state transducer (and normally with a mechanical transformer driving a hefty crystal), and can drive several yards of cable well. This was good enough to make crystals dominant in low-price PA work for several decades.
The dynamics have much larger power outputs, but low impedance leading to output voltage too low to drive a grid well. A ribbon always ends up sub-ohm with sub-microvolt output. A nice dynamic levers this up to 10 ohms and sub-millivolt. The voltages are low but now we have some power and can step-up with transformers. But if you put a 0.1Ω:15KΩ transformer at the amp, with a few yards of cable to the ribbon, the >0.1Ω of the cable will dim the power delivered to the transformer. If we put that transfo at the mike, cable capacitance will kill the treble. For practical size/cost wire, the line should work around 20Ω to 1,000Ω, depending who writes the specifications for length, performance, and cost. Lines with meters on them like higher impedance so the voltage overcomes rectifier loss, and if long such lines could be equalized. Microphones never drive meters, might work short-line one day and long-line another day and should not need re-EQ depending on the line-length, so lower Z is favored. In any case, we end up with a transformer at the mike and a transformer at the tube.
A fairly late development was dynamics with very fine wire working directly at ~150Ω or higher (I have some wound for 900Ω). But note that the ubiquitous SM58 is old-school: 10Ω internally with a step-up transformer.
Before tubes existed, there were several mike types, but the carbon button was by far the most common. The diaphragm+button mechanical layout puts pretty good acoustic power to the button, the carbon grains give good change of resistance which can easily be made similar to line and earphone impedance, but the killer trick is that a carbon mike needs DC power and IS an amplifier that can deliver line-level directly. It isn't a very linear amplifier and early broadcasting used push-pull double-button carbon mikes to lessen the nasties. It isn't a very quiet amplifier, marginal for AM radio use. But before tubes, and even into the tube era, carbon was king.
