3 · RC step response

Status: ✅ Runs today

Goal: simulate in the time domain.

Build

03-rc-step.circuit.tsx

import { analog } from "tscircuit"

export default () => (
  <board routingDisabled>
    <voltagesource name="V1" voltage="3.3V" />
    <resistor name="R1" resistance="1k" footprint="0402" />
    <capacitor name="C1" capacitance="1uF" footprint="0402" />
    <trace from=".V1 > .pin1" to=".R1 > .pin1" />
    <trace from=".R1 > .pin2" to=".C1 > .pin1" />
    <trace from=".C1 > .pin2" to=".V1 > .pin2" />
    <voltageprobe name="VOUT" connectsTo=".C1 > .pin1" referenceTo=".V1 > .pin2" />
    <analog.transientsimulation name="RC_STEP" spiceEngine="ngspice"
      duration="5ms" timePerStep="10us" />
  </board>
)

• duration is how long to simulate.
• timePerStep is the largest step the solver may take.
• A bare number means milliseconds, so write units such as "10us".

The simulation starts with the capacitor empty, so the source acts like a step at t = 0.

Run

bunx tsci simulate 03-rc-step.circuit.tsx

What you see

Index  time         v(n1)        v(n2)        i(vsimulation_voltage_source_0)
…      9.996000e-4  3.300000e+0  2.085522e+0  …
510    5.000000e-3  3.300000e+0  3.277766e+0  -2.223431e-5

Check by hand

• τ = RC = 1k × 1 µF = 1 ms.
• At t = τ: 3.3 × (1 − e⁻¹) = 2.086 V ✓ (sim: 2.0855 V)
• At t = 5τ: 3.3 × (1 − e⁻⁵) = 3.2778 V ✓
• The current at the end is (3.3 − 3.2778) / 1k = 22 µA ✓

Try this

Change C1 to 10uF. Predict V at 5 ms before you run it. The answer is 3.3 × (1 − e⁻⁰·⁵) = 1.30 V.