A new method for calculating the time-domain (TD) transfer function of ultra-wide band (UWB) antennas, which is used for measuring the electromagnetic pulse (EMP) at VHF, is proposed. The phase of the complex antenna factor is constructed based on the Hilbert transform that describes the relationship between the phase and amplitude of a signal in frequency domain (FD). The detailed steps for calibrating the TD transfer function are discussed, and the calibration uncertainty, whose maximum value equals 2.79 dB, is estimated. The presented method is verified by TEM cell calibration, in which the TD transfer function of a wideband antenna is calculated and used to reconstruct time domain electromagnetic pulse. The results show that the difference between the calibrated result with TEM cell calibration and the reconstructed result is 0.58 dB.
2. Shi, L. H., B. H. Zhou, and B. Q. Tao, "A discrete transfer function model for the time-domain calibration data of EMP sensors," Proc. 13th Int. Zurich Symp. Electromagn. Compat., 149-152, Zurich, Switzerland, 1999.
3. Rubinstein, M., J. L. Bermudez, V. Rakov, F. Rachidi, and A. Hussein, "Compensation of the instrumental decay in measured lightening electric field waveforms," IEEE Trans. Electromagn. Compat., Vol. 54, No. 3, 68-688, 2012.
4. Carro, P. L. and J. D. Mingo, "Ultrawide-band antenna distortion characterization using HermiteGauss signal subspaces," IEEE Antennas Wireless Propag. Lett., Vol. 7, 267-270, 2008.
5. Ma, R., L. Shi, Z. Huang, and Y. Zhou, "EMP signal reconstruction using associated-hermite orthogonal functions," IEEE Trans. Electromagn. Compat., Vol. 56, No. 5, Oct. 2014.
6. Srgel, W., F. Pivit, and W. Wiesbeck, "Comparison of frequency domain and time domain measurement procedures for ultra wideband antennas," 2003 Antenna Measurement and Techniques Association (AMTA) Conference, 2003.
7. Lawton, R. A., S.M. Riad, and J. R. Andrews, "Pulse and time-domain measurements," Proceedings of the IEEE, Vol. 74, No. 1, 77-81, 1986.
8. Tesche, F. M., "On the use of the Hilbert transform for processing measured CW data," IEEE Trans. Electromagn. Compat., Vol. 34, No. 3, 259-266, 1992.
9. Oppenheim, A. V. and R. W. Schafer, Discrete-Time Signal Processing, Prentice Hall, 2009.
10. Yu, Y. and M. Liu, "Research on the uncertainly of transition duration of broadband sampling oscilloscope based on nose-to-nose technology," ACTA Metrologyica Sinica, Vol. 28, No. 1, 81-84, 2007.
11., JCGM 100:2008 Evaluation of measurement data-Guide to the expression of uncertainty in measurement, Corrected version 2010.