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Generator and circuit
The stages charge to the set voltage in parallel, then the spark gaps fire and they discharge in series. The front resistor and load capacitance set the rise time; the tail resistor and the generator capacitance set how slowly the pulse decays.
Model checks
The science
What is modelled
An ideal Marx generator charges N capacitors C in parallel to the voltage V and discharges them in series. The result behaves like one capacitor C/N charged to N V. That capacitor discharges through the front resistor Rf into the test object Cload, which the tail resistor Rt discharges in parallel. The page integrates these two coupled first-order equations with fourth-order Runge-Kutta steps.
Equations
V0 = N V,Ce = C/N,E = ½ Ce V0² = N · ½ C V².dvc/dt = -(vc - vo)/(Rf Ce),dvo/dt = (vc - vo)/(Rf Cload) - vo/(Rt Cload).- Closed form:
vo = V0 b (eλ1t - eλ2t)/(λ1 - λ2)with the eigenvalues of the 2 x 2 system. - Front time
T1 = (t90 - t30)/0.6; time to half value T2 measured on the tail.
Checks run in the page
- Stage sum N V.
- Stored energy two ways.
- Numerical output against the closed form.
- Energy balance: released = dissipated + stored in the load.
Honest simplifications
Ideal equal stages, no stray inductance or capacitance, no spark-gap delay or resistance, no stage-to-stage losses and a purely capacitive test object. The gap field is a uniform-field estimate V/d and the air limit is a rough textbook figure. A teaching model, not a high-voltage design or test procedure.
What to try
- Press Lightning impulse 1.2/50 and read T1 and T2 near 1.2 and 50 microseconds.
- Raise Rf and watch the front slow down while the peak falls.
- Press Heavy load: a bigger Cload lowers the peak because of the capacitive divider.