What effect does adding a resistor in parallel with the feedback capacitor have on stability in a differentiator circuit?

What effect does adding a resistor in parallel with the feedback capacitor have on stability in a differentiator circuit?

• A. It creates a dominant pole that ensures faster settling.
• B. It has no effect on stability.
• C. It introduces a real pole that improves phase margin and stability.
• D. It worsens phase margin.

Answer: (C)

Adding a resistor in parallel with the feedback capacitor changes how the feedback impedance behaves as frequency changes, and that stabilizes the circuit. In a practical differentiator, the input is designed to differentiate within a mid-band, but without compensation the gain grows with frequency and the op-amp’s own bandwidth can cause excessive phase lag and possible oscillations. When you put a resistor in parallel with the feedback capacitor, the feedback impedance becomes Zf = Rf || 1/(sCf). This introduces a real pole at s = -1/(Rf Cf) in the closed-loop transfer function, while the input path still provides the differentiating action at lower frequencies. The result is that high-frequency gain is limited, which improves the phase margin and overall stability. In short, it creates a real pole that stabilizes the differentiator.

Adding a resistor in parallel with the feedback capacitor changes how the feedback impedance behaves as frequency changes, and that stabilizes the circuit. In a practical differentiator, the input is designed to differentiate within a mid-band, but without compensation the gain grows with frequency and the op-amp’s own bandwidth can cause excessive phase lag and possible oscillations. When you put a resistor in parallel with the feedback capacitor, the feedback impedance becomes Zf = Rf || 1/(sCf). This introduces a real pole at s = -1/(Rf Cf) in the closed-loop transfer function, while the input path still provides the differentiating action at lower frequencies. The result is that high-frequency gain is limited, which improves the phase margin and overall stability. In short, it creates a real pole that stabilizes the differentiator.