Identification of the natural resonance frequencies of a conducting sphere from a measured transient response

Abstract

Abstmct-The natural resonance frequencies of a conducting sphere are determined experimentally by using measured transient scattered field and surface charge responses. Comparison to theory is shown to be excellent for the imaginary parts of the complex frequencies.

An analysis of VLF electric field spectra measured in Titan's atmosphere by the Huygens probe

“…The electromagnetic cavity therefore forms a damped system with high losses and highly attenuated resonances. The energy of these weak resonances is negligible compared to that of the excitation and their contribution to the global spectrum is practically zero, making necessary the use of a late time analysis based essentially on splitting the entire temporal signal into two parts, differentiating the excitation in the early time from the late time part containing only the system resonances [ Miller and Landt , 1980; Gharsallah et al , 1990; Li et al , 1998].…”

Reply to comment by R. Grard et al. on “An analysis of VLF electric field spectra measured in Titan's atmosphere by the Huygens probe”

“…The ideal situation would be to know the amplitude and phase of a large number of spectral lines; but in fact we have only 32 spectral lines with unknown phase and, although the temporal series obtained via inverse DFT of the spectral lines with zero phase do not correspond with the signals measured in Titan's atmosphere, they have the same resonances and to find these resonances is our main goal. We continue to use the notation "early" and "late time" used by Poggio et al [1973], Gharsallah et al [1990], and Li et al [1998], although the temporal series are not real signals. However, we would like to reiterate that taking null phase can help to obtain the system resonances because the pulses included in the original temporal signal are shifted to the origin of the time, allowing us on some Figure A3.…”

“…The analysis procedure, before being applied to the Huygens data, was first checked using an analytical function and later with the data for the electric field generated by the computational simulation of Titan's atmosphere using the transmission line matrix (TLM) method. Our methodology is an adaptation of the one used in the radar field, particularly useful for finding natural frequencies of low Q scatters with relatively low late time energy [ Gharsallah et al , 1990; Li et al , 1998] and is based on distinguishing two parts in the time domain electromagnetic field scattered by a radar target, the early time directly related to a distorted and attenuated excitation and the late time containing information about the waveguide‐geometrical form and the electromagnetic parameters of the boundaries and wave pathway.…”

A Late-Time Analysis Procedure for Extracting Weak Resonances. Application to the Schumann Resonances Obtained With the TLM Method

“…The late-time unforced transient response of an electromagnetic system excited by an electromagnetic pulse can be written as a series of natural oscillation modes expressed as the product of sine and decreasing exponential functions [38]. Therefore, at the first time as an example, let us consider the following time-varying function:…”