What is the formula for TIA Optimal Bandwidth?

The TIA Optimal Bandwidth formula is f−3dB = √(fGBW / (2π × Rf × Cin)), where f−3dB—Closed-loop bandwidth (Hz); fGBW—Amplifier gain-bandwidth product (Hz); Rf—Feedback resistor (Ω); Cin—Total input capacitance (F).

What does f−3dB mean in the TIA Optimal Bandwidth formula?

f−3dB is Closed-loop bandwidth (Hz).

TIA Optimal Bandwidth

Q: How do you calculate TIA Optimal Bandwidth?

Use the formula f−3dB = √(fGBW / (2π × Rf × Cin)). When a transimpedance amplifier is compensated for maximum flatness, its achievable closed-loop bandwidth is the geometric mean of the amplifier’s gain-bandwidth product and the feedback-network pole. Enter the values you know in the calculator above and it solves for the remaining variable.

f−3dB = √(fGBW / (2π · Rf · Cin))

Calculator

Bandwidth

Gain-Bandwidth

Feedback Resistor

Input Capacitance

Result

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Formula

f−3dB = √(fGBW / (2π × Rf × Cin))

Description

When a transimpedance amplifier is compensated for maximum flatness, its achievable closed-loop bandwidth is the geometric mean of the amplifier’s gain-bandwidth product and the feedback-network pole. This sets the speed limit of a photodiode front end: higher gain (larger Rf) or more input capacitance reduces bandwidth, while a faster op-amp raises it.

Variables

f−3dB — Closed-loop bandwidth (Hz)
fGBW — Amplifier gain-bandwidth product (Hz)
Rf — Feedback resistor (Ω)
Cin — Total input capacitance (F)

Practical Notes

Bandwidth scales only as the square root of GBW, so doubling speed needs 4× the GBW. There is a direct gain-bandwidth trade: raising Rf for more transimpedance gain lowers the 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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