I saw this weird circuit solution for the first time yesterday and it immediately caught my attention. Obviously there was some clever idea of suppressing common-mode signals. What was it like?
In order to grasp the fundamental idea, I first removed all the minor details that hindered understanding and started trying to see familiar circuit building blocks and principles. I simplified and sketched out the circuit diagram and focused around the part with AD705 op-amp (А3):
Structure. I saw two single-ended input voltages (VIN- and VIN+) between the signal electrodes and reference electrode. Surprisingly their input "sources" were not grounded... but connected to the op-amp output. What the hell was that?!? Aha... they were connected to a "moving" ground, which probably allowed their simultaneous (common-mode) variations to be suppressed.
The input voltages were buffered by amplifying stages (A1 and A2) with high input impedance. In regard to the common-mode signals, these stages acted as voltage followers. That is why I did not draw the network of three resistors between the outputs of the input amplifiers because it was important only for the differential mode.
But what did the 2-resistor circuit between the follower outputs serve? I realized that an op-amp inverting summer was built with the help of Rf and A3.
Operation. Imagine that initially both input voltages are zero. So the op-amp output voltage VREF (of the right leg) is zero as well.
If both input voltages tries to increase (due to some common-mode noise voltage above the real "immovable" ground), the op-amp output voltage decreases (approximately) with the noise voltage below the real ground. And since the input voltage "sources" are connected not to real but to "movable" ground, their voltages move down with the noise voltage. Figuratively speaking, the op-amp output "pulls down" the input voltages with the magnitude of the common-mode voltage (the op-amp output subtracts equivalent voltage from the common-mode voltage). As a result, in respect to the real ground, the common-mode signal will be (almost) zero.
So, in respect to the common mode, the weird RDL circuit can be thought as of an op-amp inverting summer with input sources "grounded" to its output instead of the true ground. Because of this "movable ground", the common-mode signals are suppressed.
If we combine both input voltages and resistors in one, we can think of this arrangement as an inverting amplifier with gain of 200, which output is fed back by VIN... i.e., there are two negative feedbacks - local (implemented by Rf, R1 and R2) and global (by VCM).
I have attached the genuine circuit diagrams sketched with pencil and rubber yesterday to illustrate more realistically the course of my thoughts that led me to this explanation. Of course, I can outline them beautifully... but so they will become less informative...