School me on preamp input impedance

Oh and heres a lot of math stuff if you want:

whirlwindusa.com/support/tech-articles/high-and-low-impedance-signals/

EmRR's explanation is perfect.

On the mechanics side, what those are doing is changing the effective turns ratio in the transformer being used. In your Tree Audio example there are probably two coils with a center tapped winding on the primary (mic) side of the transformer. In the first two the "hi" signal goes into the "hi" side of both windings. For 37.5 setting the "low" is connected to the center tap of the coils, presenting 1/2 of the primary windings, in parallel. When you switch to 150, you get both of the windings in full, still in parallel. This doubles the effective turns on the primary side. When you switch to 600, you're connecting both windings in series - "hi" goes to the fist winding, the "low" of 1 and the "hi"of 2 are connected together end to end, and the "low" side of the mic is connected to the "low" end of the second winding, doubling the turns on the primary side again.

You can use this number to figure the turns ratio too. For example, if the transformer is a 37.5/150/600:10k, this is the same as saying the turns ratio in each setting is 1:16, 1:8, and 1:4. If it makes it easier you can think of it as 1:16, 2:16, and 4:16, since the secondary side isn't changing but the primary is doubling each time. This shows you why the gain changes. Each one of those represents a different step-up ratio. Since it is doubling each time, you have 6 dB steps: 24 dB, 18 dB, and 12 dB. The impedance changes with the square of the turns ratio, which is why going from parallel to series on the primary side is a 4x change, not a 2x.

This also shows how the turns ratio changes the impedance presented to whatever source you're using. If the transformer secondary side is terminated by a load resistor, this load is "seen" by the mic on the primary side divided by the same square of the turns ratio. Using the same ratios above, a 150k load resistor is seen by a mic as 562 ohms, 2250 ohms, and 9000 ohms in each setting.

As mentioned, different mics may prefer different loadings.

It's also important to note that transformers themselves do not have an "impedance" per se. They reflect loads on the secondary back to the primary based on the impedance ratio, and that's generically what you see if we only consider ideal components.

So, lets say we know our turns(voltage) ratio, 1:2 (pri/sec) and we want to know our impedance ratio.. That's just the turns ratio squared, or 1:2x2 = 1:4. For the sake of simplicity, lets say that the secondary has a grounded lead and a lead that has a resistor to ground and no other loads. That resistor value will reflect back through the transformer based on the impedance ratio.

Lets say that you want an "impedance" of 1200 at the primary, so since this is a 1:4 impedance ratio transformer, you'd multiply 1200x4 and get 4800. You'd want that resistor to be 4.8K.

But as EmRR states, transformers are not linear devices. There's a lot of other reactive and parasitic components to the equation of using transformers. You'll see a lot of transformer secondaries in preamps with compensating networks that help "fix" the flatness problems and such.

This doesn't even get into the fact that the source impedance is also reflected back into the transformer and can cause issues as well!

Here's the audio transformer bible that will answer any question you've ever had on audio transformers:

jensen-transformers.com/wp-content/uploads/2014/09/Audio-Transformers-Chapter.pdf

EmRR in which case the impedance presented to the mic is that of the input stage reflected through the transformer plus the transformer impedance load itself, ya? At this point my head starts to hurt. A tube presents a nonlinear impedance by frequency doesn't it?

This is some good shit.

I would say that's a reasonable trial/error situation.  Some mics like the SM57 were designed in their earlier forms to work with lower input impedances, and later adapted to the modern impedances we're used to seeing.

One trick with the SM57 is to load it considerably with a 600R pad of some low attenuation value.  This seems to have the effect of flattening out it's bottom end some, so you get less proximity effect.  Some anecdotal evidence says that it might help flatten the high-mid peaking as well, but random graphs on the internet seem to say that's false.

Most active mics will have output buffering with such low output impedance that loading them down will not appreciably affect their output response.  

The *standard* (there are no standards in audio interconnections unfortunately) is somewhere between 1K and 5K for preamp inputs, which is *roughly* 10x the output impedance for a dynamic mic, which is around 100-300ohms.  For maximum voltage transfer, the rule-of-thumb ratio is usually 1:10 which gives some balance between impedance matching and voltage transfer while maintaining some loading.

Why they do that is because in transmission line theory, you typically want maximum power transfer through a 1:1 match of source and load impedances, but you lose 50% of your voltage in doing so!  In the low voltage audio world this is akin to killing 6dB of signal..

You can see this in action by using the following formula if you wish:

dB loss = 10Log(Vin/Vout)^2

Vin is voltage from the source, Vout is voltage with load.

or if you want to do it with impedance in ohms:

dB loss = 20Log(RL/RL+RI)

RL is input impedance at the preamp input (or any load really), RI is the source impedance from the mic(or any source).

Doing the math, you'll see that moving either the source impedance higher, or the load impedance lower, will decrease the signal.  

Let's not forget non-transformer coupled mics.

I’m going to read this over and over and over. Thank you for sharing this, all y’all.

Take it with a grain of salt as Audio Precision tells you that measuring the impedance of inductive loads is prone to error, but many old tube preamps with highest quality input transformers measure well over 5K at some frequencies, some up to 20K, with lowering Ω at lower and higher frequencies. The 6dB down point (you guessed it) will be a matching condition. So you get an idea of the kind of impedance curves that exist, and that is a lot of the 'transformational magic' of many vintage preamps, every mic and preamp combo will make a different sound because it's essentially an EQ, similar to changing speakers in a speaker cabinet on a tube amp.

I could only find one example that I captured with my phone:  

old tube preamp input Z curve

Every time I do a custom rack job on some old preamp with multi-tap input transformers, I get asked to set it up for every available impedance. No one ever used those taps like that, they set them for what they think they need. I always talk people out of it, as most people are never going to change them very often, and it's a huge labor cost to make it an option on every channel. It's mostly useless bling for most things and it puts another mechanical switch in the low level audio path to eventually get dirty, intermittent, or fail. It's another thing that can be set or left in the non-optimized or wrong position. If the taps allow it, I'd rather use separate XLR's for each Z to keep the switch out of the path, but no one ever wants to do that.

I do like having a channel or 2 set up for 50 ohm Western Electric or Altec mics, or RCA and Shure ribbons with 50 ohm taps. 50 ohm setting on an SM57 can make for a fat band-passed sound. Etc.

Important clients can be perfect loads.