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Voltage follower square-wave output with slew rate

Short answer

At 100 Hz, the 4 µs slew ramp is negligible; output is a ±1 V square wave. At 100 kHz, the output is trapezoidal: ramps linearly between −1 V and +1 V in 4 µs, with 1 µs flat tops, peak-to-peak remains 2 V.

Draw the waveform of output voltage of voltage follower operational amplifier having square wave as input signal with peak-to-peak voltage of 2V and frequencies (i) 100Hz and (ii) 100KHz. Assume that op-amp has slew rate of 0.5V/μs. Label the waveform neatly illustrating timing and amplitude details.

A voltage follower has gain 1, so ideally the output equals the input square wave: 2 V peak-to-peak, i.e. a step of 2 V at every edge (from −1 V to +1 V and back). The output cannot change faster than SR = 0.5 V/µs, so each edge becomes a ramp.

Time to slew through 2 V:
  t_r = ΔV / SR = 2 V / 0.5 V/µs = 4 µs

(i) f = 100 Hz

T = 1/100 = 10 ms,  half-period = 5 ms
Ramp time / half period = 4 µs / 5 ms = 0.08 %

The 4 µs ramps are negligible, so the output is practically a perfect square wave of ±1 V.

 +1 V  ____________            ____________
      |            |          |
      |            |          |
 -1 V |            |__________|
      0           5 ms       10 ms      t
  (each edge is a 4 µs ramp, too short to see)

(ii) f = 100 kHz

T = 1/100 kHz = 10 µs,  half-period = 5 µs
Ramp takes 4 µs, flat top lasts 5 - 4 = 1 µs

The output is a trapezoidal wave: it rises linearly from −1 V to +1 V in 4 µs, stays at +1 V for 1 µs, falls linearly to −1 V in 4 µs, stays for 1 µs, and repeats. The peak-to-peak value is still 2 V because the 4 µs ramp fits inside the 5 µs half-period.

 +1 V      ___         ___
          /   \       /   \
         /     \     /     \
 -1 V __/       \___/       \__
       0   4  5   9 10  14 15   t (µs)
  rise 0-4 µs, flat 4-5 µs, fall 5-9 µs,
  flat 9-10 µs, next rise 10-14 µs ...

If the frequency were raised above 125 kHz (half-period < 4 µs), the output would become a triangle wave of reduced amplitude.

✓ Answer checked by Claude Opus 5.5 (high effort)

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