1122334455667788AABBCCDDEE

/ ROOT / CIRCUIT-STUDIO    ◂ back to sheet 1

Circuit Studio solvers

The circuit engine inside Quodra, the presentation editor I'm building: a DC operating point by modified nodal analysis, an AC small-signal sweep, and transient steps. It is written to refuse rather than guess.

RC STEP, FROM QUODRA'S SAMPLE LECTUREV11 V stepR116 kΩOUTC110 µFτ = RC = 16 kΩ × 10 µF = 0.16 sEACH STEP h, C1 BECOMESOUTGC / h(C/h)·v(n)
0102τ4τ6τ8τexact, 1 − e−t/τ

backward Euler lags by at most 20 % trapezoidal overshoots by 9 %

FIG. 1  The lecture's RC step integrated two ways at a step you choose. Push h past 2τ and the trapezoidal points start to swing across the answer; the backward-Euler points only fall behind. Computed on this page.

DESIGN DECISIONS, FROM THE SOURCE

  1. Modified nodal analysis over real pins and nets. Every result carries the document and revision it was computed for, so a stale answer can never render as current.
  2. Diodes use the piecewise-linear hand-analysis model, settled by deterministic assumption iteration: no Newton convergence roulette. A network that will not settle refuses by name.
  3. Transients step with backward-Euler companions: a capacitor becomes C/h beside a source holding its last voltage. Backward Euler, not trapezoidal, on purpose: it damps, where trapezoidal rings on every diode that switches, and a ringing artefact is indistinguishable from real ringing.
  4. The AC sweep linearises about the DC operating point. A saturated transistor has no small-signal gain, so the sweep refuses instead of returning a fiction.
▸ Hover a wire to name its net.NET IN V1's step into R1NET OUT the capacitor voltage the chart plotsNET GND reference, 0 V

ANALYSES

DC operating point. AC sweep, 1 Hz to 1 MHz at 20 points a decade by default. Transient, 50 ms in 20 µs steps by default.

PARTS IT KNOWS

Resistors, capacitors, inductors, lamps, switches, diodes and LEDs, NPN and PNP transistors, NMOS and PMOS, DC and AC sources, probes and transformers.

WHERE IT RUNS

Inside a Quodra slide, in the browser. A circuit, an equation and a chart on one slide read the same solved values.

REVISIONSREVDATEDESCRIPTIONA2026-08-03DC operating point by modified nodal analysisB2026-08-07AC small-signal sweep, complex admittancesC2026-09-11Transient steps with backward-Euler companionsD2026-09-23Transistor readings; AC testsTITLECircuit Studio solversSHEET/ circuit-studioNO.3 of 7REVDDATE2026-09-23DRAWND. BrownSIZEA3GO TO◂ sheet 2sheet 4 ▸OTHER VIEWSDEVPHYSICSACADEMICee.desmondbrown.me

/ ROOT / CIRCUIT-STUDIO

Circuit Studio solvers

The circuit engine inside Quodra, the presentation editor I'm building: a DC operating point by modified nodal analysis, an AC small-signal sweep, and transient steps. It is written to refuse rather than guess.

SHEET3 of 7REVDDATE2026-09-23
OTHER VIEWSDEVPHYSICSACADEMIC
RC STEP, FROM QUODRA'S SAMPLE LECTUREV11 V stepR116 kΩOUTC110 µFτ = RC = 16 kΩ × 10 µF = 0.16 sEACH STEP h, C1 BECOMESOUTGC / h(C/h)·v(n)
0102τ4τ6τ8τexact, 1 − e−t/τ

backward Euler lags by at most 20 % trapezoidal overshoots by 9 %

FIG. 1  The lecture's RC step integrated two ways. Push h past 2τ and the trapezoidal points swing across the answer; backward Euler only falls behind. Computed on this page.

DESIGN DECISIONS, FROM THE SOURCE

  1. Modified nodal analysis over real pins and nets. Every result carries the document and revision it was computed for, so a stale answer can never render as current.
  2. Diodes use the piecewise-linear hand-analysis model, settled by deterministic assumption iteration: no Newton convergence roulette. A network that will not settle refuses by name.
  3. Transients step with backward-Euler companions: a capacitor becomes C/h beside a source holding its last voltage. Backward Euler, not trapezoidal, on purpose: it damps, where trapezoidal rings on every diode that switches, and a ringing artefact is indistinguishable from real ringing.
  4. The AC sweep linearises about the DC operating point. A saturated transistor has no small-signal gain, so the sweep refuses instead of returning a fiction.

ANALYSES

DC operating point. AC sweep, 1 Hz to 1 MHz at 20 points a decade by default. Transient, 50 ms in 20 µs steps by default.

PARTS IT KNOWS

Resistors, capacitors, inductors, lamps, switches, diodes and LEDs, NPN and PNP transistors, NMOS and PMOS, DC and AC sources, probes and transformers.

WHERE IT RUNS

Inside a Quodra slide, in the browser. A circuit, an equation and a chart on one slide read the same solved values.

REVISIONS

A2026-08-03DC operating point by modified nodal analysis
B2026-08-07AC small-signal sweep, complex admittances
C2026-09-11Transient steps with backward-Euler companions
D2026-09-23Transistor readings; AC tests
TITLECircuit Studio solvers
◂ sheet 23 / 7sheet 4 ▸