Transimpedance Amplifier Bandwidth

f3dB = √(GBW / (2π × Rf × Cf))

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Formula

f_3dB = √(GBW / (2π × Rf × Cf))

Description

A transimpedance amplifier (TIA) converts photodiode or sensor current to voltage using a feedback resistor Rf. The feedback capacitor Cf is required for stability because the photodiode capacitance and Rf create a pole that can cause oscillation. The −3 dB bandwidth of the TIA depends on the op-amp gain-bandwidth product (GBW), the feedback resistance, and the feedback capacitance. Higher Rf gives more gain (V = I × Rf) but reduces bandwidth. This is the fundamental gain-bandwidth trade-off in TIA design.

Variables

  • f_3dB — Amplifier −3 dB bandwidth (Hz)
  • GBW — Op-amp unity-gain bandwidth (Hz)
  • Rf — Transimpedance feedback resistor (Ω)
  • Cf — Feedback capacitor for stability (F)

Practical Notes

For a Butterworth (maximally flat) response, set Cf = √(Cd/(2π × GBW × Rf)), where Cd is the total input capacitance (photodiode + parasitic). The resulting bandwidth is f_3dB = √(GBW/(2π × Rf × Cd)). Typical TIA applications: fiber optic receivers (Rf = 5-50 kΩ, BW = 100 MHz − 10 GHz), spectroscopy (Rf = 1-100 MΩ, BW = 1-100 kHz), particle detectors (Rf = 100 kΩ − 10 MΩ).

Related Formulas

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