What justifies the complexity of Marx generators? When I need a 300 kV pulse, it seems like it would be so much easier to wire up three 100 kV low-inductance pulse capacitors and discharge them through a single spark gap rather than tangling with Marx multiple stages. Sparky, my dog, definitely feels this way. It sure would make it easier to give him that new 300 kV impulse generator he’s been wagging his tail for.
The heart of the problem is DC voltage grading. If I wire a pair of 100 kV capacitors in series and hook the configuration up to a 200 kV high voltage power supply, nothing guarantees that both capacitors will each see 100 kV. One might get charged to 75 kV while the other is being overstressed at 125 kV: the total voltage is not graded evenly across the series stack of capacitors. This is because the steady-state voltage across each capacitor is determined by small uncontrolled currents due to capacitor leakage and corona discharge. The effective resistance of these parasitics depends on environmental conditions, nearby components, and manufacturing variability - all things that are hard to control. Like herding ducks, I hear from Sparky.
Ignoring voltage grading requires unacceptably large design margin. Naively, for capacitors hooked up in series, I would need (300 kV)/(100 kV) = 3 capacitors, but if I’ve done that, and some of the capacitors overstress and fail, which then overstresses the remaining capacitors even more. Sparky doesn’t like the smoldering heap this produces. I could add a healthy design margin by wiring 6 capacitors in series each rated for 100 kV with a total voltage across the stack of 300 kV. But, each additional capacitor that I add to the stack decreases performance by adding series resistance and series inductance to the circuit.
Going to higher voltages than 300 kV requires increasingly more margin. The total voltage rating of a bunch of capacitors wired in series scales as the log of the number of capacitors. Or looking at it another way, the number of capacitors that I need to wire together increases exponentially with total voltage. This means that Sparky would have to donate his whole doghouse to capacitors to generate a mere 300 kV, 100 ns pulse. I don’t need to tell you what he says about that.
Achieving even voltage grading across all capacitors requires additional components. Parasitic currents might be difficult to control, but putting a stiff voltage divider in parallel with the capacitor stack can ensure even grading. Resistive voltage grading networks are only effective if the resistors are well-matched. Matching large numbers of resistors is difficult given the realities of thermal gradients and component aging. The value of each resistor also needs to be much smaller than the leakage resistance of a capacitor. That’s the same as saying that the current through the divider network needs to be much greater than the total parasitic current due to capacitor leakage and corona. Even small current at high voltages represent significant power, so resistive grading isn’t a free lunch. The price to pay is high power consumption, oversized power supplies, and resistors catching fire.
Marx generators solve the voltage grading problem. Instead of attempting to divide a large DC voltage like 300 kV evenly across a bunch of capacitors, a Marx generator has all capacitors charged in parallel so that by definition they each see exactly the same voltage. Parallel charging means that the charging resistors only dissipate power during charge and discharge transients, unlike a resistive grading network that always burns power. This has the added perk of multiplying the output voltage of the capacitor charging power supply so that the capacitor charging voltage doesn’t need to equal the required output pulse amplitude.
The catch is that each capacitor in a Marx generator is paired with a triggered spark gap switch. Each of the spark gaps should be triggered simultaneously for best performance, but this is usually impractical. A commonly used approach is to only trigger the spark gap closest to ground. Spark gaps farther up the chain then breakdown due to overvoltage. Only triggering the first spark gap is convenient, but reliable triggering depends on shunt capacitance from each stage of the Marx generator to ground. Optimizing that can feel a little like chasing your tail.
Marx generators aren’t so bad once triggering is ironed out. These circuits multiply the output of a small power supply to create fast pulses using the minimum number of capacitors. When Sparky and I build the 300 kV pulse generator he’s been running after in his dreams, it will be a 3-stage Marx generator made from 100 kV low-inductance capacitors and 100 kV triggered spark gap switches.