Feedback & Stability

Phase margin is measured at the gain crossover frequency (where |loop gain| = 0dB). It is the difference between the phase at that frequency and −180°:

Stable: PM > 0°. Typically want PM ≥ 45° for adequate transient response (minimal ringing). PM ≥ 60° is preferred for critically damped response. PM < 0° means the system oscillates.

Miller compensation places a capacitor (C_c) between the output and input of the second gain stage. Through the Miller effect, this capacitor is multiplied by the stage gain, creating a large effective capacitance at the first stage output. This:

• Pushes the dominant pole to a lower frequency (pole splitting).
• Pushes the second pole to a higher frequency.
• Ensures the gain crosses 0dB before the phase reaches −180°, providing adequate phase margin.

A series nulling resistor with C_c can cancel the right-half-plane zero created by the feedforward path through C_c.

The maximum rate of change of a sinusoid V(t) = V_p·sin(2πft) is:

In practice, choose an op-amp with SR ≥ 2× this value (~63 V/µs) to provide adequate margin and avoid slew-rate limiting distortion on signal peaks.

1. Measure the oscillation frequency — this indicates where the phase margin is insufficient (near the gain crossover).
2. Check for parasitic capacitance: Probe capacitance, PCB trace capacitance, or load capacitance creating extra poles.
3. Verify the feedback network: Check for stray capacitance across feedback resistors (creating unwanted zeros/poles).
4. Check power supply bypassing: Insufficient decoupling can cause oscillation through supply feedback.
5. Measure the open-loop Bode plot (break the loop with an injection transformer) to determine actual phase margin.
6. Add compensation: Reduce bandwidth with a feedback capacitor, add lead compensation, or reduce capacitive loading.