Slew-rate distortion check, 470 kΩ/10 kΩ inverter

Slew rate

Slew rate (SR) is the maximum rate of change of the output voltage of an op-amp, SR = (dVo/dt)max, in V/µs. It is limited by the current available to charge the internal compensation capacitor (SR = I/C).

Checking for distortion

Given: Rf = 470 kΩ, R1 = 10 kΩ, vin = 0.1 sin(200000t) V, SR = 0.5 V/µs.

Closed-loop gain |Av| = Rf/R1 = 470/10 = 47
Output peak     Vm   = 47 × 0.1 = 4.7 V
Angular freq    ω    = 2 × 10⁵ rad/s
Frequency       f    = ω/2π = 31.83 kHz
vo = -4.7 sin(ωt)
Max slope of output = ω·Vm
   = 2 × 10⁵ × 4.7 = 0.94 × 10⁶ V/s = 0.94 V/µs

Required rate 0.94 V/µs > SR 0.5 V/µs, so the output will be distorted (the sine wave turns into a triangular-like wave of smaller amplitude).

Equivalently, the full-power bandwidth for 4.7 V peak is fmax = SR/(2πVm) = 0.5 × 10⁶/(2π × 4.7) = 16.93 kHz, which is below the signal frequency of 31.83 kHz.

Remedies

Any one of the following:

1. Use an op-amp with higher slew rate: SR ≥ 0.94 V/µs (e.g. LF351 with 13 V/µs).
2. Reduce the gain: the largest undistorted output peak is Vm = SR/ω = (0.5 × 10⁶)/(2 × 10⁵) = 2.5 V, so gain ≤ 2.5/0.1 = 25. With R1 = 10 kΩ, Rf ≤ 250 kΩ.
3. Reduce the input amplitude: for gain 47, Vin(peak) ≤ 2.5/47 = 0.0532 V (53.2 mV).
4. Reduce the signal frequency below 16.93 kHz (if the application allows).

Answer: required 0.94 V/µs > 0.5 V/µs, so the output is distorted; use Rf ≤ 250 kΩ or an op-amp with SR ≥ 0.94 V/µs.