Impulse voltage generator circuit

An impulse voltage generator circuit is used to generate high voltage pulses for testing electrical equipment and insulation systems. One common circuit configuration for an impulse voltage generator is the Marx generator.  In a Marx generator circuit, multiple capacitors are charged in parallel and then discharged in series through a spark gap. This configuration allows for the generation of high voltage pulses by cascading the capacitors' voltages. 

The output voltage of a Marx generator can be calculated using the formula:

$V_{out} = N \times V_{cap}$

where:
- $V_{out}$ is the output voltage of the Marx generator
- $N$ is the number of stages in the Marx generator
- $V_{cap}$ is the voltage across each capacitor stage

The voltage across each capacitor stage can be calculated using the formula:

$V_{cap} = \sqrt{2 \times C \times \frac{Q}{N}}$

where:
- $C$ is the capacitance of each capacitor stage
- $Q$ is the total charge stored in all capacitors
- $N$ is the number of stages

The total charge stored in all capacitors can be calculated using the formula:

$Q = C \times V_{in}$

where:
- $V_{in}$ is the input voltage used to charge the capacitors

These formulas can be used to design and analyze the performance of an impulse voltage generator circuit, such as a Marx generator.