Measurement uncertainty of the target scattering parameters built in the uncertainty estimation of ESD simulator

In a previous paper by the author (see 14^th Int. Zurich Symposium on EMC, p.189-92, 2001) uncertainty estimation of current wave by calibration of ESD simulator is presented The uncertainty is defined there as discrepancy between current wave calculated for low frequency transfer impedance and for frequency dependent transfer impedance. This is termed here the basic uncertainty. Such definition of basic uncertainty is entitled because the low frequency transfer impedance is introduced as the coefficient between output voltage and input current of the target. Frequency dependent transfer impedance is burdened with uncertainty which also reflects in current wave uncertainty. This is called here additional uncertainty. A geometrical sum of basic and additional uncertainty builds total uncertainty. The formula used in the previous paper for frequency dependent transfer impedance is so complex that derivation of additional uncertainty with commonly used sensitivity coefficients between measurand (scattering parameters) and output quantity (transfer impedance) is impossible. Contribution of the additional uncertainty is however essential for the total uncertainty budget. In this paper simplified formula for transfer impedance is introduced. Simplification is achieved with replacing the actual load of the target (input impedance of the oscilloscope) with idealised 50 Ω resistance. Suitability criterion of the simplified formula is comparison of the basic current peak uncertainty calculated for actual and simplified transfer impedance. The method is illustrated with uncertainty calculation of the current peak with different rise time varying from 360 ps to 1030 ps. The comparison of the basic uncertainty shows very good agreement specially for the rise time which is of practical interest (from 700 ps to 1 ns). The additional uncertainty dominates the basic uncertainty so strongly that the total uncertainty increases as the rise time increases.