Generation of Impulse Voltages

Chapters 11 and 12 made steady voltages — DC held for minutes, AC held for a withstand test. But the most violent stresses a power system ever sees are not steady at all. A lightning stroke to a line injects a surge that rises to millions of volts in about a microsecond and decays in tens of microseconds. The opening and closing of a circuit breaker launches a slower but still brief switching surge. These transient overvoltages — the subject of Part 7 — are what destroy insulation in service, so equipment must be proven against them before it is trusted.

That proof is the impulse test: we apply, in the laboratory, a single voltage pulse of the same shape and magnitude as the surge the equipment might meet in the field, and confirm the insulation holds. To make the test repeatable and comparable worldwide, the waveshape is standardised. Two waves cover the two threats: a fast lightning impulse and a slower switching impulse.

A standard impulse voltage is a unidirectional pulse with no appreciable oscillation: it rises rapidly to a crest and then falls more slowly back to zero. Mathematically it is the difference of two decaying exponentials — a fast one that builds the front and a slow one that governs the tail:

Two times define the shape. The front time \(T_1\) measures how quickly the wave rises, and the time to half-value \(T_2\) measures how long it takes to decay to half its crest. Because the true foot of the wave is hard to pin down, \(T_1\) is defined from the steeper, well-defined part of the front — the interval between the 30% and 90% points, scaled up by \(1.67\) to a virtual origin. The standard lightning impulse is \(1.2/50~\mu\mathrm{s}\): a \(1.2~\mu\mathrm{s}\) front and a \(50~\mu\mathrm{s}\) time to half-value.

The standards allow tolerances — about \(\pm 3\%\) on the peak, \(\pm 30\%\) on the front and \(\pm 20\%\) on the tail — because no real circuit hits the nominal figures exactly. The slower switching impulse is \(250/2500~\mu\mathrm{s}\), a far gentler rise used to test the long air gaps and apparatus of EHV and UHV systems, where switching surges, not lightning, set the insulation level. Both waves come from the same kind of circuit; only the resistor and capacitor values differ.

The circuit that makes this wave is disarmingly simple. A large generator capacitor \(C_1\) is slowly charged to a DC voltage \(V_0\) from a source of the kind built in Chapter 11. A sphere gap \(G\) holds the charge back until, set to break down at \(V_0\), it sparks over and connects \(C_1\) to the wave-shaping network: a series front resistor \(R_1\), a small load capacitor \(C_2\) (the test object plus the measuring divider), and a tail resistor \(R_2\).

The sequence is quick and clean. While charging, the gap is open and \(C_1\) simply fills to \(V_0\). When the gap fires, \(C_1\) is suddenly thrown across the network and the wave begins: \(C_2\) charges rapidly through \(R_1\) (the front), then the whole store bleeds away through \(R_2\) (the tail). Two resistors, two capacitors, and the double-exponential falls out of the arithmetic — as the next section shows.

The beauty of the circuit is that the front and the tail are controlled almost independently, by two separate time constants. The front is set by how fast the small load capacitor \(C_2\) charges through the series resistor \(R_1\); the tail is set by how slowly the whole charge drains away through \(R_2\). Writing the two time constants:

Because \(\beta \gg \alpha\), the fast term dies away soon after the crest, leaving the slow term to define the long tail. Inverting these into the standard time definitions gives the two design rules every impulse-generator designer carries — one for each resistor:

The peak the wave reaches is always less than the charging voltage \(V_0\), because the moment the gap fires, the charge on \(C_1\) must share itself with \(C_2\) and some is lost in \(R_1\). The fraction recovered is the generator's voltage efficiency, dominated by the capacitance ratio:

The lesson is immediate: make the generator capacitor \(C_1\) much larger than the load \(C_2\). When \(C_1 \gg C_2\) the ratio approaches one and almost all the charging voltage appears across the test object. A generator with \(C_1 = 0.2~\mu\mathrm{F}\) feeding a \(2~\mathrm{nF}\) load is about \(99\%\) efficient; load it more heavily and the efficiency — and the peak voltage — drop. This is also why a generator's energy rating, not just its voltage, matters: a big test object demands a big \(C_1\) to stay efficient.

A single stage can only reach the voltage to which \(C_1\) is charged — and charging one capacitor to several megavolts is impractical, for exactly the insulation reasons that drove us to cascades in Chapter 12. The elegant escape, devised by Erwin Marx in 1924, is to charge many capacitors in parallel to a modest voltage \(V_0\), then suddenly reconnect them in series so their voltages add. With \(n\) stages, the output leaps to

The trick is in the switching. Each stage capacitor is charged through high-value charging resistors \(R_c\) that link all the stages in parallel to the DC supply; these resistors are large enough to carry the slow charging current but to look like open circuits during the fast discharge. Between successive stages sit spark gaps. When the bottom gap is triggered, it fires, and the resulting voltage step is passed up the column so that each gap in turn is over-stressed and breaks down — the stages snap into series in a few nanoseconds, and the full \(nV_0\) appears at the top, feeding the same kind of \(R_1\)–\(C_2\)–\(R_2\) shaping network as before.

The Marx generator is the standard way to make megavolt impulses, and laboratory units of a dozen or more stages routinely reach several million volts. It is also the direct ancestor of modern pulsed-power systems, where the same charge-parallel, discharge-series principle — refined with fast solid-state switches in place of spark gaps — drives everything from radar to materials processing. The arithmetic that governs it is the same as the single stage, scaled \(n\)-fold.

The instant of firing — the erection of the Marx — deserves a closer look, because a generator that fires unreliably is useless for testing. Everything hinges on the first gap. It is built as a controlled gap, set just below its natural breakdown voltage so it will not fire on its own, and then deliberately broken down by a small trigger pulse at a chosen instant. Once it fires, the voltage redistribution drives the second gap above its breakdown level, which fires the third, and so on up the column in a self-propagating cascade lasting only nanoseconds.

Reliable erection demands that each gap be set so the firing of the one below reliably over-volts it, and that the charging resistors be large enough not to bleed away the surge before the column has fully erected. The detailed art of triggering — trigatrons, three-electrode gaps, and the precise control of when and how the first gap fires — together with the closely related problem of generating high impulse currents, is the subject of the next chapter. For now, the key idea is enough: a single controlled trigger releases the whole stored charge of the stack as one clean megavolt pulse.

For each item, first identify what it tests — the waveshape definition, the front rule, the tail rule, the efficiency, or the Marx output — then apply it. Difficulty rises down the list.