Tricky Circuit

A ramp differentiator

Measure how quickly a signal changes

A differentiator responds to a signal’s rate of change, not its final size. Op amp means Operational Amplifier, a powered amplifier. A ramp is a steady voltage change over a finite duration. Slew rate is a real amplifier’s maximum output-voltage change per unit time; that limit is omitted here. R means resistance, C means capacitance; RC is their product, a time scale called the time constant.

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EXPERIMENT BENCH

Change the circuit settings, predict the readings, then check a challenge. These are learning models, with the assumptions explained in each lesson.

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How it works

Ideal linear input ramp with R = 100 kΩ, C = 1 µF and RC = 0.1 s. The displayed value is during the ramp. Output limits are ±10 V. No instantaneous step, start/end transient, noise or frequency limit is simulated.

ΔV is total ramp change and T its duration in seconds. During the ramp the input slope is ΔV/T, and requested output is −RC × ΔV/T. A downward ramp produces positive output.

Difficulty

  1. Build · Observe

    Power on with change +1 V over 100 ms. Obtain −1 V during the ramp.

    Need a hint?

    ΔV=+1 V; T=100 ms → −1 V

  2. Explore · Explore

    Keep change +1 V but shorten duration to 50 ms. Obtain −2 V.

    Need a hint?

    ΔV=+1 V; T=50 ms → −2 V

  3. Solve it · Solve

    Use change −2 V over 100 ms. Obtain +2 V.

    Need a hint?

    ΔV=−2 V; T=100 ms → +2 V

Extra reading and circuit recipes

A ramp differentiator

A climbing temperature and a steady hot temperature are different situations. A differentiator notices the climb: changing the same amount faster gives a larger response.

Vout = −RC × ΔV/T; RC = 0.1 s

The selected output is constant during a linear ramp because its slope is constant. Nothing here predicts a physical amplifier’s behavior at the ramp’s corners.

A useful connection

Halving ramp duration doubles the ideal response for the same voltage change.

Beyond the model

A flat input has zero slope. An ideal instantaneous step is outside this finite-ramp model.

A useful trap to avoid

A differentiator measures change over time. It is not the difference amplifier that subtracts two simultaneous inputs.

A +1 V ramp takes 50 ms instead of 100 ms. The output is…

  1. −0.5 V
  2. −2 V
  3. +2 V
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The slope doubles; inversion makes the doubled response negative.

A gentle rise

Use a +1 V change over 100 ms.

The during-ramp output is −1 V.

A downward ramp

Use a −2 V change over 100 ms.

The during-ramp output is +2 V.

Try another change

Compare +1 V/100 ms with +2 V/200 ms. They have equal slopes and both produce −1 V.

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