Transimpedance Amplifier Bandwidth

f3dB = √(GBW / (2π × Rf × Cf))

Quick answer

This calculator solves f_3dB = √(GBW / (2π × Rf × Cf)) for −3 dB Bandwidth. With Op-Amp GBW 22 MHz, Feedback Resistor 10 kΩ, Feedback Capacitor 100 pF, the result is 1.871 MHz. It solves in 3 directions, so you can enter the values you have and get the one you need.

Calculator

−3 dB Bandwidth (MHz)
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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).

Symbols and units

Symbol Meaning Default unit Accepted units
f −3 dB Bandwidth MHz Hz, kHz, MHz, GHz
GBW Op-Amp GBW MHz Hz, kHz, MHz, GHz
Rf Feedback Resistor kΩ mΩ, Ω, kΩ, MΩ
Cf Feedback Capacitor pF pF, nF, µF, mF, F

Step by step

  1. 1. What you know: Op-Amp GBW 22 MHz, Feedback Resistor 10 kΩ, Feedback Capacitor 100 pF
  2. 2. The relation: f_3dB = √(GBW / (2π × Rf × Cf))
  3. 3. Substitute: GBW = 22 MHz, Rf = 10 kΩ, Cf = 100 pF
  4. 4. Result: −3 dB Bandwidth = 1.871 MHz

Worked examples

Minimum range

Given: Op-Amp GBW 0.22 MHz, Feedback Resistor 100 Ω, Feedback Capacitor 1 pF

Result: −3 dB Bandwidth = 18.71 MHz

Low range

Given: Op-Amp GBW 2.2 MHz, Feedback Resistor 1 kΩ, Feedback Capacitor 10 pF

Result: −3 dB Bandwidth = 5.917 MHz

Typical

Given: Op-Amp GBW 22 MHz, Feedback Resistor 10 kΩ, Feedback Capacitor 100 pF

Result: −3 dB Bandwidth = 1.871 MHz

High range

Given: Op-Amp GBW 0.22 GHz, Feedback Resistor 100 kΩ, Feedback Capacitor 1 nF

Result: −3 dB Bandwidth = 0.5917 MHz

Maximum range

Given: Op-Amp GBW 2.2 GHz, Feedback Resistor 1 MΩ, Feedback Capacitor 10 nF

Result: −3 dB Bandwidth = 0.1871 MHz

Solving for each variable

Solve for −3 dB Bandwidth

Op-Amp GBW 0.22 MHz, Feedback Resistor 100 Ω, Feedback Capacitor 1 pF → 18.71 MHz

Solve for Feedback Resistor

−3 dB Bandwidth 100 kHz, Op-Amp GBW 0.22 MHz, Feedback Capacitor 1 pF → 3.501 MΩ

Solve for Feedback Capacitor

−3 dB Bandwidth 100 kHz, Op-Amp GBW 0.22 MHz, Feedback Resistor 100 Ω → 35.01 nF

How −3 dB Bandwidth changes with Op-Amp GBW

Op-Amp GBW (input) −3 dB Bandwidth (result)
4.84 MHz 0.3989 MHz
12.1 MHz 0.6308 MHz
24.2 MHz 0.8921 MHz
36.3 MHz 1.093 MHz
48.4 MHz 1.262 MHz
72.6 MHz 1.545 MHz
96.8 MHz 1.784 MHz
0.1936 GHz 2.523 MHz
0.3388 GHz 3.338 MHz
0.484 GHz 3.989 MHz

The same result in other units

Unit Value
Hz 1871000
kHz 1871
MHz 1.871
GHz 0.001871

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Frequently asked questions

How do you calculate Transimpedance Amplifier Bandwidth?

Use f_3dB = √(GBW / (2π × Rf × Cf)). With Op-Amp GBW 22 MHz, Feedback Resistor 10 kΩ, Feedback Capacitor 100 pF, −3 dB Bandwidth works out to 1.871 MHz.

What is the formula for Transimpedance Amplifier Bandwidth?

The formula is f_3dB = √(GBW / (2π × Rf × Cf)). A transimpedance amplifier (TIA) converts photodiode or sensor current to voltage using a feedback resistor Rf.

How do you find Feedback Resistor when you know the other values?

Rearrange for Feedback Resistor: with −3 dB Bandwidth 100 kHz, Op-Amp GBW 0.22 MHz, Feedback Capacitor 1 pF, Feedback Resistor is 3.501 MΩ.

How do you find Feedback Capacitor when you know the other values?

Rearrange for Feedback Capacitor: with −3 dB Bandwidth 100 kHz, Op-Amp GBW 0.22 MHz, Feedback Resistor 100 Ω, Feedback Capacitor is 35.01 nF.

What units does Transimpedance Amplifier Bandwidth use?

−3 dB Bandwidth is shown in Hz, kHz, MHz, GHz. Values are held in SI base units internally, so you can mix prefixes without converting by hand.

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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