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But if the two terminal source is already balanced ... The balance is already there
Consider: The secondary of an output transformer and the primary of an input transformer.
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Yes, but it is easily destroyed. As soon as you connect that source (say, a cart) to a receiver, everything goes out the window. The receiver ends up defining the mode of operation, whether single-ended or balanced.
Excellent example, Steve. This situation works best when only one of the center taps is grounded. That prevents ground loops via power cords, etc.
In your example, you connect center taps, which is fine. You are correct that no current will flow in the center conductor. It can be disconnected and you still preserve the balance, no change in performance. However, this again ignores the big picture. What did we miss? That damn third terminal again. It is still there, although in a minimal fashion. The connection is via leakage. The insulation in the transformers and wiring is imperfect. But it exists. It may be 1000M ohm from primary to secondary, or to ground, yet it is there. It keeps the common mode voltage of the system in check. Sometimes. If the insulation is really good, then the cable can pick up static charge over time. Without any common mode connection, the coils float, and are at the whim of external corruptive influences. It is possible that the static charge build-up is so great that the voltage difference ends up breaking down the insulation, causing an arc. That is, unfortunately, the real world we live in. In this example, the leakage path is actually needed to keep the common mode voltage within reasonable limits.
Another good example is the telephone system. It appears at first glance to be a two-wire system. Tip and Ring. But that is only with blinders on. In the big picture, there is an Earth connection too. No currents are supposed to flow through Earth, but it does provide a handy common mode reference. It is only connected at the CO. Now if the balance between Tip and Earth and Ring and Earth gets unbalanced, guess what? We get currents through the Earth, which is not good. Hence, maintaining balance is again crucial for performance.
This is a clever connection that accommodates a 3-wire system. But it's not really a balanced transmitter because there is no signal on pin 3.
Unless! Unless you receive with a center-tapped transformer, which then back drives the cable so that the signals are indeed balanced. That is why this is so clever.
Let's say we do connect the two center taps. How does that amoeliorate any static charge?
Do you mean a literal connection to the literal earth?
everything to do with a balance of impedances
What are you going to do with the center tap?
No, no. The connection has to be to ground or some other reference voltage that defines the common mode operation. And you only do it to one side. If the cable floats, you can get into trouble. You have to have at least some leakage path. Really, it's not a stretch. Same diagram, just that the R1 and R2 values get big.
Yep. Same thing with power transmission. Same with the old telegraph system, which of course predates telephone. They all connect to Earth using copper rods and salts. This is how one gets the phantom connection (a common mode signalling technique).
The idea was to tie the center-tap of the receiving transformer to the return (opamp ground, actually). The signal on pin 2 is then forced onto pin 3 because of autoformer action, but of opposite polarity. In this way we achieve both impedance and signal balance.
If it's the phono stage I think it is, ... Even using the adapters supplied by the manufacturer you should be able to ascertain for yourself whether the balanced input is offering superior sound to the RCA's (but keep in mind-once again if it's the stage I'm thinking it is-that you will have to adjust for impedance using the RCA's where you do not with the balanced in). ...