Analysis of the equiangular spiral antenna

This thesis presents an analysis of the behavior of an equiangular spiral antenna using a mixture of numerical and measurement techniques. The antenna is studied as an isolated element and as a part of a spiral-based ground-penetrating radar (GPR) detection system. The intention is to isolate the effect of varying different geometrical parameters that define the spiral element or the spiral GPR system. With some notion of each parameter's effect, systems that use the spiral antenna can be more easily designed.;In the isolated spiral element work, prototype antennas are constructed and measured for characteristic impedance and boresight gain. In addition, a numerical model based on the finite-difference time-domain method is constructed for studying the spirals. The measurements closely agree with numerical models for the antennas. Next, the models are used to construct design graphs that relate the geometry of the antenna to the characteristic impedance in the operating band and the lower-frequency cutoff of the operating band. Additional features of the boresight gain and patterns are studied.;The prototype antennas are incorporated into a full GPR system. The system has two spiral antennas that can be used as a bistatic or monostatic radar and each antenna is backed with an absorbing can. The system is tested in a sand box using several buried scattering objects. The numerical model is also extended to incorporate all relevant features. Good agreement is shown between measurements of the system and the model.;To characterize the system using the model directly required too much computing time, so two techniques to extrapolate the performance of the system were explored. First, reciprocity and the planar symmetry of the ground could be used to extrapolate the radar response of a scatterer located at different positions from the fields induced in the ground by the antennas. Second, the antennas could be characterized in terms of their plane-wave spectrum, which could then be used to calculate the fields in different ground types from the field on a surface in front of the antennas when they radiate into free-space. Aspects of both techniques are explored in this thesis, but only the first is applied to the spiral system.;The reciprocity model described is developed and shown to agree well with measurements for sufficiently small scatterers. The model is then used to characterize the GPR system's ability to detect scatterers with different types of geometries. It is found that the bistatic pair is much less efficient than the monostatic antenna. In addition, the monostatic antenna is far more sensitive to scatterers very near the air-ground interface than away from it. This could make the monostatic system much less useful when dealing with clutter.;In addition, the claim that the circular polarization of the spiral antenna is useful for identifying the geometry of a target in the ground is examined. Because circular polarization is a far-field concept, some redefinition of the term is required to study it in the near-field under the ground. In this work, the question of whether circular polarization exists in the ground under the antennas is replaced with the equivalent question of whether a symmetric scatterer is rejected by the antennas. This symmetric-scatterer rejection is well-defined even directly next to the antennas, and it is found that symmetric-scatterer rejection occurs well into the near-field, however for grounds with high permittivity, the angular width of the region where rejection occurs becomes smaller.;The use of the plane-wave spectrum for characterizing the GPR system was found to have two difficulties. The first difficulty is that the calculation of the plane-wave spectrum from some finite plane of field data can only be done accurately when the antenna under test is highly directive in the direction normal to the sampling plane. The second difficulty is that the plane-wave spectrum can only be used to predict the fields in the ground when the antenna under test has a small scattering cross-section. The spiral antennas in this work are not particularly directive and they have a fairly large scattering cross-section, so the technique was not coupled with the reciprocity model. However, the problem of calculating the plane-wave spectrum of a low-directivity antenna was looked into extensively, and a technique for improving this calculation is presented as the final part of this thesis.