What does this op-amp circuit do? (part of an ECG)

My answer to SE EE question What does this op-amp circuit do? (part of an ECG)

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I have realized that my meeting with TL Fong somehow changed the course of my life... The fact that still there are such curious, enterprising and, above all, well-meaning and honest people on the web seems to multiply my creative abilities. Every day he asks me more and more questions to discuss... which makes me think, over and over again, about great circuit ideas... understanding them better... and finding better explanations...

Three days ago, he put the topic of ECG amplifiers and thus he brought me back to my answer above in SE EE from a year ago. I temporarily stopped thinking about his previous question about Tunnel Diode I-V Curve Plotting and begin thinking again about this ingenious circuit idea implemented in the so-called "right leg driven circuit" (RDL). So I realized even more deeply the great idea behind it and expanded my answer in EE. Here it is...

Answer

I saw this weird circuit solution for the first time a year ago and it immediately caught my attention. Then I managed to reveal and roughly describe the idea behind the circuit. Now I want to expand these explanations with some new insights. Here is another more detailed circuit diagram - Fig. 1:

Fig. 1. Detailed right leg driven circuit (chegg.com)

Obviously there was some clever idea of suppressing common-mode signals. What was it like?

Basically, the next amplifier stage with differential input suppresses the common-mode input voltage. However, since ECG amplifiers operate at extremely low input voltages, it is desirable that there is no common-mode signal at all (only the differential signal).

In order to grasp the fundamental idea, I first removed all the minor details that hindered understanding - Fig. 2, 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:

Fig. 2. A simplified circuit diagram of the right leg driven circuit

Structure. First I saw two single-ended input voltages (VIN- and VIN+) between the signal electrodes and reference electrode. Surprisingly their input "sources" (the human body) were not grounded; instead, they were 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. Usually, they were implemented as two paired non-inverting amplifiers (Fig. 1) but, in regard to the common-mode signals, they acted as voltage followers. That is why I did not draw the network of three resistors between the outputs of the input amplifiers (the input part a classic instrumentation amplifier) 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 with the purpose to produce the common-mode voltage.

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 try to increase (due to some common-mode noise voltage above the real "immovable" ground), the op-amp senses this change at its inverting input and begins decreasing its output voltage below zero until makes its value equal to the common-mode noise voltage. 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 even when the input voltages change in a differential manner. 

So, in respect to the common mode, the weird RDL circuit can be thought of as 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 - Fig. 3:

Fig. 3. DRL circuit presented as an inverting amplifier

We can see here two negative feedbacks - local (implemented by Rf, R1 and R2) that is used to make the op-amp summer and global (by VCM) that compensates the common-mode voltage. The latter has another important function - to compensate for the contact resistance between the human body and the reference electrode. How does this magic work?

This undesired resistance is put into the negative feedback loop and the op-amp observes the voltage after this disturbance (at its inverting input)... and keeps it almost zero. So, it lowers its output voltage even more to compensate for the undesired contact resistance.

I have attached circuit diagrams sketched with pencil and rubber to illustrate more realistically the course of my thoughts that led me to this explanation. Of course, I could outline them beautifully... but so they will become less informative...