David F. Kelley

Piecewise linear recursive convolution for dispersive media using FDTD

Electromagnetic propagation through linear dispersive media can be analyzed using the finite-difference time-domain (FDTD) method by employing the recursive convolution (RC) approach to evaluate the discrete time convolution of the electric field and the dielectric susceptibility function. The RC approach results in a fast and computationally efficient algorithm; however, the accuracy achieved is not generally as good as that obtained with other methods. A new piecewise linear recursive convolution (PLRC) method is described here that has greatly improved accuracy over the original RC approach but retains its speed and efficiency advantages.

Array antenna pattern modeling methods that include mutual coupling effects

Results from an investigation into methods of modeling the radiation patterns of phased arrays that include the effects of radiative mutual coupling are presented. The approaches are based on either the principle of pattern multiplication or the use of active element patterns. Theoretical derivations of the various active element pattern methods are presented. A new method, the hybrid active element pattern method, is introduced. It accurately predicts the patterns of small and medium-size arrays of equally spaced elements. Example arrays of center-fed dipoles are analyzed to verify and illustrate the representations. The results are general and can be applied to arrays of any type of element. The array patterns computed using both the classical pattern multiplication approach and the methods based on active element patterns are compared to those computed using accurate numerical codes based on the method of moments. >

Debye Function Expansions of Complex Permittivity Using a Hybrid Particle Swarm-Least Squares Optimization Approach

With appropriate modifications, the finite-difference time-domain (FDTD) method can be used to analyze propagation through linear isotropic dispersive media. Although materials characterized by the Debye permittivity model can be analyzed accurately and efficiently using well established methods, the treatment of other types of frequency dependence is more difficult. This paper proposes the use of a weighted sum of Debye functions to approximate more general complex permittivity functions. A combination of the particle swarm optimization method and linear least squares optimization is used to find the relaxation frequencies and weights in the expansion, which can then be accommodated in the FDTD method using one of the established methods. Two key advantages of the proposed approach are that the relaxation frequencies are bandlimited and the weights are always positive. These two characteristics help to maintain the accuracy and stability of the FDTD solution. It is also shown that the correlation between the imaginary parts of two Debye functions is the same as that between the real parts.

Relationships between active element patterns and mutual impedance matrices in phased array antennas

In the context of phased array antennas an active element pattern is the radiation pattern of an array when only one element in the array is excited and all of the others are terminated in some specified impedance, typically the output impedance of the sources that normally drive the elements. It is shown here that a combination of two types of active element patterns can be used to find the mutual impedance matrix that relates the element terminal voltages of a phased array to the terminal currents. The first type is found by forcing the terminal voltage of the active element to be unity at zero phase while the terminals of all the other elements are shorted. The second type is obtained by forcing the terminal current to be unity while the undriven feed points are open-circuited. The former is called the short-circuit active element pattern and the latter the open-circuit active element pattern.

Embedded element patterns and mutual impedance matrices in the terminated phased array environment

An embedded element pattern is the radiation pattern of a phased array when one array element is excited and all other elements are terminated in a specified impedance. Previously (Kelley, D.F. Proc. IEEE Int. Symp. Antennas and Propag Soc., vol.1, p.524-7, 2002), a relationship was derived between the mutual impedance matrix of a phased array and its short- and open-circuit embedded element patterns. Although this relationship is interesting in a theoretical sense, it is probably not of much practical value. Primarily, this is because it is difficult to obtain a good short or open circuit termination. Additionally, the terminal voltage (or current) at the excited element must be maintained at a value of unity with zero relative phase while the element pattern data is being collected. It is now shown that the mutual impedance matrix can also be calculated using embedded element patterns obtained using non-zero (and finite) terminations. This result is potentially more useful, because it requires that constant available power be supplied to each excited element rather than constant voltage or current maintained at the terminals.

Debye function expansions of empirical models of complex permittivity for use in FDTD solutions

The method described provides an intuitive and straightforward approach for approximating arbitrary complex permittivities using sums of Debye functions. Because the distribution of relaxation frequencies is guided by the actual frequency range of interest, there is a greater chance that a minimum number of Debye functions will be required in the expansion. This leads to a more efficient FDTD solution, since computer memory requirements decrease as the number of Debye functions decreases.

Efficient calculation of radiation patterns for reactively-steered array antennas

There is growing interest in the use of directive antennas in wireless systems. An alternative approach to traditional designs, such as mechanically-rotatable reflector antennas and phased arrays, is the reactively-steered array (Gyoda, K. and Ohira, T., 2000; Thiel, D.V. and Smith, S., 2002), in which only a single array element is excited by the RF source, and the other elements are parasitically excited. The parasitic elements are loaded by reactances that can be varied to adjust the relative phases of the element excitations. Through an appropriate selection of reactive loads, the main beam of the array, or a null, can be scanned to any desired direction. These arrays have the advantage of electronic pattern control without the complicated, expensive, and heavy feed network associated with traditional phased arrays. The paper presents a method that permits the fast calculation of radiation patterns of reactively-steered arrays for new sets of reactive loads applied to the parasitic elements. It is a much faster approach than applying full-wave analysis every time the load reactances change. The scan element pattern matrix and the mutual impedance matrix used in the method incorporate all of the effects of nearby scatterers to the extent that they are accurately modeled, but the matrices are computed only once for a given array geometry.

Calculation of dispersion errors for the piecewise linear recursive convolution method

Young et al. (1995) introduced a simple procedure for calculating the dispersion errors inherent in several techniques for modeling frequency-dependent media in the finite difference time domain (FDTD) method. The authors present closed-form expressions for the numerical permittivity, the apparent permittivity of the medium due to numerical grid dispersion. The numerical permittivity is then used to compute the dispersion. Here, the dispersion analysis technique of Young et al. is applied to the new piecewise linear recursive convolution (PLRC) method of Kelley and Luebbers.

A scattered field FDTD formulation for dispersive media

In the scattered field formulation of the finite difference time domain (FDTD) method, the electric and magnetic fields are decomposed into incident and scattered components. This approach is often used in scattering problems in which a wave of known shape is incident on a region of interest. The scattered field approach presented for analyzing propagation through dispersive media can be used with any incident field waveform. The use of a look-up table to hold the convolution data yields a method that is faster and less complex than those based on the use of analytical functions. Finally, the additional computer memory and time requirements are insignificant.

A reactively controlled array over ground plane for hemispherical coverage

The results presented here represent the beginning of an investigation of a new class of reactively controlled arrays. The array extends only lambda/2 above the ground plane. Hence, it could find use in applications where a quasi- conformal antenna with a moderate amount of pattern control is needed. Although fully excited conformal phased arrays are likely to provide better performance than this one, reactively controlled arrays have the advantages of low cost, light weight, and simplicity of construction.