Figure 1. A perfectly matched system of three transmission lines and terminating impedances. Current and voltage conventions are shown on the left.

Figure 1 shows the general system of transmission lines modeled by Transmission Line Animator. Three lines are connected as shown. Each line can have characteristic impedance, phase velocity, and loss constant set without restriction. As shown, four terminating resistances are connected at the ends of the lines. These can also be set and incremented without restriction. The total electrical length To of the three lines can be set to any value. The lengths of the individual lines, set interactively by slider, can be any values subject to the restriction on total electrical length. Sliders are used to simultaneously lengthen and shorten lines connected at the two discontinuities, leaving the total length unchanged. Most transmission line phenomena can be vividly exhibited by this interactive structure.

Figure 2. Voltage, current, and impedance along the system of Figure 1. The locations of the discontinuities are set as shown by the sliders. The wavelength of the fields along the line is shown. This matched system is insensitive to changes in wavelength, and to changes in line lengths as set by the sliders.

The system of lines can be energized in various ways before initiation of the animation. Voltage sources at far left and right are connected as shown. These sources can launch virtually any waveform on the system during the animation. Currents and voltages along the lines at the start of the animation can also be imposed as initial conditions. TEM waves propagating left or right can be launched. Purely electrical or magnetic disturbances on the lines can also be set. These fields of course resolve immediately into left and right propagating TEM waves as the animation proceeds. Like the voltage sources, currents and voltages imposed on the system at initiation can be of virtually any waveform.

Before launch, the duration of the animation is set, usually to some multiple of the system total electrical length. After the animation, properties of the system under consideration can be presented in various ways. Specifically after animation any subsection of the system can be specified, and the waves of current and voltage on this section can be presented stroboscopically. Also probes can be positioned along the system to graph the secular evolution at any point on the lines. This can include voltage and current, and power flow and integrated power flow at the probe position, to illustrate continuity or discontinuity of the voltages and currents, and conservation of energy and power.

An important special case is that of phasor excitation. Without loss of generality the voltage source on the left can be sinusoidal, with the right source set to zero. In this configuration standing waves appear on a mismatched system. VSWR, power flow, and related quantities for each section are computed for display in this configuration.

Figure 3. Power considerations on the matched system of Figure 1.The power delivered by the source on the left equals the total power absorbed in the four resistors. The flow of power is reduced in steps as power escapes into the resistors. The electrical and physical length of each line is shown. The VSWR along each element is 1. Terminating impedances can be interactively changed at the top.

Figure 4. Conditions on the system with R4 changed to 300 ohm, mismatching the entire system. The standing waves are here highly sensitive to changes in the locations of the discontinuities, as set by slider, and to changes in the operating frequency. The voltage along the system is continuous and the current is discontinuous, due to the terminating impedances.

Figure 5. Power considerations for the mismatched system. The power delivered by the source on the left equals the total power absorbed in the four resistors. In spite of the mismatch, the power flow along each element is constant.