Op-Amp Bandwidth from Gain Calculator
Estimate closed-loop small-signal bandwidth from an op-amp gain-bandwidth product and intended gain.
Inputs and tolerances
Estimate closed-loop small-signal bandwidth from op-amp gain-bandwidth product and intended gain.
For a simple single-pole op amp, increasing closed-loop gain reduces available small-signal bandwidth because the gain-bandwidth product is approximately constant.
Estimated closed-loop bandwidth
- Stability note: Meeting the bandwidth estimate does not guarantee stability. Noise gain, capacitive loading, phase margin, feedback layout, and multi-pole behaviour still need review.
- This calculator uses a first-order small-signal approximation. It does not model slew rate, full-power bandwidth, output swing, distortion, phase margin, multi-pole roll-off, input capacitance, capacitive load stability, or gain peaking.
Use GBW to screen whether an op amp is fast enough
For a simple single-pole op amp, the product of closed-loop gain and small-signal bandwidth is approximately constant. Higher gain leaves less bandwidth available for the signal.
Sensor front ends
Check whether the chosen gain still leaves enough bandwidth for the sensor signal.
Amplifier stage planning
Compare candidate op amps before committing to a gain split or cascaded stage design.
Stability review trigger
Passing the bandwidth estimate does not guarantee phase margin or capacitive-load stability.
Worked example
An op amp with 10 MHz gain-bandwidth product used at closed-loop gain of 10 has an estimated small-signal bandwidth of about 1 MHz.
Calculation
BW = GBW / gain.
BW = 10 MHz / 10.
BW = 1 MHz.
Design meaning
The result is a small-signal estimate. Large output swings may be limited by slew rate before the GBW estimate is reached.
Feedback layout, capacitive loading, and noise gain still need a stability review.
Common mistakes and limits
Confusing gain and noise gain
Loop stability follows noise gain, which may differ from the signal gain in some amplifier topologies.
Ignoring slew rate
Large signals can hit slew-rate limits even when the small-signal bandwidth estimate looks acceptable.
Assuming one-pole behaviour
Real op amps may have extra poles, gain peaking, compensation limits, and capacitive-load restrictions.
Related calculators and next checks
Op-amp slew rate requirement calculator
Check large-signal output-speed requirements after the small-signal bandwidth estimate.
Op-amp gain calculator
Calculate the closed-loop gain before checking the GBW-limited bandwidth.
Rise time bandwidth calculator
Relate bandwidth to signal edge rate for first-pass signal-path planning.
dB ratio converter
Convert voltage gain in V/V to dB before comparing amplifier stages.
Frequency period wavelength converter
Convert the estimated bandwidth into period or other frequency context.
Engineering reference
Equations, assumptions, and design guidance
Estimates closed-loop small-signal bandwidth from op-amp gain-bandwidth product and closed-loop gain using the standard single-pole approximation.
Equations and variables
BW = GBW / ACLT = 1 / BW- GBW
- Gain-bandwidth product or unity-gain bandwidth (Hz)
- ACL
- Closed-loop gain as a linear ratio (V/V)
- BW
- Estimated closed-loop small-signal bandwidth (Hz)
Assumptions and limitations
Assumptions
- The op amp behaves approximately like a single-pole amplifier over the gain and bandwidth of interest.
- Closed-loop gain is entered as a linear ratio rather than dB.
Limitations
- Slew rate, full-power bandwidth, output swing, distortion, phase margin, multi-pole roll-off, input capacitance, capacitive load stability, and gain peaking are not modelled.
Worked example and design use
10 MHz GBW at gain of 10
Inputs: GBW = 10 MHz, closed-loop gain = 10 V/V
Outputs: estimated bandwidth = 1 MHz, period at bandwidth = 1 us
Design guidance
- Use this estimate to screen whether an op amp is roughly fast enough before checking slew rate and stability.
- For non-inverting stages, remember that noise gain drives loop stability and bandwidth behaviour.