Yep no volume increase. That surprised me too. RCA and BAL same loudness despite being 2v vs 4v. I guess they are both 0db unity gain.
Well, it's actually a design that has different relative gain (and different input impedance) for the different inputs, making sure that "nominal" inputs all produce 2V for "full scale" when going into the volume control. I would call that of course competent.
On the RCA input the input circuit (which is needed because of the balanced input) is configured as unity gain buffer.
So 2V SE in = 2V SE out to Volume control.
Switch to the 3.5mm input meant for portable devices that commonly have around 1V at maximum output (e.g. Apple products) and the circuit is switched to have 6dB gain (2x).
So 1V SE in = 2V SE out to Volume control.
Switch to the balanced 4.4mm input meant for the common 4V at maximum output for balanced HiFi components (or +14dBU in pro parlance) and the circuit is reconfigured to a balanced differential input with in effect the same configuration as a for example the TI INA137 or the THAT1246 balanced line receiver with -6dB gain (1/2).
So 4V BAL in = 2V SE out to Volume control.
The result is that for the same gain set and the volume control position the playback level is the same, given the source is designed according to expectations, which is how I think it should be.
Incidentally the 2V reference level for the internal signal is selected as with +/-12V supplies the circuitry can handle 8V or 12dB greater than 2V which is incidentally the maximum boost of the EQ circuitry in the Zen can, so it is not overloaded. The EQ is placed before the Volume Control so it's noise contribution is minimised.
As to "why does the balanced input cause ground loop", it does not. The problem is an incorrectly manufactured Cable and/or source with a missing ground, not a ground loop.
The 4.4mm Connector is known as Pentaconn and not Quadconn. It has 5 connections. The 5th should be grounded (see electrical safety requirements in various national and international standards) for mains powered equipment in Equipment Class A and for reasons of compatibility obviously in any other equipment. Leaving it floating is acceptable for headphones only.
If either the cable manufacturer or source manufacturer omitted to connect ground to the fifth connection, then there is a problem, as the Common Mode rejection of balanced Inputs is limited, usually around 90dB. If all grounds float the ground will be 1/2 mains voltage (115V in europe or 57V in the US and other 115V countries). Now 90dB CMRR and 110V mean the mains noise will be reduced to around 3.5mV referred to a 4,000mV nominal 0dB reference.
In other words, despite using industry standard balanced circuitry, the SNR is degraded to around 60dB by the missing ground connection.
Solution? Use a 5-wire cable and make sure to use a correctly manufactured source.
If neither is possible run a ground connection via RCA or 3.5mm connectors or in extreme cases a wire between source and ZEN CAN case screws.
Thor