A new approach to conductive electromagnetic interference （EMI） noise source modeling, i. e. the source internal impedance extraction, is presented. First, the impedance magnitude is achieved through an exciting probe and a detecting probe, or through calculations based on insertion loss measurement results when inserting a series nigh-value known impedance or a shunt low-value known impedance in the circuit. Then the impedance phase is extracted by the Hilbert transform （HT） of the logarithm of the obtained impedance magnitude. Performance studies show that the estimated phase error can increase greatly at a zero frequency in the Hilbert transform because of the existence of a singular point, and this effect can be eliminated by introducing a zero-point when the noise source does not include a series-connected capacitive component. It is also found that when the frequency is nigher than 150 kHz, the estimated phase error is not sensitive to the inductive source but sensitive to the capacitive source. Finally, under the conditions of the same measurement accuracies for impedance magnitude, the accuracy of complex impedance based on the HT can be improved about 10 times when compared with the accuracy of estimated parameters based on the impedance magnitude fitting method （IMFM）.
The convergence performance of the minimum entropy auto-focusing（MEA） algorithm for inverse synthetic aperture radar（ISAR） imaging is analyzed by simulation. The results show that a local optimal solution problem exists in the MEA algorithm. The cost function of the MEA algorithm is not a downward-convex function of multidimensional phases to be compensated. Only when the initial values of the compensated phases are chosen to be near the global minimal point of the entropy function, the MEA algorithm can converge to a global optimal solution. To study the optimal solution problem of the MEA algorithm, a new scheme of entropy function optimization for radar imaging is presented. First, the initial values of the compensated phases are estimated by using the modified Doppler centroid tracking （DCT）algorithm. Since these values are obtained according to the maximum likelihood （ML） principle, the initial phases can be located near the optimal solution values. Then, a fast MEA algorithm is used for the local searching process and the global optimal solution can be obtained. The simulation results show that this scheme can realize the global optimization of the MEA algorithm and can avoid the selection and adjustment of parameters such as iteration step lengths, threshold values, etc.
