Time-averaged Stored Energy Research Articles

Derivation of expression of time-averaged stored energy density of electromagnetic waves

Derivation of expression of time-averaged stored energy density of electromagnetic waves

Time-modulated reactive elements for control of electromagnetic energy

Accumulation of electromagnetic field energy in classical passive structures such as resonators and reactive circuit elements is limited by the amplitude of time-harmonic external sources. In the steady-state regime, all incident power which is not absorbed is fully re-radiated (reflected), and the time-averaged stored energy is constant, even though the external source continuously supplies energy. Recently, we have shown that lossless objects can continuously accumulate energy if their properties are properly modulated in time. Here, we discuss this possibility and study means to release this accumulated energy in the desired moment or moments of time in form of pulses of the desired shape. Furthermore, we discuss a possibility of keeping the energy inside the load, turning off the incident wave and changing the modulation function of the load. Finally, instead of a single time-reactive element we consider a parallel time-varying LC circuit, that gives the same functionality, in addition allowing to engineer currents flowing through the load circuit elements.

Stored energy density of electromagnetic wave in dispersive media

In this work, we shall demonstrate that usual expression of time-averaged stored energy density (TASED) for disperisve medium is invalid, which is mainly attributed to the fact that there exist mathematical errors in derivation of this expression. Noting connection between TASED and time-averaged Poynting vector (TAPV) and the case that TAPV of a pulse is the sum of TAPVs of its components, similarly, it is verified that TASED of a pulse in disperisve medium can be taken as the sum of TASEDs of all its components. This work may be helpful to gain a better understand of stored energy of electromagnetic wave in material media.

Formal Expression of Sensitivity and Energy Relationship in the Context of the Coupling Matrix

Precise formulas to express the formal relationship between the time average stored energy in the resonators of a low-pass filter network and the sensitivity of the reflection <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</i> -parameter with respect to the coupling matrix terms are demonstrated in this paper, considering the normalized frequency axis. These relationships are found in the modern context of the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> +2 coupling matrix, and for both diagonal and general nondiagonal coupling elements of the matrix. The results are valid for any type of coupling topology represented by the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> +2 coupling matrix. Different examples are included as validation. Furthermore, important implications and applications derived from the new relationships are highlighted.

Electromagnetic field energy density in homogeneous negative index materials

An exact separation of both electric and magnetic energies into stored and lost energies is shown to be possible in the special case when the wave impedance is independent of frequency. A general expression for the electromagnetic energy density in such a dispersive medium having a negative refractive index is shown to be accurate in comparison with numerical results. Using an example metamaterial response that provides a negative refractive index, it is shown that negative time-averaged stored energy can occur. The physical meaning of this negative energy is explained as the energy temporarily borrowed by the field from the material. This observation for negative index materials is of interest when approaching properties for a perfect lens. In the broader context, the observation of negative stored energy is of consequence in the study of dispersive materials.

Prediction of peak internal fields in direct-coupled-cavity filters

In this paper, an explicit expression of the peak electric-field strength in the cavities of Chebyshev direct-coupled-cavity waveguide filters is derived. It is shown that the electric-field strength can be predicted from the analysis of the time-averaged stored energy in the lumped low-pass prototype, from which the cavity filter was derived. This simplifies the analysis and study of the power-handling capability of these types of filters considerably, as the stored energy in the prototype filters is easily computed. The analysis of the field distribution in the cavities of an example third-degree Chebyshev direct-coupled-cavity filter shows that the explicit expression for the peak electric-field strength derived in this paper agrees closely with results obtained from a TE/sub 10/ circuit model of the filter, from a full-wave electromagnetic solver and from measurements.

Comments on "Relationship between group delay and stored energy in microwave filters"

For original paper, see ibid., vol.49, no.1, p.192-6 (2001). In the original paper, it is shown that the time-averaged stored energy in a passive lossless reciprocal symmetrical or antimetrical two-port is proportional to the group delay. The authors point out that some of their results were previously reported in a book by Penfield et al. (1970) and apologize for claiming credit for the work.

Relationship between group delay and stored energy in microwave filters

In this paper, an expression for the time average stored energy (t.a.s.e.) in a passive lossless two-port is derived in terms of its scattering parameters. In particular, it is shown that the t.a.s.e. in a passive lossless reciprocal symmetrical or antimetrical two-port is proportional to the group delay. One implication of this result is that the t.a.s.e., which is linked to the power-handling capability in many passive filters used in practice, is proportional to the group delay of the filter. This rigorous derivation is based on a variational theorem, which has been used in the past to prove energy storage results for passive lossless one-ports and periodic two-ports.

The Variational Principle for Non-Self-Adjoint Electromagnetic Problems

A systematic and intuitive procedure is proposed to derive the variational (or stationary) principle for non-seff-adjoint electromagnetic problems with various boundary conditions. Several physical interpretations of this principle in terms of generalized reactions, time-average stored energy, and reactive powers, respectively, are discussed in detail. This general variational principle which makes the generalized reactions a stationary value is actually an extension of the least action principle in physics. The applications of the principle to establish the variational expressions for a waveguide, a cavity resonator, and a Ioasy one-dimensional inhomogeneous slab are presented.

Observable stored energies of electromagnetic systems

The conventional definition of quality factor Q in terms of time-average stored energy is widely assumed to be a measure of the input bandwidth of any ordinary electromagnetic system. But the extent to which this assumption is true has never been established. In the case of all radiating systems, for example, it is known to fail completely. It can be made true quite generally, however, by including only those parts of the total time-average stored energy that give a physically observable contribution to the input bandwidth. Explicit formulas for these newly defined observable stored energies are developed that are valid for any electromagnetic system that is linear, passive, and time-invariant.

Permutation Symmetry of Nonlinear Susceptibilities and Energy Relation

Permutation symmetry for generalized nonlinear susceptibilities is derived from the microscopic theory. It is shown that this permutation symmetry is essential for the existence of a time-averaged stored energy density or free energy for wave propagation in a nonlinear, nondissipative medium.

Power Flow and Stored Energy in Thin Electron Beams

The kinetic and electromagnetic components of ac power and stored energy are evaluated for space-charge waves along thin drifting beams of simple geometry. It is found that: (a) when a modulated beam is decelerated, it radiates power into the surrounding space; (b) when both fast and slow waves are excited by a common source, the real kinetic power varies periodically with distance, exchanging energy with the electromagnetic field; and (c) when a finite-area beam is current modulated with zero ac velocity, the total power need not be zero. The energy transport velocity of a space-charge wave is shown to equal its group velocity, when the time-average stored energy is properly evaluated. A small portion of the stored kinetic energy propagates, together with the field energy, as an electromechanical wave along the beam. The larger part of the kinetic energy, which can be positive or negative, is transported by the motion of the beam itself.