Slew-rate check for 40 dB amplifier at 20 kHz

Given: SR = 1 V/µs, gain = 40 dB, input = 100 mV peak, f = 20 kHz.

Gain: 20 log10 Av = 40 dB  →  Av = 10^(40/20) = 100
Output peak: Vm = 100 × 0.1 = 10 V
Required slope of output (sine wave):
  (dVo/dt)max = 2πf·Vm
              = 2π × 20 000 × 10
              = 1.2566 × 10⁶ V/s = 1.257 V/µs

Since 1.257 V/µs > SR = 1 V/µs, the output will be distorted by slew-rate limiting (the peaks are rounded into a triangular shape and the amplitude falls).

Check with full-power bandwidth: fmax = SR/(2πVm) = 10⁶/(2π × 10) = 15.92 kHz < 20 kHz, confirming distortion.

Remedies

1. Use a faster op-amp: SR ≥ 1.257 V/µs (for margin, 2 V/µs or more, e.g. LF351 with 13 V/µs).
2. Reduce the gain: the largest undistorted output at 20 kHz is Vm = SR/(2πf) = 10⁶/(2π × 20 000) = 7.96 V, so gain ≤ 7.96/0.1 = 79.6 (about 38 dB). For example, with R1 = 1 kΩ use Rf ≤ 79.6 kΩ (standard 75 kΩ).
3. Reduce the input amplitude: at gain 100, Vin(peak) ≤ 7.96/100 = 79.6 mV.
4. Operate below 15.92 kHz if the signal frequency can be lowered.

Answer: output is distorted (needs 1.257 V/µs > 1 V/µs); use SR ≥ 1.26 V/µs or gain ≤ 79.6.