Tricky Circuit

An inverting integrator

Let voltage accumulate with time

An integrator accumulates input over time. Op amp means Operational Amplifier, a powered amplifier; a feedback capacitor makes its output remember accumulated charge. An initial condition is the starting value needed before predicting a changing system. Here output starts at 0 V. R means resistance, C means capacitance; RC is their product, a time scale called the time constant.

Open interactive experiment

EXPERIMENT BENCH

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

Sign in to save progress. Guest progress stays on this device.

Open laboratory in a full window

How it works

Constant input, R = 10 kΩ and C = 10 µF. Choose an elapsed-time sample, not a running clock. Requested output is clipped at ±10 V. Every calculation starts from 0 V; offsets and leakage are omitted.

RC = 0.1 s sets the accumulation scale. For a constant input Vin, requested output Vout = −Vin × t/RC. t is elapsed time in seconds; 100 ms is 0.1 s. The minus sign reverses the accumulation.

Difficulty

  1. Build · Observe

    Power on at input 1 V and elapsed time 100 ms. Obtain −1 V.

    Need a hint?

    Vin=1 V; t=100 ms → −1 V

  2. Explore · Explore

    Set input 2 V and elapsed time 250 ms. Obtain −5 V.

    Need a hint?

    Vin=2 V; t=250 ms → −5 V

  3. Solve it · Solve

    Set input −2 V and elapsed time 500 ms. Reach +10 V, the model’s upper limit.

    Need a hint?

    Vin=−2 V; t=500 ms → +10 V

Extra reading and circuit recipes

An inverting integrator

Imagine keeping a total rather than reading only the latest value. A capacitor in feedback lets a small constant input keep changing the output as time passes.

Vout(t) = Vout(0) − Vin × t/(RC); Vout(0) = 0 V; RC = 0.1 s

At 1 V for 0.1 s, the factor t/RC is one. Positive input drives the inverting output downward; negative input drives it upward.

A useful connection

Before clipping, doubling input or elapsed time doubles the output change.

Beyond the model

The starting capacitor voltage matters. This model fixes it at zero instead of tracking previous experiments.

A useful trap to avoid

The time slider selects a fresh calculation from the same start. It does not continue a previous run.

Input remains 1 V. Time grows from 100 ms to 200 ms. Output becomes…

  1. −0.5 V
  2. −1 V
  3. −2 V
Read more

Twice the duration accumulates twice the change from the fixed zero start.

A small accumulated total

Use input 1 V for 100 ms.

The output reaches −1 V.

Reverse the accumulation

Use input −2 V for 500 ms.

The output reaches +10 V.

Try another change

Set input 2 V and compare 100, 200 and 300 ms. Predict −2, −4 and −6 V before checking.

ti.com