Abstract-Electric permittivity and magnetic permeability of linear passive dispersive medium were defined using the circuit equation of an electrically small antenna (scatterer) with resonant and antiresonant properties. It was shown that the average macroscopic energy stored by the scatterers is proportional to frequency derivative of the input admittance of corresponding antenna. It was found that the average macroscopic energy density of electric and magnetic fields in dispersive lossy medium is a function of frequency derivatives of its effective constitutive parameters in accordance with Poynting's theorem in dispersive lossy medium clarified for this case in the paper.

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The average energy density of the macroscopic quasimonochromatic electromagnetic field U ts (t, r) in a linear passive chiral lossy medium described by the constitutive E-H relations is determined using a microscopic model. According to the model, U ts (t, r) is equal to the sum of the average energy densities of the electromagnetic field in free space U t0 (t, r) and electromagnetic oscillations in structural elements U s (t, r) induced by the electromagnetic wave. Making use of the Poynting theorem, the energy density U ts (t, r) U t0 (t, r) and power density of losses are derived as functions of the Poynting vector, polarization of the electromagnetic waves, phase shift between the field vectors and refractive index of a chiral medium. The exact energy velocity of the quasimonochromatic electromagnetic waves satisfying relativistic causality is determined using U ts (t, r). The approximate energy velocities of the quasimonochromatic electromagnetic wave are determined using energy density components approximating U ts (t, r) (e.g., the sum of the positive energy densities of the macroscopic electric and magnetic fields as well as the energy density of magnetoelectric cross-coupling). Comparison of the exact and approximate energy velocities with the group velocity in the case of a chiral lossy medium with a single-resonant frequency clarifies the concept of the electromagnetic energy and demonstrates the fundamental significance of the exact energy velocity.

Abstract-Accurate approximations of the conductance and the conductance bandwidth of an electrically small antenna valid in resonant and antiresonant ranges were found. It was shown that the conductance bandwidth of an antenna tuned on maximal power of radiation is inversely proportional to the magnitude of the frequency derivative of the input impedance |Z (ω cd )| of the antenna at frequency of maximal conductance.That is a generalization of the well known relationship, according to which, the conductance bandwidth of an antenna tuned on resonance in a resonant range is inversely proportional to the magnitude of the frequency derivative of the input reactance of the antenna |X 0 (ω 0 )| at resonant frequency. Obtained approximate formulas display inverse proportionality of the conductance bandwidth to the approximate quality factor of the antenna in resonant and antiresonant ranges.A differential definition of the fractional conductance bandwidth was formulated, which is convenient for the case of closely spaced resonances of an antenna.As an example, numerical calculations for oblate spheroidal and spherical antennas in shells with negative permittivity in resonant and antiresonant ranges was used to confirm accuracy of the obtained approximations of the conductance and the conductance bandwidth of an electrically small antenna.

The exact and corrected approximate quality factors of an electrically small antenna were derived by using an equivalent circuit of the antenna. The quality factors complying with the lower bound on the quality factor were defined by means of magnitudes of frequency derivatives of reactance of resonant and antiresonant subcircuits to provide their additivity in the vicinity of an antiresonant frequency . The quality factor was used to approximate the conductance bandwidth of an antenna with overlapped resonances. The quality factors at the maximums of the bands of conductance and return loss were utilized to calculate the composite quality factor of the antenna .