Read the circuit as a numerical reference
This reference describes a driven circuit with three resistors, an inductor and a capacitor. Its specified component values and initial states determine both the decaying transient and the continuing sinusoidal response. Lemonergy's current and charge example expresses the same differential equations as connected Gain, Sum and Integrator blocks.
The attributed source is MathWorks, Solve Differential Equations of RLC Circuit Using Laplace Transform. The retained contract identifies the “Declare Equations” and “Substitute Values” portions of that workflow. It contains transcribed mathematical parameters and analytical expressions, not a vendor model, measured circuit data or digitized plot.
Retained circuit parameters
In the table, S1 links to the campaign containing the downloadable reference contract. Its rlc.source.parameters and rlc.source.equations fields preserve these values. Component values remain constant, and the current directions follow the retained equations.
| Quantity | Symbol | Value | Unit | Conditions and use | Basis |
|---|---|---|---|---|---|
| First resistance | R1 | 4 | Ω | Current damping coefficient | Retained input · S1 |
| Second resistance | R2 | 2 | Ω | Couples current and charge-rate equations | Retained input · S1 |
| Third resistance | R3 | 3 | Ω | Charge-rate denominator with R2 | Retained input · S1 |
| Inductance | L | 1.6 | H | Current-rate coefficients | Retained input · S1 |
| Capacitance | C | 0.25 | F | Charge-to-voltage relation | Retained input · S1 |
| Initial inductor current | I1(0) | 2 | A | State at t = 0 s | Retained initial condition · S1 |
| Initial capacitor charge | Q(0) | 2 | C | State at t = 0 s | Retained initial condition · S1 |
| Voltage amplitude | E0 | 1 | V | Prescribed sinusoidal source | Retained input · S1 |
| Angular frequency | ω | 1 | rad/s | E(t) = E0 sin(ωt); time measured in seconds | Retained source equation · S1 |
The equations are:
dQ/dt = [E − Q/C + R2 I1] / (R2 + R3)
dI1/dt = (R2/L) dQ/dt − [(R1 + R2)/L] I1
Here Q is charge in coulombs, while C is capacitance in farads. Negative values of current or charge can follow from the chosen directions and oscillating source; their sign alone does not indicate a failed calculation.
What the Lemonergy comparison adds
The reference contract retains the published closed-form expressions for current and charge. Lemonergy evaluates those expressions at the native solver's output times and compares the full traces. Two additional integrators generate the sine input numerically, so source-voltage accuracy is checked independently as well.
| Quantity | Symbol | Value | Unit | Conditions and use | Basis |
|---|---|---|---|---|---|
| Comparison interval | t | 0–25 | s | Union of the source's 0–15 s and 2–25 s plot intervals | Authored comparison window · S1 |
| Current error limit | εI | 0.0000001 | A | Maximum absolute error at all retained native times | Internal numerical gate · S1 |
| Charge error limit | εQ | 0.0000001 | C | Maximum absolute error at all retained native times | Internal numerical gate · S1 |
| Source-voltage error limit | εE | 0.0000001 | V | Numerical oscillator compared with the specified sine | Internal numerical gate · S1 |
These limits test implementation consistency, not component tolerances or measurement uncertainty. There is no parameter fitting or measured holdout. The graph currently uses dimensionless block ports with a documented SI mapping: a current value of 1 means 1 A, charge 1 means 1 C, and voltage 1 means 1 V. The tutorial explains the coefficients and this dimensional limitation.
Lemonergy solves the connected equations numerically; it does not invoke a symbolic Laplace-transform solver. Follow the worked example for the complete model, application pictures, expected checkpoints and instructions for a fresh Rust/WebAssembly run.
Publication date and retained provenance
The publication date is unknown. The frozen contract and campaign notes record retrieval/checking on 30 September 2026. The wiki's record-review date refers to local bibliographic work and does not assert another visit to the live source.
No full source-page copy is retained, and the external application was not executed for this comparison. Documentation URLs can change; use the frozen equations and parameters when reproducing the result. Numerical agreement for this problem does not establish hardware accuracy or general equivalence between software products.