in Fig. 1. Charge, initially stored on the Marx generator capacitor (Cm), is transferred via the series resistors (Rs & At AWE, ringing-gain voltage waveforms are analysed Rb) and inductor (L) to the Blumlein PFL load which is to calibrate pulsed-power machines in which electrical essentially a capacitor (Cp). Parallel losses in the system energy, stored in a Marx generator, is switched into a are represented by resistors (Rm & Rp) in parallel with the Blumlein pulse-forming line (PFL) via inductance and in Marx generator and load. The initial conditions are that the presence of serial and parallel resistive losses. the Marx generator capacitor is charged to voltage Vo [i.e. Traditionally, an equivalent circuit comprising lumped Vm(0)=V0], the PFL voltage is zero [i.e. Vp(O)=O], and the capacitors, inductors and resistors is used which allows current through the inductor is zero [i.e. i3(0)=O]. the determination of three unknown electrical parameters from two decay constants and the frequency of an i2 RV 13 L i P J/ oscillatory component calculated from the ringing-gain t7 7 waveform. The Blumlein transmission line can be t=O 12-3 i3-il represented as a lumped capacitor since its transit time is '4 Cp much smaller than the time to reach peak voltage. Rm Rp Generally, the serial inductance and resistance of the Cm < PFL Marx generator and its parallel resistance are assumed Marx unknown whereas the Marx-generator capacitance, Blumlein capacitance and voltage-monitor resistance are Vb i2 i3 Rb 1-assumed known. The ringing-gain analysis also yields the sensitivity of the voltage monitor.Figure 1. Schematic diagram of equivalent circuit with 2 A new approach to ringing-gain analysis allows the parallel and 2 series resistors. Initial conditions are Vm=V0, determination of one of the decay constants from the Vp=O and i3=O when thO (time when switch closes). current waveform and the other from the voltage waveform. This should improve the calibration accuracy of x-ray machines with relatively few 'rings' on their II. UNDERLYING ASSUMPTIONS ringing-gain waveforms, such as the PIM inductive voltage adder (IVA) machine at AWE.* The machine is assumed representable by lumped The dynamic resistance associated with Marx generator electrical components including Marx bank capacitance spark-gaps, which reduces with time, is also considered. Cm (known), PFL capacitance Cp (known), and inductance This can cause the first cycle of the ringing-gain and resistors detailed below. waveform to deviate from that predicted by the equivalent + The time to reach peak voltage on the transmission-line circuit unless time variability of the serial resistance is load (PFL) is assumed to be much greater than the transit properly accounted for.time of the line, allowing a lumped capacitor to represent Coupling the Blumlein output of an AWE prototype the PFL from the Marx generator point of view. IVA machine to ground via an inductor, to reduce pre-+ Machine series resistors are assumed lumped together pulse voltage, is found to affect adversel...