Electrical – Some questions about a single ended system and common mode noise

1. No ground loop. That comes from having multiple ground connections forming a literal loop, and you don't have that. If the source's case were also connected to AGND, then it would be a loop.

2. There is always both capacitive and inductive coupling:

   • Capacitive applies to the entire wire as a unit and follows nearby voltages
   • Inductive goes from one end of a wire to the other and follows nearby currents

   A low-impedance path to somewhere* typically overrides capacitive coupling to the point that you don't care anymore, but it does nothing for inductive coupling. So far, you've solved half of the problem for one of the two wires. The other wire may or may not be okay, depending on the output impedance of the sensor.

   Inductive coupling makes the sensor's ground "wiggle", so its output also follows that "wiggle", and then adds the opposite "wiggle" to the signal return wire. So you'd think the "wiggles" would cancel, but only if the wires were to exactly coincide, which they obviously don't...unless you use coax.

   * "Somewhere" is usually an AC ground, which could be the circuit reference or anything else that can hold a steady DC value.

3. If you leave the sensor completely floating, then the common-mode voltage becomes uncontrolled. It'll pick up lots of noise from everywhere and probably run into the input protection diodes. These built-in diodes are there for a variety of good reasons, but they also create their own noise as they switch. Plus, you're relying on the Common-Mode Rejection Ratio (CMRR) of your input stage to take that noise back out, which also isn't perfect.

A better idea:

Take a cue from professional audio and use a shielded twisted pair (STP) to carry a balanced signal. This arrangement done right will carry a microphone-level signal unamplified from stage to a mid-audience or balcony sound booth while keeping the noise inaudible:

^{simulate this circuit – Schematic created using CircuitLab}

The upper one appears to be what you're doing, and is exactly how it ends up for a typical hand-held microphone.

• The grounded shield takes care of capacitive coupling, and you'll notice that it remains a shield/case and does not connect to the sensor itself.
• Now both wires are used as inputs, one subtracted from the other to take out whatever capacitive coupling might be left. (the shield does pick up some at the far end because of its finite impedance, and this couples again onto the signal wires)
• The common-mode voltage is set by R1/R2. Their value of 6.8k is standard for pro audio, but you can use whatever you like as long as they're equal.
• The twisted pair puts both wires as close as possible to the same position so that the inductive coupling can cancel.
• The supply voltage is pretty standard for lots of analog electronics, not just audio. Again, you can adjust as needed, as long as the Common Mode Voltage + Signal + Coupled Noise never exceeds the Input Amp's ratings.

The lower one is included for completeness, showing how a sensor can be powered through the same set of wires.

• You'll notice that the sensor only drives one signal wire, but the other has an equal resistor to ground. The important thing to remember is to keep the impedances equal so that both types of coupling affect them equally.