Section 4
First-order transients
The complete response is an exponential interpolating v0 and v∞ with time constant τ.
- Piecewise-constant linear first-order circuit; τ>0.
Capacitor charging: v(t)=V(1−e^{−t/τ}) rises from 0 toward V exponentially.
- Piecewise-constant linear first-order circuit; τ>0.
Capacitor discharge: v(t)=V e^{−t/τ} falls exponentially toward 0.
- Piecewise-constant linear first-order circuit; τ>0.
Computes Capacitor current from the circuit model and the stated conditions.
- Piecewise-constant linear first-order circuit; τ>0.
The RL current interpolates i0 and i∞ with τ=L/R.
- Piecewise-constant linear first-order circuit; τ>0.
iL build-up: inductor current grows as 1−e^{−t/τ}.
- Piecewise-constant linear first-order circuit; τ>0.
iL decay: inductor current falls as e^{−t/τ}.
- Piecewise-constant linear first-order circuit; τ>0.
Computes Inductor voltage from the circuit model and the stated conditions.
- Piecewise-constant linear first-order circuit; τ>0.
Computes Value at one time constant from the circuit model and the stated conditions.
- Piecewise-constant linear first-order circuit; τ>0.
Computes Practical settling time from the circuit model and the stated conditions.
- Piecewise-constant linear first-order circuit; τ>0.
Computes Capacitor initial condition from the circuit model and the stated conditions.
- Piecewise-constant linear first-order circuit; τ>0.
Computes Inductor initial condition from the circuit model and the stated conditions.
- Piecewise-constant linear first-order circuit; τ>0.