Tricky Circuit

Sample and hold with passive leakage

Freeze a measurement, then watch it fade

Sample and hold means capture a voltage and retain it for later use. A capacitor stores the selected sample; a buffer follows it without drawing current in this model. Droop means the held voltage drifts during hold. Here a leakage resistor to ground makes it decay. 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

Select the initial sampled voltage and elapsed hold time; there is no capture button or live history. C = 1 µF and the leakage path is 100–1000 kΩ. This passive RC model omits real switch, buffer and capacitor leakage mechanisms.

Vsample is voltage at the start of hold. Rleak is leakage resistance, C capacitance, and τ = Rleak × C the time constant. Held voltage Vhold = Vsample × exp(−t/τ), with exp(x) meaning e to the power x.

Difficulty

  1. Build · Observe

    Power on at sample 3 V, hold time 0 ms and leakage resistance 100 kΩ. Obtain 3 V.

    Need a hint?

    Vsample=3 V; t=0 ms; Rleak=100 kΩ → 3 V

  2. Explore · Explore

    Keep sample 3 V and 100 kΩ; choose hold time 100 ms. Obtain about 1.1036 V.

    Need a hint?

    Vsample=3 V; t=100 ms; Rleak=100 kΩ → 1.1036 V

  3. Solve it · Solve

    Keep sample 3 V and 100 ms; increase resistance to 1000 kΩ. Obtain about 2.7145 V.

    Need a hint?

    Vsample=3 V; t=100 ms; Rleak=1000 kΩ → 2.7145 V

Extra reading and circuit recipes

Sample and hold with passive leakage

A measurement system may need a stable snapshot while it processes a value. The hold capacitor provides a temporary analog memory, but its leakage path slowly changes the snapshot.

τ = Rleak × C; Vhold = Vsample × exp(−t/τ)

100 kΩ × 1 µF gives 100 ms. At the same 100 ms hold, 1000 kΩ gives only one tenth of its time constant, so much more voltage remains.

A useful connection

After one time constant, passive exponential decay retains about 36.8% of the starting voltage.

Beyond the model

Increasing leakage resistance slows this model’s decay; real droop can have other causes and shapes.

A useful trap to avoid

Changing Sampled voltage chooses a different starting sample. It does not secretly capture a live signal.

Only leakage resistance becomes ten times larger. The time constant…

  1. becomes ten times larger
  2. halves
  3. stays unchanged
Read more

With C fixed, τ = Rleak × C grows in direct proportion to resistance.

A fresh snapshot

Use a 3 V sample at hold time 0 ms and 100 kΩ.

No time has passed, so the held voltage is 3 V.

Keep the snapshot longer

Use a 3 V sample, 100 ms and 1000 kΩ.

The held voltage is about 2.7145 V.

Try another change

At sample 3 V and 100 kΩ, compare hold times 0, 100 and 200 ms. Predict 3, about 1.104 and 0.406 V.

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