Optimal Radiated Waveforms From an Arbitrary UWB Antenna

Solutions are presented for the optimal electric field waveforms radiated by an arbitrary ultrawideband (UWB) antenna. Optimization criteria include maximization of the electric field amplitude at a particular time and location, or maximization of energy density over a specified time interval at a particular location. Assuming bandpass signals, constraints are placed on the total radiated energy, the Q of the antenna, and the size of the antenna. The solution is developed using a spherical mode expansion of the fields radiated by an arbitrary antenna enclosed by a spherical mathematical surface, and optimized using variational methods. A closed-form result is obtained for the case of amplitude maximization, while an integral equation must be solved numerically for the case of energy maximization in a time interval. An interesting result from these solutions is that the shapes of the optimal radiated field waveforms are largely independent of the size of the antenna. The solutions also indicate that the antenna characteristics that provide optimum field amplitude or energy in the transient case are identical to those associated with maximum gain in the CW case.     

Optimization of pulse radiation from dipole arrays for maximum energy in a specified time interval

The optimum solution for maximized radiated energy in a specified time interval from anN-element dipole array at a specified farfield position is presented. The solution is obtained in terms of time-domain dipole terminal voltages which are constrained in bandwidth and total input energy, with the currents on the dipoles satisfying Pocklington's integral equation. The orthogonality of characteristic terminal modes is used in the derivation of the optimum solution, and the far-zone field is expanded as a finite sum of characteristic modal fields with unknown mode coefficients. The optimum mode coefficients are found in terms of prolate spheroidal wave functions. An additional constraint can be used to find the optimum solution with a reduced sidelobe level. The effects of signal bandwidth and time interval specification on the peak field intensity and energy density in the direction of optimization are shown and limiting cases are found to agree with previous results.     

Waveform optimizations for ultrawideband radio systems

Solutions are presented for various optimizations of transient waveforms and signals used in ultrawideband radio systems. These include the transmit antenna generator waveform required to maximize receive antenna voltage amplitude (with bounded input energy), the transmit antenna generator waveform that provides the "sharpest" received antenna voltage waveform, and the transmit antenna generator waveform that maximizes received energy with an inequality constraint on the radiated power spectral density. Using variational methods, general optimization results are derived for arbitrary antennas, including the effects of generator and load impedances, and numerical examples are provided for lossless dipoles and resistively loaded dipoles using moment method solutions. Closed-form results are provided for short dipole antennas for some special cases.     

Theory of a corner-driven loop antenna immersed in a warm plasma

A linearized hydrodynamic theory and potential function technique arc used to formulate the theory of a corner-driven loop antenna immersed in a warm plasma. The theory explains some of the experimental observations obtained from impedance measurement of a loop antenna on the Ariel 3 satellite. The far-zone fields and the normalized radiated power for different antenna sizes are calculated. The results suggest that much of the radiated energy is radiated in longitudinal plasma waves     

Maximum energy window with constrained spectral values

The optimum energy criterion continuous and discrete prolate spheroidal wave function windows had a profound effect on the basic understanding and practical optimization of many problems in communication theory, signal processing, and antenna theory. However, in many situations, there is interest in not only packing maximum window energy in some frequency interval, but also interest in imposing precise spectral window values and spectral nulls over some specified frequencies. We have formulated and solved such an optimization problem in an analytical sense as well as in an efficient computational sense. The problem is first expressed as a constrained maximization of a normalized quadratic form w′Aw/w′w, where A is a positive-definite matrix specified by the window energy concentration interval, w is the window weighting vector, and the constraining subspace is specified by the spectral window values and locations. This problem is then transformed to a nonconstrained maximization of a normalized quadratic form w′ PAPw/w′w, where P is a projection operator onto the orthogonal complement of the original constraining subspace. Persymmetric properties of A and PAP are used to reduce the computational complexity of the solution of the optimum window. Numerical maximization can be readily performed using the iterative power method. Specific examples are presented.     

Optimization of the transient radiation from a dipole array

The optimum solution for the transient radiation from a dipole array is derived in terms of the time-domain voltages which are required at the input terminals of dipoles in an array so that the amplitude of the transient radiated field at a specified timet_{0}and far-field positionr_{0},theta_{0}, phi_{0}is maximized. Constraints are placed on the energy and bandwidth of the input signal voltages with current restricted by Pocklington's equation. Further constraints on the sidelobe level are used to obtain a modified solution for suppressed sidelobes in the radiation pattern. Results of numerical optimization are presented, and the effects of scan angle, element spacing, and a sidelobe constraint on the optimization are discussed.     

A Transmission Line Method to Compute the Far-Field Radiation of Arbitrarily Directed Hertzian Dipoles in a Multilayer Dielectric Structure: Theory and Applications

A transmission line method is proposed to compute the far-field radiation patterns of arbitrarily directed Hertzian dipoles that are embedded in a multilayer dielectric structure. The evaluation of the field in the far-zone region is transformed into the evaluation of the field inside the multilayer structure by applying the reciprocity theorem. The horizontal field component inside the structure is derived by analyzing a transmission line circuit, and the vertical component is obtained from the horizontal component by separating the forward and backward waves. This method is implemented and verified by IE3D for the case of a three-layer structure excited by either electric Hertzian dipoles, magnetic Hertzian dipoles, or their combination. The radiation patterns of any antenna embedded in a multilayer dielectric structure can be computed with this method after replacing the physical antenna with a set of Hertzian dipoles. As examples, a quarter wavelength thin wire monopole antenna and a dielectric resonator antenna, both embedded in a multilayer structure, are investigated. Furthermore, the arrangement of the structure is optimized to maximize the antenna directivity. The results are also verified by the simulation of the entire structure with IE3D.     

Optimization of the TEM feed structure for four-arm reflectorimpulse radiating antennas

This paper considers the optimization of the feed arm geometry of four-arm crossed-coplanar plate impulse radiating antennas (IRAs) when the angular position and extent of the arms are taken as free parameters. Previously, optimization of this class of antenna considered only the symmetric case where the two pairs of crossed feed arms were perpendicular to each other. Comparison is made using the prompt aperture efficiency, and the results indicate that the efficiency of four-arm IRAs can be increased from ~25% for the perpendicularly crossed arms to ~35% for the optimum configuration. In addition to the optimization, the feed impedance of coplanar feeds is presented for general values of feed arm angle and plate width, and the optimum feed impedance is computed for each feed arm angle. The results can be used to design the optimal four-arm IRA with an arbitrary specified input impedance     

Electromagnetic energy around Hertzian dipoles

This paper considers the behavior of electromagnetic energy around Hertzian dipoles. The method of “causal surfaces” (surfaces through which there is no net flow of electromagnetic energy) is used to partition and track the energy. A variety of examples, involving both transient and harmonic time dependence, are presented, to illustrate the way in which static and/or reactive energy is converted to outgoing, uncoupled, “radiated” energy around a Hertzian or point dipole. The principal conclusion is that although accelerating charge may be thought of as the source of the radiation fields, the source of the radiated energy lies in the static and/or reactive field energy near an antenna, and not “in” or “on” an antenna itself     

A diagnostic technique used to obtain cross-range radiation centersfrom antenna patterns

A diagnostic technique for obtaining cross-range radiation centers based on antenna radiation patterns is presented. The method is similar to the synthetic aperture processing of scattered fields normally associated with radar applications; however, in this case it is applied to evaluate antenna radiation pattern performance. Coherence processing of the radiated fields is used to determine the various radiation centers associated with the far-zone pattern of an antenna for a given radiation direction. The technique can be used to identify an unexpected radiation center that creates an undesired effect in a pattern. It can also be used to improve a numerical simulation of the pattern by identifying other significant mechanisms. Cross-range results for two 8-ft-diameter reflector antennas are presented to illustrate as well as validate this technique     

Optimum load for a linear antenna fed by a short duration pulse

An analysis is described to calculate the optimum load which maximizes the radiated electromagnetic field from a linear dipole antenna fed by a very short pulse. For each frequency in the band, the analysis is carried out by solving Pocklington's equation via a Galerkin moment method, together with a variational technique. A constraint on the energy of the radiated signal is used as an isoperimetric condition, so that the solution is physically realizable. The optimum solution is also compared with the response of an unloaded antenna.     

Transmitter-to-Antenna Power Transfer Under Unmatched Conditions

One phase of the electromagnetic compatibility program is the determianation of the electromagnetic energy actually radiated into space by an antenna. Methods have long been established, or proposed, for measuring the power output of a transmitter, the antenna impedance, and the antenna-radiation pattern. However, very little definitive work has been published regarding the methods for computing the transmitter energy coupled to the antenna and radiated at harmonic and spurious frequencies. It is the purpose of this paper to reduce to a simple form the equations for determining the power absorbed by an antenna connected through a coaxial transmission line to a transmitter. Most discussions of transmission-line-power transfer assume the matched conditions so universally desired at the operating frequency. When harmonic and spurious frequencies are considered, both the transmitter and the antenna are likely to be poorly matched to the transmission line and to each other. This paper points out what measurements need to be made and gives the functional relations necessary to compute the power radiated under unmatched conditions. Since the actual power coupled to the antenna in a given instance may be critically dependent upon the exact length of transmission line, some means must be available to take this into account. The expressions derived give the maximum and minimum power that will be absorbed, and also give the probability that any specified intermediate power will be exceeded if a random choice of transmissionline length is used.     

On the transient radiation of energy from simple currentdistributions and linear antennas

Smith (1998) examined the radiation from two simple filamentary current distributions: traveling-wave and uniform. The radiated or far-zone electric field was computed for an excitation that was a Gaussian pulse in time. Two interpretations for the origin of the radiation were presented, based on the far-field results. The present article continues this investigation; however, the emphasis is on an examination of the near field and the related transport of energy away from the current filament. We examine traveling-wave and standing-wave current distributions, because these distributions are frequently used to model practical antennas. Exact analytical expressions are presented for the electric and magnetic fields of the assumed, filamentary current distributions when the excitation is a general function of time. For the filamentary distributions, the current and charge are confined to a line (a line source). There is no radius associated with the filament. The expressions for the fields apply in both the near and far zones, and are used to determine the Poynting vector. For an excitation that is a Gaussian pulse in time, exact analytical expressions are obtained for the energy leaving the filament per unit time per unit length, the total energy leaving the filament per unit length, and the total energy radiated. Graphical results based on these expressions are used to study the energy transport from the filamentary current distributions. The results for the standing-wave current distribution are compared with those from an accurate analysis of a pulse-excited, cylindrical monopole antenna, performed using the FDTD method     

Optimal design of multiply fed dipole antennas

The gain of a mulitply fed dipole antenna of lengthL, small radiusaand arbitrary locations of feed voltages along the antenna is computed using the well-known moment method. An optimization routine is then employed to study the possibility of maximizing the gain in a specified angular direction and minimizing it at other directions for any given number of excitations and antenna length in order to determine the optimum complex values and location of each source. The results are presented in tables and graphs for a wide range of antenna length and number of feeds. It is shown that both the gain and beamwidth are improved by this technique at the expense of appearance of new sidelobes and requirement to design a more complicated feed network. The Fourier series expansion method is extended in order to determine the gain of a multiply fed wire antenna, and the results for the radiation pattern show good agreement with those based on the moment method.     

Modélisation d’une antenne-réseau et traitement optimal

An array antenna is modeled after a linear multipole filter, one part of which is connected to a distant source, radiating in a specified direction, while the relations between the other parts are characterized by the antenna admittance matrix. This modeling technique is applied to an array of parallel linear wire antennas. It is shown how the array admittance matrix can be evaluated numerically by a discrete quantization of the Maxwell’s equations with the proper boundary conditions (Harrington’s method of moments). The admittance matrix is then used to formulate the optimum signal processing for transmission (maximization of antenna gain, with or without constraints) and for reception (maximization of signalto-noise ratio). Along with the model of the array antenna that is submitted, a method of signal processing is developed in which accurate estimates are included of the losses that occur within the array elements as well as of the coupling between elements and of the noise arising in the receiving system. The antenna designer can thus optimize the geometric configuration of the array and study the phenomenon of superdirectivity with a more realistic approach than was hitherto possible.     

Complex-Point Dipole Formulation of Probe-Corrected Cylindrical and Spherical Near-Field Scanning of Electromagnetic Fields

A probe-corrected electromagnetic theory based on complex-point dipoles is presented for computing the field of an arbitrary source of finite extent (for example a test antenna) from measurements of its near field on a cylindrical or spherical scanning surface. By representing the probe with complex-point dipoles, probe correction is achieved by simple factors that involve Hankel functions evaluated at complex points. Only four complex-point dipoles are needed to represent a typical precision probe used in near-field measurements. The theory uses neither translation and rotation theorems nor differential operators. One disadvantage of the theory is that it employs nonlinear optimization to determine the parameters of the probe model. The complex-point dipole representation of the probe makes realistic simulations of near-field scanning systems straightforward. The cylindrical theory is validated through a numerical example. The spherical theory is validated by experimental data.     

Selection of the microwave-beam parameters in a wireless system for energy transportation from a space electric power station to the Earth

An algorithm for finding the parameters of the microwave beam used for power transportation from a space electric power station to the Earth is considered. It is shown that, for specified geometries of antenna and rectenna systems, it is possible to increase the received power if the density of the radiated power at the antenna center and the truncation parameter of the Gaussian field distribution are simultaneously increased. It is found that, in this case, the transmission efficiency decreases only slightly as compared to the case of optimum transmission.     

Optimal control of the feed voltage of a dipole antenna

An iterative algorithm is described for the construction of the input voltage of a dipole antenna for a specified electric field response at a given far-zone point. A functional is optimized subject to the state equation, which is an ordinary differential equation. The state equation used is Pocklington's equation where the control is the input voltage waveform and the state is the current distribution on the antenna. The Lagrange multiplier function, which is introduced by augmenting the functional, satisfies the adjoint Pocklington's equation. In the descent algorithm these two equations are solved at each step. All calculations are carried out in the time domain, so there is no need for additional specification related to frequency domain. However, the procedure implicitly determines the frequency bandwidth of the signals used     

Target identification using optimization techniques

A scheme for synthesizing bandlimited radar waveforms for detection and discrimination of targets is presented. The procedure, which involves a maximization of the ratio of the energy within a specified time interval to the total energy of the received waveform, can be used to synthesize a bandlimited generator waveform that produces a target response with the majority of its energy concentrated in the specified time duration. For an appropriate time interval, which depends on the bandwidth, such response exhibits energy concentration comparable to that produced by the K-pulse and E-pulse waveforms. The analysis does not require a numerical or empirical determination of the target's complex poles, since the desired waveform is obtained directly from the knowledge of the system transfer function over the frequency band of interest. The procedure is based on an analytical optimization, so no iterations or nonlinear programming techniques are required. The method is illustrated using simple thin-wire models as targets and antennas. Numerical examples are given, and the effects of bandwidth, duration of optimization, and aspect angle are discussed