I am working with a driven right leg circuit, whose purpose is to attenuate the common-mode voltage \$V_{cm}\$ on the body by sensing the common-mode voltage, amplifying it (and reversing polarity), and then injecting the amplified voltage back into the body in a feedback loop. The common-mode voltage exists on the body due to stray capacitors \$C_{pow}\$ and \$C_{b}\$ between power line and body, and body and ground. The goal of this circuit is to minimize \$V_{cm}\$. Because of the feedback, there is a possibility that the circuit might become unstable. An indication of when this happens, is when the phase margin of the open loop system becomes negative - so I decided to run an AC sweep on my open loop circuit to check it out. The circuit and results are here: -
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The thick green trace is the magnitude of the output voltage and the dashed trace is the phase of the output voltage. Technically, this circuit actually uses positive feedback, because \$V_o\$ is fed straight back to \$V_{cm}\$, but because of the inverting amplifier stage constituted by R1, R2 and C1 the total feedback loop becomes negative feedback. This is why I in the AC sweep am plotting \$-V_o\$. Note that the input voltage to the circuit in a control sense is \$V_{cm}\$, not \$V_{powerline}\$.
From the AC sweep, I see that the magnitude of the open loop output voltage (actually open loop transfer function) crosses 0 dB two times. The first time it happens, the phase is around \$-100^\circ\$ which does not make the system unstable. However, the magnitude curve then rises above 0 dB, and then crosses 0 dB again at around 5 MHz. This time, the phase is roughly \$-255^\circ\$ which causes a negative phase margin. This to me, implies that the system is unstable. However, when I close the feedback loop and run a transient analysis, subjecting my circuit to a sinusoidal waveform stemming from the powerline, the circuit seems happily stable: -
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What is going on? Why is my system stable? Is this a special case of crossing the 0 dB line multiple times?
In addition to the Bode plot, LTspice can also plot the Nyquist plot. Nyquist's stability criterion states, that if the point (-1,0) is encircled clock-wise once (and is not encircled counter-clockwise) the closed loop system will have one pole in the RHP. The Nyquist plot is seen here and it seems (-1,0) is indeed encircled: -
