Engineering
Op-Amp Gain, Closed-Loop Bandwidth (GBWP) & Slew-Rate Limit formulas
Explore ideal resistor-set gains, a single-pole noise-gain bandwidth estimate and the sine-wave slew-rate boundary.
Separate ideal gain, small-signal bandwidth and slew rate
The resistor formulas approximate closed-loop gain when loop gain is large and the amplifier operates linearly. Rin and Rf are in the same units. In the non-inverting circuit Rin is the ground-leg resistor; the inverting circuit is a different connection.
GBW divided by noise gain is a single-dominant-pole approximation for a voltage-feedback amplifier, not a universal rule for current-feedback or multi-pole devices. Check minimum stable gain and load conditions in the device data. Rf=0 describes the non-inverting follower limit only; it is not a useful inverting amplifier configuration.
SR/(2πVpeak) is the sine-wave slew boundary, not a guarantee of low distortion. B6 is output peak amplitude, not peak-to-peak or input voltage. Output swing, supply rails, load current, common-mode range and stability still constrain operation.
| Op-Amp Stage Parameter | Formula | R_in=2k, R_f=18k, GBWP=1MHz, SR=0.5V/us, Vp=5V | Non-inverting follower limit (Rf=0) |
|---|---|---|---|
| Non-Inverting Gain (V/V) | 1 + (B3 / B2) | +10.0 V/V (+20 dB) | +1.0 V/V (Follower) |
| Inverting Gain (V/V) | -(B3 / B2) | -9.0 V/V | Not a useful inverting stage |
| Closed-Loop -3dB BW (kHz) | B4 / (1 + (B3 / B2)) | 1,000 / 10 = 100.00 kHz | 1,000.00 kHz |
| Full-Power Slew BW (kHz) | ((B5 * 1e6) / (2 * PI() * B6)) / 1000 | 15.92 kHz slew boundary | 15.92 kHz at 5 Vp |
Closed-Loop -3dB Small-Signal Bandwidth (kHz) = GBWP / (1 + R_f / R_in)
Divides unity-gain bandwidth B4 by Noise Gain 1 + (B3 / B2).
=IF(COUNT(B2:B6)<>5,"Invalid inputs",IF(OR(B2<=0,B3<0,B4<=0,B5<=0,B6<=0),"Invalid inputs",ROUND(B4 / (1 + (B3 / B2)), 2)))Slew-Rate-Limited Full-Power Sine Bandwidth (kHz)
Converts Slew Rate B5 (V/microsecond) to V/s and divides by 2 * PI() * V_peak * 1000.
=IF(COUNT(B2:B6)<>5,"Invalid inputs",IF(OR(B2<=0,B3<0,B4<=0,B5<=0,B6<=0),"Invalid inputs",ROUND(((B5 * 1000000) / (2 * PI() * B6)) / 1000, 2)))Ideal non-inverting voltage gain
Dimensionless voltage ratio for the corresponding circuit topology; use within linear operating limits.
=IF(COUNT(B2:B6)<>5,"Invalid inputs",IF(OR(B2<=0,B3<0,B4<=0,B5<=0,B6<=0),"Invalid inputs",1 + (B3 / B2)))Ideal inverting voltage gain
Dimensionless voltage ratio for the corresponding circuit topology; use within linear operating limits.
=IF(COUNT(B2:B6)<>5,"Invalid inputs",IF(OR(B2<=0,B3<0,B4<=0,B5<=0,B6<=0),"Invalid inputs",IF(B3=0,"Not an inverting stage",-B3/B2)))Try the example
Use the original values or change them to test your understanding.