This invention is an electrostatic discharge testing circuit that can deliver current pulses to a component under test (CUT) with a custom amplitude versus time profile shape. Pulse generation with customized shapes is accomplished by discharging an energy storage network comprised of capacitor(s), transmission line(s) and other passive components. Current pulses compliant to the European International Electrotechnical Commission IEC 61000-4-2 standard can be so produced. These current pulses are delivered to the CUT with low distortion through a constant impedance electrical path, such as a combination of cables and controlled impedance conductors of printed wiring boards compatible with packaged IC devices, assemblies, and wafer probes. The current pulses can be delivered with various impedances, and measurements made that allow the CUT currents and voltages to be calculated.