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While the FDTD method provides the flexibility to model any feed type in detail, usually the cell size required precludes this approach if any meaningful amount of space is to be included to incorporate the rest of the antenna structure. In such cases it is necessary and convenient to use a sub-cell feed model to excite the antenna structure.
Various feed models have been published in the literature. Three of these have been selected and used within Celia, these are the lumped parameter feed of Luebbers and Langdon[1] and the transmission line feeds of Maloney et al[2] (unbalanced coax type) and Bourgeois and Smith[3] (balanced).
With the lumped parameter feed a Thevenin equivalent drive circuit is attached to an electric field node within the FDTD mesh. This is shown in Figure 1. In this case the load impedance is the FDTD cell and whatever is attached to it (usually the antenna under study). The output values from this feed are the voltage across the load impedance, ZL, and the current through ZL. This data allows the calculation of such parameters as input impedance, return loss etc, depending on the type of analysis required.
There are two primary disadvantages to this feed. Firstly the load impedance includes a parallel capacitance associated with the FDTD cell. While this value is usually small, if large source resistances Rf are used then the time constant RC can be significant and the capacitance must be taken into account. This can be overcome by configuring the drive circuit as a Norton equivalent current source for high source impedances. The second disadvantage of this feed is that the voltage and current are half a timestep out of phase. While this is not important most of the time, in certain instances it can lead to inaccurate results.
The second feed type applied is the transmission line feed of Maloney[2]. This has appeared in the literature in two versions. Firstly an unbalanced coaxial type feed originally published by Maloney, and secondly a development of this into a balanced two conductor style transmission line feed published by Bourgeois and Smith[3] . Both are implemented in Celia.
The feed looks schematically as shown in Figure 2 when applied as a balanced feed to a bi-polar antenna (dipole say). The feed transmission line is solved as a separate 1D solution to the Telegraphers equations. The line is attached to an electric field node at the right hand side of the feed transmission line illustrated in Figure 2, where it joins with the antenna structure. The way in which this feed operates is that a characteristic impedance for the line is specified (real as it is assumed lossless), and a wave is launched at the left end (denoted Vapplied). During the calculation the wave traverses the line and at the point of attachment with the antenna the wave is reflected. The output from this feed type is the applied and reflected voltages on the feed transmission line. From this data the reflection coefficient of the antenna drive point can be calculated and hence the impedance mismatch at the drive point. This gives directly the drive point impedance of the antenna.
As far as the FDTD mesh is concerned the excitation mechanism is identical to the lumped parameter feed (via an applied voltage at an electric field node), however, the output data from the transmission line circumvents the phase problem inherent in the voltage and current output from the more primitive feed.
The line is terminated on the left with an absorbing boundary condition so that the line looks infinite in extent for the reflected wave.
When configured as an unbalanced feed the schematic looks like Figure 3. In this feed the concept is the same with a 1D transmission line representing the coax. In Figure 3 all parts of the domain above the ground plane are included in the 3D FDTD mesh with the electric field node at the base of the monopole being excited by the 1D transmission line. It is expected for this feed type that the electric field node chosen lies adjacent to and normal to a high conductivity surface (where the outer conductor of the coax is assumed connected).
Again, a wave is launched on the coax and the reflected voltage is measured to give the antenna characteristics.
With either the lumped parameter feed or the transmission line feed linear and non-linear lumped element components (capacitors, resistors, diodes etc) can be included in the feed model. Later, during the discussion of the validation cases, a case will be shown where the extra stray capacitance of the connector at the end of the coaxial cable used to mount the antenna is included in the model.
1 Luebbers R J, Langdon H S
'A Simple Feed Model that Reduces Time Steps Needed for FDTD Antenna and
Microstrip Calculations'
IEEE Transactions on Antennas and Propagation
Vol 44, No 7, July 1996, pp 1000-1005
2 Maloney J G, Shlager K L, Smith G S
"A Simple FDTD Model for Transient Excitation of Antennas by Transmission
Lines"
IEEE Transactions on Antennas and Propagation
Vol 42, No. 2, Feb 1994, pp 289-292
3 Bourgeois J M, Smith G S
'A Fully Three-Dimensional Simulation of Ground-Penetrating Radar: FDTD
Theory Compared with Experiment'
IEEE Transactions on Geoscience and Remote Sensing
Vol 34, No 1, Sept 1996, pp 37-44