A related topic I found in my PM. I think it should be discussed in the open.
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Looking at this section
This balanced Line input plan was widely used in 1970s DBX and several other brands.
This is not good for a Mike input, as Aharon was asking. It has a lot of "dead resistance" between the source and the amplifier. Working with 200Ω mikes, the resistance noise will be much higher than mike noise. But it is a good plan for general line inputs, because the resistance noise is not a problem at line level, and all that resistance tends to make it immune to abuse.
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Could it be replaced with an input transformer?
Possibly. But there is a BIG difference between a transformer and an amplifier. An amplifier can output more power than it inputs. The transformer only passes the power it gets, or takes the power it needs to drive its load.
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how do I determine what the impedence ratio the TX would need to be
The differential input impedance of this plan is 44KΩ. We know the output impedance of the op-amp is super-low, and that it can drive a couple-KΩ load. The differential gain of this plan is 1:1. (However, the single-ended gain, one hot to ground, is also 1:1, so this is not a Floating input or a Center-Tapped input.)
IF the next stage load is 44KΩ or higher, we can just use a 1:1 44KΩ:44KΩ transformer. Or if we know that the source can drive a lower impedance, we could use a lower-Z 1:1 transformer. 10KΩ:10KΩ is a popular bridging input transformer.
In this case, I happen to know the next stage's input impedance is switched 30KΩ or 3KΩ. So we would have to use a 3KΩ:3KΩ transformer, and present a 3KΩ load to the input jack. That's fairly low "bridging input" impedance.
That next stage could be redesigned, or not, depending what it is (and whether you really need the switched gain).
If the real problem is: you need a transformer for extreme ground-rejection or for "color", simple. Put a 10KΩ:10KΩ bridging transformer in front of this amp, at the screw terminals.
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how would I go about measuring the ratio of an unknown transformer?
That's easy. Put a small audio voltage on one winding and measure the other winding.
Determining the impedance is harder, and strictly impossible. Transformers don't really have an exact impedance. You can use them over a range of impedances, with a range of frequency response and loss curves. The short-cut is to assume that the designed impedance is about 20 times the DC resistance. Then mock it up with the actual impedances you hope to use, and check response, loss, and distortion.