Precision requirements for specifying transmitter waveforms used for modelling the off-time electromagnetic response

In order to obtain an accurate EM response with modelling software, most people assume that it is necessary to know or specify the excitation current waveform (or its derivative) precisely. A mathematical analysis shows that accurate model results can be obtained during the off time if the amplitude of the waveform is specified precisely in the latter parts of the waveform; however, in the earlier parts of the waveform, the amplitudes can be approximate as long as the area under the waveform is specified accurately. This means that the discretization should be fine in the latter parts of the waveform, but can be coarse in the early parts of the waveform. Coarse sampling of the waveform means that the convolution integrals can be calculated more efficiently. An example shows that the exponential rise and linear ramp assumed by some modelling software to approximate a waveform can give poor results with errors close to 10%. Another approximate waveform that is precise in the final parts of the waveform and has an accurate area under the waveform curve gives errors less than 0.15%.