Impulse Measurement and the Travelling Wave Problem

Measuring a microsecond event is harder than generating one.

Module 6 ended with a provocation: the generator delivers the impulse, but who guarantees that the number on the screen is the voltage that actually stressed the insulation? A lightning impulse is over in less time than a relay takes to pick up. Everything that will ever be known about it has to be captured, transmitted, digitized and processed in that window, by a chain of components that each have their own opinion about high frequencies. This module walks that chain end to end — divider, coaxial cable, attenuator, digitizer, software — and confronts the two ghosts that haunt it: the imperfect dynamic response of dividers, and the travelling wave that reflects inside the measuring cable.

The stakes are commercial, not academic. A 20 m cable with the wrong termination shifts the front time of a 1.2/50 µs wave, changes the reported overshoot, and can flip a type test from pass to fail on paper while the object under test never noticed. Two laboratories measuring the same physical event with different chains will report different numbers and both will believe their own. This is the content that separates the engineer who operates a laboratory from the engineer who understands what the laboratory is saying.

What you will be able to do

• Specify impulse dividers — resistive, purely capacitive, damped capacitive and universal RC — from their step response and the parameters derived from it: experimental response time T_N, partial response time T_alpha, overshoot of the response and settling time.

• Explain wave reflection in measuring cables using transmission line theory, calculate reflection and transmission coefficients, and size the impedance match at both ends of the cable.

• Configure digitizers and oscilloscopes to IEC 61083-1:2021 — sampling rate, analog bandwidth, effective vertical resolution, record memory and pre-trigger — for faithful capture of impulse parameters.

• Extract the standardized parameters (U_p, U_b, U_t, T1, T2, overshoot beta') with software validated against IEC 61083-2:2013 and assess waveform conformity to IEC 60060-1.

• Diagnose suspect waveforms, separating physical oscillation of the test object from artifacts of the measuring circuit — reflections, divider resonance and electromagnetic interference.

The measuring system is a chain, and the scale factor belongs to the chain

For normative purposes the measuring system is not the divider. It is the whole chain: converting device, low-voltage unit, coaxial cable, attenuator or termination, digitizer and evaluation software. The assigned scale factor K_sys = U_HV/U_digitizer belongs to every link at once. Calibrating the high-voltage column alone and then changing the secondary unit, the cable length, the termination, the digitizer channel or the software version is not admissible — any of those moves the scale factor, the step response and the bandwidth, and with them U_t, T1 and T2.

IEC 60060-2 splits the world into the approved measuring system (AMS) that runs daily tests and the reference system it is calibrated against. In the 2010 generation the expanded uncertainty limits are 3% on the test value of a full or tail-chopped lightning impulse (1% for reference), 5% on the peak of a front-chopped impulse (3% for reference) and 10% on T1, T2 and Tc (5% for reference). IEC 60060-2:2025 relaxed the front-time limit from 10% to 15% at the insulation levels of IEC 60071-1. State which generation governs before the first shot.

Dividers: three families, three failure modes

The resistive divider, K_R = (R_H+R_L)/R_L, is the instrument of choice for full, tail-chopped and front-chopped lightning impulses — if it is built with genuinely non-inductive resistors, short elements, field grading electrodes, a damping resistor at the HV connection and a wide low-inductance ground return. Its weakness is distributed capacitance to ground. The diverted capacitive current is larger near the HV terminal, which distorts the instantaneous potential distribution and produces initial overshoot, damped ringing and a gap between static and dynamic scale factor. It also dissipates u²(t)/(R_H+R_L), which is why impulse columns use R_H of 5 to 15 kΩ and are useless for continuous duty.

The purely capacitive divider dissipates nothing and doubles as generator load capacitance, but its effective lower arm is C_L,eff = C_L + C_cable + C_input + C_stray. At a typical 100 pF/m, swapping a 10 m cable for a 30 m cable adds roughly 2 nF and materially changes the scale factor. The damped capacitive divider is the accepted compromise — damping resistors in series with the column capacitors, 120 to 480 Ω internal plus 150 to 350 Ω external in 600 kV to 4 MV designs — resistive at high frequency, capacitive at low. Note the vocabulary trap: a true universal RC divider uses mixed R∥C arms with R_H·C_H = R_L·C_L, which makes K frequency-independent from DC through impulse.

Step response is the divider's health exam

Apply a fast known step, record the output, normalize as g(t) = K·u_o(t)/U_i. The quantitative tool is the response integral T(t) = ∫[1−g(τ)]dτ, the accumulated area between ideal and real response. Experimental response time T_N = T(2t_max) is an integral quantity, not a 10–90% rise time, and confusing the two ruins specifications every year. Partial response time T_alpha = max[T(t)] dominates accuracy on chopped and very fast impulses. Typical values: a compact resistive divider reaches T_N of 5 to 20 ns, a 1 MV column about 40 ns, a 2 to 3 MV column 60 to 70 ns. Taller is slower, and the complete system is always slower than the divider alone.

The cable is a transmission line and it charges 5 ns per meter

A cable is a lumped element only while its delay is negligible against the shortest relevant time. For a 1.2 µs front it is a distributed line, Z0 ≈ √(L'/C') and v_p ≈ 1/√(L'C'). With solid polyethylene the velocity factor is about 0.66, roughly 5 ns per meter. A 20 m cable returns its own reflection at 2τ = 200 ns — 16.7% of nominal front time, inside the 30–90% window that determines T1.

At the load, Γ_L = (Z_L − Z0)/(Z_L + Z0) and τ_L = 1 + Γ_L. Three cases are worth memorizing. A 1 MΩ oscilloscope input is not a termination: Γ_L ≈ +1, the wave doubles on arrival and bounces, giving steps at 2τ, 4τ, 6τ. A "small" 50/75 Ω mismatch gives Γ = +0.20 and τ = 1.20 — a 20% error, nearly seven times the 3% AMS limit. And the beginner's classic, internal 50 Ω enabled with the external terminator still fitted, makes 25 Ω and Γ = −0.333. Match at both ends, put the feedthrough termination at the instrument connector rather than mid-cable, and remember the cable also attenuates and disperses.

Overshoot: the peak on the screen is not the test voltage

Five quantities need distinct names. U_p is the raw recorded maximum. U_b is the peak of the fitted double-exponential base curve. U_t is the test voltage after the normative procedure. beta = U_p − U_b, and beta' = beta/U_b × 100% is the relative overshoot, limited to 10% by the standard waveform. For a smooth curve U_t = U_p; with overshoot, U_b < U_t < U_p.

The procedure fits u_b(t) = A(e^(−αt) − e^(−βt)), forms the residual r(t) = u(t) − u_b(t), transforms it, applies k(f) = 1/(1 + 2.2·f²) with f in MHz, inverse transforms and rebuilds u_t(t) = u_b(t) + r_k(t). T1 and T2 are read on the processed curve, never the raw one. The filter encodes the fact that fast oscillation stresses the dielectric less than its peak suggests: k = 0.6452 at 0.5 MHz, 0.3125 at 1 MHz, 0.1020 at 2 MHz. With U_b = 1000 kV and an 80 kV oscillation at 1 MHz, U_p = 1080 kV but U_t ≈ 1025 kV. The 1.2/50 tolerances are ±3% on U_t, 0.84 to 1.56 µs on T1, 40 to 60 µs on T2 and beta' ≤ 10% — and IEC 60060-1:2025 now permits T1 to 2.4 µs for equipment with U_m > 800 kV.

Digitizer, software and the metrological Bermuda triangle

IEC 61083-1:2021 sets f_s ≥ 30/T_x, where T_x is the shortest interval used to determine a parameter. For the 1.2/50 impulse that interval is 0.72 µs, so the floor is about 41.7 MS/s; use 100 MS/s for full waves and 200 to 250 MS/s for chopped waves. Rate does not buy bandwidth — with t_r ≈ 0.35/BW a 10 MHz channel has a 35 ns rise time. At 10% of a 14-bit converter's range you throw away log₂(10) ≈ 3.32 bits. Jitter becomes amplitude error as u_V ≈ |du/dt|·u_t, so 1 ns on a 1 MV/µs front is 1 kV. The final number comes out of software, which IEC 61083-2:2013 validates with the Test Data Generator.

The three villains conspire. A genuine 1 MHz crest oscillation is weighted 0.3125; if the cable attenuates it 20%, the filtered contribution falls to 0.25·ΔU and the result depends on the cable, not the object. Validate on three levels: physical layout and bonding, metrological calibration of the complete system, algorithmic validation by TDG. Bonding is not optional — 1 µH carrying di/dt = 1 kA/µs develops 1000 V, larger than the divider's own signal. Use a wide, short, continuous equipotential plane, 360° shield bonding with no pigtails, and where available digitize at the divider and send the result over fiber.

Syllabus

• The 2010 to 2025 standards transition and why the governing set must be stated in the contract

• The measuring system as a chain: converting device, secondary unit, cable, attenuator, digitizer, software

• Approved measuring system (AMS) versus reference measuring system (RMS) and the expanded uncertainty limits

• Why a 60 Hz scale factor does not characterize behavior on a 1.2 µs front

• Resistive dividers: low inductance construction, stray capacitance to ground, thermal limits

• Purely capacitive dividers, effective low-voltage arm and the cable-length trap

• Damped capacitive (Zaengl) dividers and true universal RC dividers

• Step response: normalized response g(t), the response integral T(t), T_N, T_alpha and settling time

• Transmission line behavior of the coaxial cable: Z0, velocity factor, 5 ns/m

• Reflection and transmission coefficients, TDR, and the three classic mismatch cases

• Matching at both ends, attenuation, dispersion and their effect on front time

• Coaxial attenuators and the signal budget: full-scale utilization and effective bits

• Shielding, bonding and EMC during a generator discharge; fiber optic front ends

• Sampling rate, analog bandwidth, ENOB, memory and jitter to IEC 61083-1:2021

• Software validation by Test Data Generator per IEC 61083-2:2013

• Overshoot: U_p, U_b, U_t, beta and beta', the ten-step procedure and the k(f) test function

• Differential diagnosis of suspect waveforms

Laboratory work

An instrumented demonstration with a single objective: watch the same wave told by two different narrators. Build the reduced impulse generator from the Module 6 activity and measure one shot simultaneously on two channels. Channel (a) is the correct system — a damped divider with known step response, 50 Ω cable properly terminated at the digitizer. Channel (b) is the wrong one — a purely capacitive divider with no damping and the termination removed, so the input sits at 1 MΩ. Compare the traces: channel (b) shows the divider's own ringing plus reflection steps spaced by 2τ, and the software reports different U_p, T1 and overshoot for the same physical event. Then vary the cable length from 5 m to 20 m and watch the steps move, and close by measuring the step response of both arrangements with a low-voltage step generator. Verification routine: (1) compute the expected 2τ for each length and find it on the oscillogram; (2) compute Γ for the 1 MΩ input and for the 50 Ω ∥ 50 Ω = 25 Ω case; (3) measure T1 on both channels and quantify the deviation against the 0.84 to 1.56 µs tolerance; (4) run the evaluation software on raw data from both channels and compare U_t; (5) argue which channel could be approved as a measuring system under IEC 60060-2.

Key takeaway

When a customer disputes an oscillation on the crest, four tests settle it in twenty minutes. Change the cable length: if the oscillation's timing tracks 2τ, it is a reflection. Switch the input between 1 MΩ and 50 Ω: if the peak moves, there was a mismatch. Compare the oscillation frequency with the divider's step response resonance: if they coincide, it is the divider. If it survives all three and its frequency matches the stray inductance of the generator-to-object loop, it is real — and the correct treatment is not to hide it but to apply k(f) and report U_t. U_t defines the stress, beta' defines waveform conformity, and both come out of the ten-step procedure, not from a cursor on the peak.

Module 7 of the Atlas Energy Academy · Generating & Measuring · about 4 hours · Video series plus instrumented demonstration · Prerequisites: Module 6 — Impulse Voltage Generation