SemiSimTech

RLC Transient Explorer

Interactive Prototype (MVP)

Turn the knobs and watch the transient like an oscilloscope. Freeze a trace, then tweak one knob to compare.

Knobs —
More R → less ringing (more damping).
More L → slower oscillation (current has “inertia”).
More C → slower oscillation (voltage changes more slowly).
Initial energy matters: try Vc0 or I0 to “kick” the circuit.
Freeze keeps the previous trace faint while you tweak one knob.
Scope Series RLC RK4

Tip: set R low to see ringing. Click Freeze & Compare, then increase R to watch damping.

Explain Math + Intuition

This demo uses the series RLC driven by a voltage step. The “knobs” change the physics directly: R dissipates energy, while L and C store energy and exchange it back and forth.

Model used (two-state ODE)

We simulate two state variables: series current i(t) and capacitor voltage vC(t). For a source vs(t) (step), KVL gives:

vs(t) = R·i(t) + L·di/dt + vC(t)
i(t) = C·dvC/dt

Combine them into two first-order ODEs:

di/dt = (vs(t) − R·i − vC)/L
dvC/dt = i/C

The page integrates these equations with a lightweight RK4 solver (fast enough to update while you drag sliders).

Natural frequency and damping

Two simple quantities predict the waveform shape:

ω0 = 1/√(LC)    (sets oscillation speed)
ζ = (R/2)·√(C/L)    (sets damping)

Interpretation: ω0 gets smaller if you increase L or C → oscillations slow down. ζ increases with R → ringing dies out faster.

Underdamped / Critical / Overdamped

  • Underdamped (ζ < 1): oscillates with a decaying envelope (ringing).
  • Critical (ζ ≈ 1): fastest return without overshoot.
  • Overdamped (ζ > 1): no oscillation; slower, “heavy” return.

For a series RLC, the critical resistance is:

Rcrit = 2·√(L/C)

Energy story (why the meters matter)

In a lossless LC, energy would “sloshe” forever between electric and magnetic storage. Adding R converts some of that energy into heat. We track:

EC = ½·C·vC2
EL = ½·L·i2
ER(t) = ∫ i2·R·dt

Try this: make R small (ringing), turn Energy: On, then increase R. You’ll see the same energy exchange, but the loss grows faster and the oscillation fades sooner.

One more “aha” experiment

Set step amplitude to a small value (e.g., 0.5 V), then inject energy using Vc0 or I0. You’ll get very different transients even with the same R, L, C — because transients are about initial energy as much as input waveforms.