Validation & Benchmark Cases
The following parameter sets serve as reproducible reference tests.
Each case defines expected analytical behavior.
1. Series RLC – Ideal Resonance (Sine)
Parameters
- L = 10 mH
- C = 2.533 µF
- R = 1 Ω
- f ≈ 1000 Hz
Expected resonance:
\[
\omega_0 = \frac{1}{\sqrt{LC}}
\]
\[
f_0 \approx 1000\,\text{Hz}
\]
At resonance:
- φ ≈ 0°
- Q_net ≈ 0 var
- |Z| minimal
Acceptable deviation: < 1e-12 (floating precision).
2. Parallel R+L || C – Sine Resonance
- L = 10 mH
- C = 2.533 µF
- R = 0.5 Ω
- f ≈ 1000 Hz
Expected condition:
\[
\operatorname{Im}(Y) = 0
\]
At resonance:
- Input current minimum
- Admittance purely real
- Reactive cancellation visible
3. RL Pulse – Time Constant Verification
Expected:
\[
\tau = \frac{L}{R} = 50\,\mu s
\]
Current should reach 63.2% of final value at t = τ.
4. Parallel Pulse – Periodicity Closure
- L = 100 µH
- C = 2.53 µF
- R = 0.5 Ω
- f = 10 kHz
- Duty = 5%
Periodic condition:
\[
i_{RL}(T^-) = i_{RL}(0)
\]
Periodicity error magnitude should be < 1e-9.
If significantly larger, investigate state metric.
5. Energy Conservation Window
\[
\Delta W_L = \frac{1}{2}L(i_2^2 - i_1^2)
\]
\[
\Delta W = \int v i dt
\]
Energy difference and integral result should match within numerical precision.