Measurement of Impulse Voltages and Currents

Everything in the last two chapters measured a steady or repetitive quantity — a DC level, an RMS, a recurring peak — and could afford to be slow. An impulse is none of these. It is a single, non-recurring event lasting microseconds, defined not by one number but by a whole curve: the front time \(T_1\), the time to half-value \(T_2\), the crest, and — if it is a chopped wave — the instant of collapse. A surge arrester or a transformer is certified against that shape, so the instrument must record the shape, faithfully, in one shot.

That splits the task in two. First we need a recorder fast enough to follow a microsecond wave — historically a special impulse oscilloscope, today a digital transient recorder. Second, and harder, we need a way to bring hundreds of kilovolts down to the few volts the recorder accepts without distorting the wave on the way. A divider that is perfectly accurate for a slow voltage can mangle a fast one, because at megahertz speeds its stray capacitances and lead inductances come alive. The whole chapter is about building a measuring chain — divider, cable, recorder — that stays faithful all the way up to the frequencies hidden inside a microsecond front.

A divider for impulses is built like the dividers of Chapter 15 — a high-voltage arm and a low-voltage arm sharing the wave so the recorder sees a fixed fraction of it. The ratio is the same:

What is new is the demand for speed. A real divider does not respond to a step instantaneously; it has a finite response time \(T\), the lag with which its output catches up to a sudden input. If \(T\) is comparable to the front time \(T_1\) of the wave, the recorded front is rounded and slowed and the peak is shaved — the divider reports a gentler, lower impulse than the real one. The rule of faithful measurement is simply that the chain must be fast compared with the wave:

Every divider type below is a different attempt to keep \(T\) small while still holding off the full voltage. Where Chapter 15 worried only about the ratio and the loading, here the ratio is the easy part — the contest is entirely about response time, and it is lost or won on the stray capacitances and inductances that a slow measurement could ignore.

The resistive divider is the natural first choice, especially for fast fronts and for impulse-current work where resistances are anyway low. Its trouble at high voltage is invisible on a circuit diagram: every point of the tall resistor column has a small stray capacitance to the earthed surroundings, \(C_e\). These distributed capacitances rob the column of current near the top and feed it near the bottom, turning the clean resistive ladder into a sluggish RC network. The result is a response time set by the product of the total resistance and the total stray capacitance:

The lesson is a squeeze. To make \(T\) small you want a small total resistance \(R\), but a small \(R\) draws a heavy current from the generator and loads the impulse. To keep the load light you want a large \(R\), but that lengthens \(T\) and blurs the front. Low-ohmic resistive dividers therefore serve well at lower voltages and for the fast fronts of impulse-current measurement, while at the highest voltages the stray capacitance makes the pure resistive divider hard to keep faithful — the cue to let capacitance work for us instead of against us.

If stray capacitance ruins a resistive divider, the obvious move is to make the divider itself capacitive, so that the strays merely add to capacitors that are meant to be there. A capacitive divider — a small HV capacitor \(C_1\) over a large LV capacitor \(C_2\) — draws no steady current, dissipates nothing, and handles long tails and switching impulses gracefully. The ratio is the capacitive one from Chapter 15:

But the capacitive divider has its own fast-front demon: the inductance of its leads and of the capacitors themselves. A capacitance and an inductance in a loop is an oscillator, and a steep front is a hammer-blow that sets it ringing — the recorded wave arrives with a parasitic oscillation riding on the front and crest, corrupting exactly the features (front time, peak) we came to measure. The pure capacitive divider, left undamped, rings; the pure resistive divider, left to its strays, sags. Each fails the fast front in its own way, which is what makes the next idea so satisfying.

The workhorse of impulse-voltage measurement combines the two and cancels their faults. In the damped capacitive divider, small series resistors are distributed down the high-voltage arm alongside the capacitors. The capacitance gives the broad, fast response and absorbs the strays; the series resistance damps the lead-inductance oscillation before it can ring — the very critical-damping idea from Chapter 14, here put to work on a measuring circuit rather than a generating one. The result is a divider that follows both the steep front and the long tail faithfully across the whole range of impulse voltages.

This is why a high-voltage impulse laboratory is dominated by tall, oil-filled or gas-insulated damped capacitive dividers: they are the one design that is simultaneously fast enough for a steep chopped front and stable enough for a long switching-surge tail. The choice among the three divider types is a clean little decision tree, summarised below.

The low-voltage output of the divider reaches the recorder through a coaxial cable, and at impulse speeds the cable is not a wire but a transmission line. If its far end is not properly terminated, the fast wave reflects off the mismatch, races back, re-reflects, and superimposes a train of echoes on the record. The cure is to match the cable — to terminate it in a resistance equal to its surge impedance, the very quantity \(\sqrt{L/C}\) that ran through the impulse-current chapter:

A matched cable swallows the wave with no reflection, delivering a clean copy to the recorder. That recorder was historically a dedicated impulse oscilloscope — a cathode-ray tube with a very fast writing speed and a single triggered sweep, started a known moment before the impulse by the same kind of trigger that fires the generator in Chapter 14, so the fleeting wave is caught on screen. Today the impulse CRO has given way almost entirely to the digital transient recorder: a fast, high-resolution digitiser that samples the divider output millions of times a second, stores the waveform in memory, and lets software measure \(T_1\), \(T_2\) and the peak automatically and archive the shot. The physics of the divider and cable is unchanged; only the eye at the end has gone digital.

Measuring the current of an 8/20 µs impulse turns on the same demand for speed. The most direct method is the resistive shunt: a small, accurately known resistance \(R\) placed in series with the current, so the voltage across it is a faithful copy of the current waveform, scaled down to a level the recorder accepts:

The whole art of the shunt is making it non-inductive. Any self-inductance \(L_s\) adds a spurious \(L_s\,di/dt\) term that distorts the fast front, so the shunt is built coaxially — a tubular or squirrel-cage geometry in which the current goes out along one path and returns along a concentric one, cancelling the magnetic field and shrinking the inductance almost to nothing. The condition for a faithful copy is that the shunt's own time constant be far shorter than the wavefront, \(L_s/R \ll T_1\). Built that way, a shunt of a few milliohms turns tens of kiloamperes into a few tens of volts the recorder reads directly.

The shunt must carry the current; the Rogowski coil need only encircle it. It is an air-cored toroidal winding looped around the conductor, and by Faraday's law the changing current threading it induces an EMF proportional to the rate of change of the current:

An RC integrator on the coil's output undoes the differentiation and recovers \(i(t)\) directly. The coil's virtues follow from its air core and its non-contact nature: with no iron it cannot saturate, so it stays linear up to enormous currents; it needs no direct connection and inserts no resistance into the circuit; and it is light and easy to clip around a conductor. The shunt and the Rogowski coil are the two complementary answers to impulse current — the shunt a small resistance the current flows through, the coil a loop the current flows past — and between them they cover everything from a few amperes to the hundreds of kiloamperes of a full lightning-current test.

For each item, first identify what it tests — the need for waveshape, a divider ratio, the response-time idea, cable matching, or an impulse-current method — then apply it. Difficulty rises down the list.