Experiment 2: Wave Propagation in Rectangular Waveguides

To open the second experiment select the File menu, then Open, and select the file expt_2.tlm.

Objective: To explore the propagation of TE_n0 waves in a rectangular waveguide, and to study the effect of waveform, electric properties of the guide, load conditions, and scattering at discontinuities.

Parameters of the Transmission Line: The file expt_2.tlm contains data for a section of rectangular waveguide. It has the following characteristics:

Length: 60 Dl; Width: 11 Dl; e_r = 1; s = 0 ; Dl = 0.646545 mm. It thus models a standard WR(28) waveguide. The height of the waveguide is irrelevant since we consider only TE_n0 modes, i.e. two-dimensional wave propagation.

The guide is terminated at both ends with wideband absorbing (Johns Matrix) boundaries, the properties of which are stored in the file Wg-11.joh.

The Source Region at the left extremity has a half-sinusoidal V_y distribution along the width of the guide with a scaling factor of 0.5. Backed by the absorbing Johns wall it represents a matched source that launches a TE_n0 wave with the wave amplitude specified in the Sin(f) option of the Input menu when the excitation is a 30 GHz sinusoidal signal.

A two-dimensional Animation Region extends over the whole waveguide but does not include the Source Region since the highly non-uniform source fields would distract from the propagation phenomena. (You can, of course, include the source in the Animation Region if you wish).

2.0 Preliminary Steps

1. Open the file Expt_2.tlm (Note: This is a hyperlink, some browsers may require that you copy Wg-11.joh from the VEL_Expmts directory to the \Windows\Temp directory or some other directory in your hard drive.)
2. Inspect the structure and identify the various elements. You must enter the Draw view whenever you want to inspect or modify the geometrical and electrical characteristics of the structure. Select any of the menu items and explore the geometry of corresponding structure elements using the digital counter at the top of the screen. Then change from the Draw to the Field view. From the Field menu select 3D. You are now ready to start the next series of simulation experiments. (The right mouse button gives you also access to these menus and options).

2.1 Propagation of a Sinusoidal TE₁₀ Wave along a Lossless Guide

1. Initialize MEFiSTo-2D by selecting Reset Simulator in the Simulation Control menu.
2. Select the Source Waveform menu and choose Sin(f). Assign its characteristics as follows: magnitude = 1, f = 30 GHz. Inspect the discretized source function.
3. In the View menu select Graph. Then click the right mouse button and select Johns Matrix 1. Inspect the Johns Matrix.  It should be 500 time steps long and have extrema between -0.5 and +0.5.  Click the right mouse button again and choose Select Johns Matrix. Navigate to the Examples folder and inspect the selection of joh files. Open Wg-11.joh. This file is now assigned to the Johns Matrix 1.
4. In the Simulation Control window set the number of time steps to 250 and the time steps between updates to 1. Then switch to the Field mode and start the simulation by clicking on . The attributes of the field display can be modified using Field Attributes in the Field menu.
5. Observe the wave propagating through the structure. The stepping movement of the wave underlines the time discrete nature of TLM. You will also notice the transient nature of the initial phase of excitation. Note that the amplitude of the traveling wave varies at a slowly decreasing rhythm. This is due to the slow decay of below-cutoff frequency components excited by the sudden injection of a sine function and trapped in the source region. The ringing can still be noticed after more than a thousand time steps. To accelerate the propagation display, replace the Animation Region by a narrower one such as in the previous set of experiments. (Enter the Draw menu to do this).
6. To stop the simulation at any time, click the red Stop button.
7. To continue the simulation, increase the current value of the number of time steps in Control Data and click on .
8. To repeat the same simulation from the beginning, click on the Reset button and then on .
    

2.2 Reflection of a Sinusoidal TE₁₀ Wave by a Short and an Open Circuit

1. Enter the Draw view and terminate the structure by an electric or a magnetic wall on the right. Then change to the Field view.
2. Initialize the Simulator by clicking on Reset.
3. From the Source Waveform menu choose Sin(f). Select its characteristics as follows: magnitude = 0.5,  f = 30 GHz, . Inspect the discretized input function.
4. Set the number of time steps to 250 and the number of time steps between updates to 1. Then start the simulation by clicking on .
5. Observe the sine wave propagating and being reflected with a -1 reflection coefficient by a short-circuit, and with a +1 reflection coefficient by an open circuit, giving rise to a standing wave. Note that like all boundaries, the reflecting termination is positioned halfway between nodes, but the voltage in the discrete TLM network is only defined at the position of the nodes. Again, it takes a certain time until all transients decay sufficiently and the steady-state has been reached.
6. To stop, continue, or repeat the simulation, and to observe or print the wave at any instant, follow the procedures described in Section 2.1.

2.3 Partial Reflection of a Sinusoidal TE₁₀ Wave by a Resistive Load

1. Enter the Draw menu and terminate the structure in a Reflection Wall at the right extremity. Don't forget to  Reset before attempting to make any changes in the structure.
2. Using the same excitation and simulation data as in experiment 2.2, observe the time behavior of a wave composed of a standing and a propagating part. Also note that the VSWR is now finite.

2.4 Excitation of a Rectangular Waveguide by a Gaussian Impulse

1. Reset the Simulator.
2. From the Source Waveform pulldown menu choose Gaussian(T). Select its characteristics as follows: mean = 30Dt, sigma = 8Dt, magnitude = 1. Inspect the input function and return to the Field  menu.
3. Set the number of time steps to 250 and the number of time steps between updates to 1. Then start the simulation by clicking on .
4. Observe the waveform propagating across the screen. It has no resemblance to the waveform observed in the TEM case. In fact, the dispersive nature of the waveguide characteristic impedance and phase constant grossly distorts the impulse (this is not an effect of the discrete TLM mesh), and since most of the injected energy is contained in frequency components below cutoff, it cannot propagate away from the source but will diffuse into the terminations of the waveguide. At the cutoff frequency, energy resonates in transverse direction and causes "electromagnetic ringing" of the waveguide.
5. To stop the simulation at any time, click the Stop button.
6. To continue it, increase the current number of time steps and click on .
7. To repeat the same simulation from the beginning, click on Reset and then on .

2.5 Propagation of a Sinusoidal TE₁₀ Wave in a Lossy Waveguide

1. Enter the Draw menu and replace the lossless Computation Region inside the guide by a new box of equal size, but enter a value of s = 0.1 S/m. Terminate the right extremity in a load of your choice.
2. Using the same excitation and simulation data as in Experiment 2.2, observe the slow decay of the wave amplitude as it travels along the now lossy line, and the variation of the VSWR along the propagation direction in case of total or partial reflection at the load.

Strictly speaking, the Johns boundary which has been created for the purpose of terminating a lossless guide, is no longer a perfect match for a lossy guide. You will find, however, that it will still work well.