[Part 1 introduces the topic of grounding and "GND-think."]
This article originally appeared in Linear Audio, a book-format audio magazine published half-yearly by Jan Didden.
The ideal differential input would be a transformer. By "ideal" I mean in terms of how well it would manage to look like a voltmeter with just two connections on it. Even if there were hundreds of volts between the chassis of the source and the receiver, this would go completely unnoticed. Other than that, a balanced connection will look more like Figure 7.
Figure 7. A typical transformerless balanced connection.
Vcm symbolises any voltage between the two chassis, however it arose. If the input had been a transformer, no current would flow through the two signal wires, but transformerless inputs necessarily have some input network, if only to provide a path for base currents. The task is to minimise the impact this current will have on the recovered audio signal.
Let's assume the source is putting out 0V and redraw the circuit as a Wheatstone bridge as in Figure 8. Any signal seen between the inputs of the difference amplifier is unwanted.
Figure 8. Input/output resistances seen as a Wheatstone bridge.
It's clear that we don't need a transformer. We can allow current to flow through the signal wires so long as Roh/Rih = Rol/Ril. If the input resistors are well-matched and so are the output resistors, no amount of common-mode voltage will get converted into an output signal.
When a Wheatstone bridge is exactly nulled, the term we use is that the bridge is balanced. That is where the word "balanced connection" comes from. It has nothing at all to do with one voltage going up while the other goes down, but with divider ratios being equal. Don't think uppy-downy. Think equilibrium. Zen. Ooohmmmmm...
The ratio between the error voltage and the common-mode voltage is the common-mode conversion ratio. The smaller it is, the better. It's more common to quote this number in relation with the wanted signal, expressed in decibels. This ratio is called the Common-Mode Rejection Ratio (CMRR):
Let's explore for a second what happens if the output resistances are matched i.e., Roh = Rol = Ro but the input resistances aren't, say Ril = Ri and Rih = Ri + Δri:
The sensitivity to an imbalance in the input resistance increases with output resistance. It pays to minimise output resistance. It also decreases, quite rapidly, with increasing input resistance. So that seems a good idea too.
Secondly, let's explore the impact of an imbalance in the output resistances:
This is fairly important. If your input network consists of two resistors to some local reference, making those resistors as large as you can is going to make a lot of difference. And when you measure CMRR, do so with an imbalance of several ohms on the source side because that test will tell you a lot more about the real-world ability of an input to reject CMRR than a bench test with the inputs perfectly shorted together.
next; “acting locally”...