Electrical – How does noise affect an unbalanced signal on a balanced cable

The "have the signal and gnd wires inside the shield but connect the shield only at the speaking end" -trick actually extends the metal shield of the speaking device. It's extended to only few millimeters apart from the metallic shielding of the listening device.

This surely reduces the effect of capacitively coupled AC fields. For example normal room lightning lamps spread strong 50Hz electric fields capacitively.

Magnetic fields which have high enough frequency, for example those of the radio waves, get killed by the eddy currents in the shield and stay away from the inductive loop between the signal and GND lines. 50Hz magnetic field isn't affected. It penetrates centimeters to copper. Fortunately in normal living house rooms there rarely are so strong 50Hz magnetic fields that the small gap between the wires catch substantial hum voltage inductively.

But the system isn't balanced. There are still all those common mode noises left which are catched by big loops. Those loops are caused by multiple connections between the signal grounds of the devices. Most harmful unwanted connections are via the mains electricity supply. In many devices the signal ground has at least some connection, often zero ohm galvanic connection to the protective earth wire or at least a capacitive connection to the mains supply wires.

The 2 different connections between the signal grounds of the devices easily collect hum and other noise voltages. It's like an unwanted noise signal source were in series with the caused loop. Because the signal grounds no more are directly together, but through a noise voltage source, that noise is directly added to the signal voltage.

Often people try to insert tape or otherwise break at least the galvanic contact via the protective earth. That often reduces the hum substantially, but compromises the electric safety. In addition microphone eaters get easily half of the mains supply voltage to their lips through the rf interference filter capacitors in the power supplies and the devices have a tendency to get damaged if they are connected or disconnected without removing the mains supply from the whole system before.

The proper solution is to have balanced audio signals if the environment is noisy and loops cannot be avoided. One trick to reduce the loops without safety compromises is to use isolation transformers to supply the mains AC.

You are correct about the feedback connections. The inverting and non-inverting inputs of both amps are reversed. Also, there is no reason for a full differential amplifier topology because the input is not balanced, so there is no "differential" other that the single-phase input and its GND.

For this most basic approach, start with two completely independent opamp circuits, one inverting and one non-inverting, both with the same gain magnitude. Note that the impedance of the inverting amp's feedback network directly sets that amp's input impedance, so keep it at around 10K or above.

A shortcoming of this approach is that if one side of the balanced output is disturbed, such as shorted to GND, the other side continues to make its full amplitude output. For a more complex balanced driver, look at app notes from THAT Corporation and Analog Devices. Both make chips for this function, and their internal schematics and explanations should be helpful.

http://www.analog.com/media/en/technical-documentation/data-sheets/SSM2142.pdf