Using a cap on the passive side is about introducing the same ESR curve on both legs so CMRR is good across the entire frequency spectrum. Now whether it actually makes enough difference to bother with is another question. Since there is no signal other than the noise component, probably not.
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As raydyo mentioned most of them (and I would say virtually all of them since the alternative is either servo or high spec op-amp both of which cost as much or more than using a dedicated true balanced out chip), will have a blocking cap on the active leg, and some of them on the passive leg for reasons I mentioned. No practical impact between whether it does or doesn’t (on the passive leg) as far as cabling goes.
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Agreed on the math. Though if the cap is large enough to get well below 20Hz, who cares?
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The resistors, caps, op-amps in my discussion with sekim would be inside the sending box, not the cable itself. Nearly everything out there will be AC coupled, either by caps or tranformer. I suppose that for going from unbalanced to balanced you could make a pseudo-balanced cable. Though it would need to account for the output resistance of the sender. For example, if you know the output resistor in your unbalanced output, adding the same resistor in the ground path on the unbalanced end of the adaptor cable would give you a pseudo balanced path. The resitor values are not critical as long as they match. There is some signal loss due to the voltage drop across the combination of resitors. But for modern line inputs with fairly high impedance inputs this is a small loss. Often 47k. Not so for a transformer input which could be as low as 600 ohms.
No way that I know of to get the pseudo-balanced effect going from balanced to unbalanced.
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