Finite Difference Time Domain (FDTD)

The Finite Difference Time Domain (FDTD) method of electromagnetic analysis has revolutionised the way many types of antenna can be modelled. The application of FDTD to a variety of antenna problems now forms the major part of our research output. Areas in which the group has been active in the application of the FDTD method in recent years include strut analysis for large geodesic radomes, analysis of planar active integrated antennas, analysis of microstrip patches and analysis of infinite arrays. Apart from the application of the FDTD method to antenna problems, the group is active in the development of new and improved techniques. A recent development of the group is a discrete Greens Function formulation for the FDTD method providing efficient analysis of metallic antennas. Current work includes the extension of the previously developed ideas to the inclusion of dielectrics to yield a more general formulation.

The application of FDTD to a variety of antenna problems now forms the major part of our research output. In the area of large geodesic radome design FDTD has been successfully applied to the modelling of the dielectric struts that form the structure supporting the radome panels. FDTD permits the accurate modelling of wire loaded struts to reduce the level of forward scattering and hence reduce the level of installed antenna sidelobe degradation. Results from the codes show excellent agreement with near-field scattering measurements of single struts.

World-wide there has been much work on patch antenna modelling but accurate prediction of their performance in an array environment remains a problem due to mutual coupling and surface wave effects. At QMUL we have developed a FDTD code for arbitrary shaped patch antennas and are currently devising an efficient FDTD scheme for modelling both infinite and finite arrays of patch elements.

We believe that one of the next major advances in millimetre and sub-millimetre wave antennas will be the integration of arrays of active antennas on a single silicon, or GaAs, substrate. To this end we have extended our FDTD software to include non-linear circuit elements in the time stepping algorithm. Schottky diodes and others active devices are included in the FDTD method as non-linear differential equations associated with a lumped element circuit model. Using this method, features such as the effect of feed/bias transmission lines, air bridges, and optimised matching between passive and active structures can be included in a design. The electromagnetic performance of the complete circuit, including the interaction of the active element with the passive part of the circuit, can thus be predicted. To experimentally verify our code a quasi optically fed ring mixer for operation at 90GHz is being manufactured on a silicon substrate (see Figure).

Many microwave devices such as antenna arrays or frequency selective surfaces (FSS) can be approximately modelled as infinite arrays of patches or waveguide elements. The response of the infinite array to field excitation can be estimated from the model of a single array element. This property has been exploited by numerical techniques in the frequency domain to reduce the complexity of the problem. However in the time domain special problems arise when modelling phase shifted arrays or non-normal incidence of plane waves onto an FSS. In these cases field excitation is produced at each element at different time instants. Thus prior knowledge of the field scattered by adjacent cells form the initial conditions for the single cell analysis. If the excitation is a single sinusoid than this can be calculated but the power of FDTD is to excite a structure with a Gaussian pulse and hence obtain the devices complete frequency response from this single calculation. To solve this problem we have developed an extended FDTD algorithm employing the Lorentz transform to convert the problem to a normal incidence case. Verification of this technique has been demonstrated by comparing the transmitted power through an FFS comprising a screen of square holes is compared with that obtained using the frequency domain Mode Matching method. This is a significant advance in FD-TD analysis and leads the way to more accurate prediction of arrays and FSS's, particularly when each element contains an active component.

For finite arrays we have used our full 3D FDTD code to analyse a finite array of aperture coupled microstrip patch antennas. The figure below shows the array and the measured and predicted mutual coupling.