TIA Feedback Capacitor (Stability)

Cf = √(Cin / (2π · Rf · fGBW))

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Result
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Formula

Cf = √(Cin / (2π × Rf × fGBW))

Description

A transimpedance amplifier (photodiode amplifier) is destabilised by the input capacitance interacting with the feedback resistor, which creates a noise-gain peak. A small feedback capacitor across Rf cancels this by adding a pole. This formula gives the value that yields about 45° of phase margin—the maximally-flat (Butterworth-like) compromise between stability and bandwidth.

Variables

  • Cf — Feedback capacitor (F)
  • Cin — Total input capacitance (photodiode + amp) (F)
  • Rf — Feedback (gain) resistor (Ω)
  • fGBW — Amplifier gain-bandwidth product (Hz)

Practical Notes

Too little Cf rings and may oscillate; too much needlessly limits bandwidth. Minimise Cin (small photodiode, low input capacitance op-amp) to allow a smaller Cf and wider bandwidth.

Related Concepts

All Op-Amps formulas →
Non-Inverting Amplifier Inverting Amplifier Summing Amplifier Difference Amplifier Gain-Bandwidth Product Common-Mode Rejection Ratio Op-Amp Integrator Gain Op-Amp Differentiator Gain

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