The equivalent circuit during the operation of the impulse voltage generator is shown in Figure 2. C1 in the figure is the main capacitor, also known as the impulse capacitor, which is equivalent to the total capacitance of each stage after series connection, i.e; C2 is the load capacitance, that is, C2=C0, which includes the modulation capacitance, sample capacitance, measurement equipment (voltage divider) capacitance, and parasitic capacitance such as connecting wires; G represents the ball gap that controls discharge; Rf and Rt are the wave head resistance and wave tail resistance, respectively, which are equivalent to the sum of all levels of rf and rt, i.e. Rf=nrf, Rt=nrt; U1 is the charging voltage, which is equivalent to the total voltage after each level is connected in series, i.e. U1=nV; U2 is the output voltage, which is the required impulse voltage. These value circuits are equivalent to the circuits of a single-stage impulse voltage generator. According to circuit analysis, the output voltage U2 (t) is a double exponential function
τ 1> > τ two
Based on this analytical solution and practical experience, the parameters of the impulse voltage waveform can be approximately estimated using the following formula: wavefront time
Half peak time
T2 ≈ 0.69Rt (C1+C2)