Lecture Notes: Two-Stage Op-Amp Phase Margin

Overview

• Discusses characteristics of a two-stage operational amplifier (op-amp) related to phase margin.
• Focus on ensuring the phase margin is within acceptable limits for stability, typically 45 to 60 degrees.

Key Concepts

Characteristics of Two-Stage Op-Amp

• Two-stage op-amps have two poles and one zero.
• DC Gain and unity gain frequency are critical parameters.
• Desired system resembles a first-order system in gain bandwidth.

Gain-Phase Relationship

• Initially, the phase starts from 0 degrees.
• First pole (P1) causes a -90 degree phase shift.
• Second pole (P2) should occur after the gain bandwidth, leading to a phase shift close to -180 degrees.
• A zero (Z1) shifts the phase back towards +90 degrees.
• The phase margin is calculated between -180 degrees and the phase at the gain bandwidth.

Phase Margin Importance

• Phase margin ensures the stability of the op-amp.
• A phase margin less than 45 degrees is not acceptable.
• Target phase margin: 60 degrees.

Design Considerations for Phase Margin

• Keep P2 away from the gain bandwidth product to maintain stability.
• Design zero (Z1) to be greater than or equal to 10x the gain bandwidth.

Transfer Function and Angle Calculations

• Derived transfer function: Vout/Vin = ADC(1 - s/z) / ((1 + s/p1)(1 + s/p2)).
• Phase angle calculation involves:
  • -tan⁻¹(ω/z) - tan⁻¹(ω/p1) - tan⁻¹(ω/p2)
• Ensure at least 60-degree phase margin by tuning poles and zeros.

Calculating Phase Margin

• Equation: Phase margin = 84.29 - tan⁻¹(gain bandwidth / P2)
  • For 60-degree phase margin: P2 should be ≥ 2.2 x gain bandwidth.
  • For 45-degree phase margin: P2 should be ≥ 1.22 x gain bandwidth.

Circuit Design Implications

• Use derived equations to simulate the circuit.
• For 60-degree phase margin:
  • P2 (gm2 / c2) ≥ 2.2 x gm1 / cc
  • Typically, c2 is the load capacitance (Cl), hence c2 = Cl.
  • Compensation capacitor (Cc) should be ≥ 0.22 x Cl.

Conclusion

• Ensuring the phase margin is crucial for op-amp stability.
• Correct design and simulation will meet the desired phase margin specifications.