Dipole Animator and Transmission Line Animator are graphical interfaces for exposition of topics in classical electromagnetism. In both applications the operator can physically manipulate, virtually, a system composed for simulation and animation of a given problem. In the Dipole Animator, this involves interactive translation and rotation in three dimensions of a radiator and reflecting surface, for study of radiation launched by an antenna into free space. In the Transmission Line Animator, lengths of transmission lines can be interactively lengthened or shortened to illustrate the behavior of guided radiation. In this way both interfaces show vividly the critical relationship between the wavelength and the dimensions of the components of a system, much as is demonstrated in the microwave laboratory.
Figure 1. Animation of circularly polarized radiation near the focus of a parabolic receive dish.
The Dipole Animator is a graphical interface for three dimensional animation and display of the fields and currents of classical electromagnetic field theory. The interface animates the fields radiated by familiar antenna structures such as dipoles, Yagis, and helices. It animates the fields of transmit and receive parabolic dishes. The interface also animates the currents induced on these structures, and on their ground planes. The Dipole Animator animates plane waves impinging obliquely on conducting surfaces or dielectric discontinuities.
Figure 2.a. dA and dL positioned near an elementary dipole
b. Resonant 5 element Yagi rotated in space
c. Radiation pattern of 5 element Yagi at three wavelengths
In interaction with the Dipole Animator the operator sets without restriction the operating frequency and the physical dimensions and positions of the elements of a system. The positions of radiator and target are subject to incremental translation and rotation in three dimensions.
Figure 3. Circularly polarized radiation impinging on dielectric substrate near Brewster angle.
As the elements of a system are positioned by the interface in three dimensions, so the Dipole Animator's algorithms for computing the electromagnetic fields of the system are also seamlessly three dimensional. The Dipole Animator displays projections of the computed fields and currents on the two dimensional computer screen. The operator positions the elements of the system for optimum projection of the animation of these fields. Dipole Animator animates the polarization of radiation as it depends upon the orientation of the source. It displays the directivity of radiators as this depends upon the operating wavelength, and on phasing.
Classical antenna theory is usually expressed using differential vector calculus in polar coordinates. The Dipole Animator explicitly adopts this notation. Quantities in the theory, for example the polar unit vectors, or the wavelength, can be displayed directly on the screen, in projection.
Figure 4. Circular currents induced on a parabolic dish by a source on axis and off axis.
Certain quantities, for example power flux or solid angle, are sometimes important in quantifying the behavior of radiating system. An example of this is the antenna directivity, defined as the power density radiated in a certain direction normalized to that of an isotropic radiator. Among many other quantities Dipole Animator computes the power flux through a target, and its area. As the area of the target and the power through it are subject to incremental change without restriction, they are differential quantities. The directivity is computed as the quotient of these differentials. In this way the Dipole Animator illustrates the fundamentals of differential vector calculus and the polar coordinate system, as it displays graphically and numerically features of interest of the system under consideration.
The Transmission Line Animator is a graphical interface for animation and display of the propagation, transmission, and reflection of guided electromagnetic waves. The interface can be configured to illustrate the currents and voltages on systems of transmission lines of any length, characteristic impedance, wave velocity, or loss constant. The interface allows virtually any waveform to be launched on the lines, in any mode, and also supports phasor excitation and analysis. The Transmission Line Animator animates current and voltage, which are of course associated with transverse electromagnetic fields propagating within a transmission line of arbitrary cross section. Concepts such as characteristic impedance, standing wave ratio, reflection and transmission coefficients, power flow, are illustrated.
Figure 5. Animation of a narrow band pulse transmitted through a quarter wave transformer from a low impedance to a high impedance line. Red is the voltage on the line, green is the current.
In using the Transmission Line Animator, the operator can change interactively the lengths of the elements of the system under consideration, to illustrate the critical role that line length plays in practice. The operator can also set without restriction all terminating impedances, as these are also critical. Transmission lines appear in RF and microwave electronics as resonators, striplines, splitters, transformers, slot lines, and many other structures. These structures can usually be modeled by a configuration of the Transmission Line Animator.
Figure 6. Standing waves of current and voltage along a mismatched 3 section transmission line.