Experiment 1: Wave Propagation on TEM Transmission Lines

To open the first experiment select the File menu, select Open, and select file expt_1.tlm

Objective: To explore the propagation of transverse electromagnetic waves along TEM transmission lines, and to study the effect of waveform, electric properties of the line, load conditions, and scattering at discontinuities on the propagating fields.

Parameters of the Transmission Line: The file expt_1.tlm contains data for a section of parallel plate waveguide with magnetic sidewalls, in other words, a uniform section of TEM transmission line. It has the following characteristics:

Length: 78 Dl in z-direction; Width: 5Dl in x-direction; Dielectric properties: e_r = 1; s = 0 (air, no losses); Dl = 1 mm.

The two horizontal blue lines are Magnetic Walls. These boundaries have an impulse reflection coefficient of +1.

The two vertical green lines are Reflection Walls. Their impulse reflection coefficient can be set by the user. In a 2D TLM network, a boundary with an impulse reflection coefficient of -0.171573 represents a matched load for a normally incident TEM wave.

The gray area inside the boundaries is a Computation Region. It defines e_r and s inside that domain. Only cells inside a Computation Region are updated during a computation. All other cells remain dead.

The Source Region at the far left (narrow dotted box around the first column of nodes) represents the source. The distribution of the source voltage is constant in x-direction. This means that we will inject identical impulses at each node in the Source Region . Backed by the absorbing wall, it represents a matched source that launches a TEM wave with the wave magnitude specified in the Source Waveform menu when selecting an excitation function. (A Gaussian pulse with magnitude 0.5, a sigma of 8Dt and a mean of 30Dt has been pre-selected).

A 1Dl wide Animation Region (thin dotted box surrounding the centerline of the structure) extends from node z = 2Dl to z = 78Dl for displaying V_y along the axis of the line. V_y is the voltage at the nodes and represents the electric field component perpendicular to the screen.

1.0 Preliminary Steps

1. Open the file Expt_1.tlm
2. The Draw menu is active. Note the colors of the structure elements. We will later discuss how you can modify the geometry and electrical characteristics of the structure. Move the cursor over the structure and observe the digital counter in the Coordinate Area.
3. Now select the View menu and select Field. The Field menu becomes active. Select the Field view and then 2D. A graph titled "Vy versus Position" appears in the window. It shows the amplitude of the electric field vs. the discretized z-axis. You are now ready to start the first simulation experiment.

1.1 Propagation of a Gaussian Impulse along a Lossless Line

1. If you have loaded the original expt_1.tlm file, you can start the simulation either by simply clicking on the  button in the toolbar, or selecting Forward in the Simulate menu. A third way is to press Alt+S then F.
2. To inspect the characteristics of the excitation function, select the Input menu and select Gaussian. Its characteristics should be as follows: magnitude = 0.5, sigma = 8Dt , mean = 30Dt . Press OK in the dialog box and inspect the input function.
3. To inspect the simulation control data, select the Simulation Control menu and then Control Data. Note the number of time steps, also called the number of iterations in the literature (170), and the time steps between screen updates (1). This means that the program stops automatically after 170 time steps unless you stop it yourself earlier by clicking the Stop button in the toolbar. The field distribution along the z-axis (within the narrow Animation Region ) is redrawn after every timestep.
4. Observe the Gaussian impulse propagating across the screen. The speed depends on the size of your window and is determined mainly by the graphics speed of your computer rather than by the TLM computation time.
5. To stop the simulation at any time, click the red stop button. Restart it with , or step it forward one step at a time using .
6. To start the simulation again from the beginning, select Reset Simulator in the Simulation Control menu. Select Field in the View menu again and click on . Note that you can change the Graph Display Attributes in the Field menu at any time, even during a simulation.
7. To capture the content of the window, click the right mouse button and select Image to Clipboard. Use the Print facility as in any other program.

Note that many features of the menu bar described above are also accessible by clicking the right mouse button.

1.2 Propagation of a Sinusoidal Wave along a Lossless Line

1. Initialize the Simulator by selecting Reset Simulator in the Simulation Control  menu, or click the Reset button.
2. From the Source Waveform  menu select Sin(f). Select its characteristics as follows: Magnitude = 0.5, Frequency [GHz] = 6 . Click "OK" and inspect the input function, then return to the Field-2D mode via the View menu or the right mouse button.
3. In the Simulation Control Data window set the number of time steps to 300 and the time steps between updates to 1. Click "OK", then start the simulation by either clicking on , or selecting Forward in the Simulation Control  menu.
4. Observe the sine wave propagating across the screen. The leading edge of the sinewave looks irregular and distorted. That is due to the dispersion characteristics of the TLM mesh and is brought about by the distortion of high frequency components generated by the sudden onset of the sine waveform.
5. Click on the Envelope Display button (second button from the right), and observe that the envelope of the traveling wave is constant.  Hence, the standing wave ratio is unity, and no reflection occurs at the load. Reset the envelope whenever you wish using the right-most button.
6. To stop, continue, or repeat the simulation, and to observe or print the wave at any instant, follow the procedures described in Section 1.1 above.

1.3 Reflection of a Gaussian Impulse by a Short-Circuit

1. Replace the matched load by an electric wall. To do this, proceed as follows:

   Reset the Simulator (Reset button). Select Draw in the View menu (or click the right mouse button and select Draw). Select  Select Element in the Draw menu (or in the menu from the right mouse button). Select the green line at the right extremity of the structure. It changes color. Then delete it using the Del key or Delete. In the Draw menu (or right mouse menu) select Electric Wall. Then draw the wall using the left mouse button The green line should now be replaced by a red line. If you make a mistake, us the Select-and-Delete sequence again. or draw over the wrong element a second time.

2. From the Input menu select Gaussian. Select its characteristics as follows: magnitude: 0.5; sigma: 8Dt ; mean: 30Dt.  Inspect the input function and return to the 2D Field display.
3. Set the number of time steps to 200 and the update interval to 1 in the Simulation Control Data window. Then start the simulation.
4. Observe the Gaussian impulse propagating and being reflected with a (-1) reflection coefficient by the short-circuit. If you increase the number of time steps to 300 it will continue propagating backwards until it is absorbed in the matched source.
5. To stop, continue, or repeat the simulation, and to observe, print, or plot the wave at any instant, proceed as in Section 1. above.

1.4 Reflection of a Gaussian Impulse by an Open Circuit

1. Terminate the structure by a magnetic wall instead of an electric wall. To do this, proceed as follows:

   Reset the Simulator (Reset button). Select Draw in the View menu (or click the right mouse button and select Draw). Select  Select Element in the Draw menu (or in the menu from the right mouse button). Select the red line at the right extremity of the structure. It changes color. Then delete it using the Del key or Delete. In the Draw menu (or right mouse menu) select Magnetic Wall. Then draw the wall using the left mouse button The green line should now be replaced by a red line. If you make a mistake, us the Select-and-Delete sequence again. or draw over the wrong element a second time.

2. Choose the same excitation and simulation parameters as in the short-circuit case and observe the reflection which occurs with a (+1) reflection coefficient this time.

1.5 Partial Reflection of a Gaussian Impulse by a Resistive Load

1. Terminate the structure by a Reflection Wall in the Draw view. To implement such a wall, draw it into the TLM grid and enter the wall property either as reflection coefficient or wall impedance.  Select the property by clicking on the appropriate radio button.  The local  impulse reflection coefficient G_i is related to the wall  impedance by the following expression (see also the "MEFiSTo-2D Theory" booklet, Section 4.2.2):
   
2. For example, in order to reflect an incident TEM wave with a TEM wave reflection coefficient of r = -0.5, the local impulse reflection coefficient G_i of the Reflection Wall must be -0.618513.
3. Choose the same excitation and simulation parameters as in the short-circuit case and verify that the reflection occurs indeed according to the predicted value r by comparing the magnitude of reflected to the incident wave.

1.6 Reflection of a Sine Wave by a Short-Circuit

1. Initialize the Simulator by clicking the Reset button.
2. Enter the Draw view and terminate the structure by an Electric Wall at the right extremity.
3. From the Input menu select Sin(f). Select its characteristics as follows: magnitude = 0.5; f = 6 GHz. Inspect the input function and return to the Draw view.
4. Set the number of time steps to 350 and the update interval to 1. Then start the simulation in the 2D Field display mode.
5. Observe the sine wave propagating and being reflected with a (-1) reflection coefficient by the short-circuit, giving rise to a standing wave. Note that the short circuit is positioned halfway between the nodes at z =78Dl  and z = 79Dl, but the voltage in the discrete TLM network is only defined at the position of the nodes. Hence, the voltage is not displayed as zero at z = 78Dl , but at the outside node at 1/2 Dl beyond the boundary.
6. To stop, continue, or repeat the simulation, and to observe, print, or plot the wave at any instant, follow the procedures described in Section 1.1 above.

1.7 Reflection of a Sine Wave by an Open Circuit

1. Reset the Simulator, select the Graph menu, and terminate the structure by a magnetic wall at the right extremity. Then change to the 2D Field mode.
2. Using the same excitation and simulation control data, observe the formation of a standing wave shifted by a quarter wavelength with respect to the short-circuited case.

1.8 Partial Reflection of a Sine Wave by a Resistive Load

1. Terminate the structure by a Reflection Wall at the right extremity. Choose a local impulse reflection coefficient of -0.6.
2. Using the same excitation and simulation data as in Experiment 1.7, observe the time behavior of a wave composed of a standing and a propagating part. Also note that the VSWR is now finite and larger than unity. Use the Field Envelope Display button to see the standing wave pattern.
3. Determine the VSWR value and the wavelength by placing the point of the cursor arrow at a maximum and click the left mouse button.  Read its z-position and the magnitude in the coordinate box.  Then do the same at a minimum. Compare your results with theoretical values.

1.9 Propagation of a Gaussian Impulse along a Lossy Line

1. Replace the lossless Computation Region  inside the structure by a new box of equal size, but with a conductivity value of s = 0.02 S/m. Terminate the right extremity in an open circuit (Magnetic Wall) or a load of your choice. Then change to the 2D Field mode.
2. To replace the Computation Region, proceed as follows 

   In the Draw menu select Select Element. Click the left mouse button anywhere in the Computation Region (but not on a boundary or box contour). The Computation Region changes color, indicating that it has been selected. Press the Delete key or click on Delete. In the Draw menu select Computation Region. Then enter the relative dielectric constant and the conductivity. The transmission line is now lossy.

3. Using the same excitation and simulation data as in Experiment 1.1, observe the slow decay of the impulse magnitude as it travels along the lossy line. By displaying the envelope of the pulse, you can clearly see the decay in amplitude. Note also the slight distortion of the wave form which is due to the loss in the structure, and the small reflection at the load due to a slight impedance mismatch between the lossy medium and the real load impedance.
    

1.10 Propagation of a Sine Wave along a Lossy Line

1. Enter the Graph menu and replace the lossless Computation Region by a new box of equal size, but enter a value of s = 0.1 S/m. Terminate the line in a load of your choice.
2. Setting the frequency to 10 GHz this time, 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.  Use the Envelope Display Option to study the VSWR behavior.

1.11 Scattering of a Gaussian Impulse at a Dielectric Discontinuity

1. Enter the Graph menu and replace the single Computation Region inside the structure by two new boxes of about equal length . The first Computation Region should include all the nodes from z = 1Dl to z = 39Dl (use the counter) with e_r = 1, and s = 0. The second Computation Region should include all the nodes from z = 40Dl to z = 78Dl with e_r = 4, and s = 0. After you have drawn the second Computation Region, replace the termination by a new Reflection Wall. You will notice that the default value for G_i is now -0.477592, which is required to match a TEM transmission line with e_r = 4 . Then change to the 2D Field display mode.
2. Using the same excitation and simulation data as in Experiment 1.1, observe the scattering of the impulse at the air-dielectric interface situated halfway between z = 39Dl and z = 40Dl. Note both the spatial compression and the reduction in velocity of the impulse inside the dielectric, as well as the continuity of the voltage across the interface at all times.
3. By terminating the line in a short or open circuit instead of an absorbing wall, you can observe repeated scatterings, resulting in a strongly attenuated resonance inside the dielectric section. At the same time the stronger numerical dispersion in the dielectric section becomes noticeable as it results in a progressive distortion of the pulse shape.

1.12 Scattering of a Sine Wave at a Dielectric Discontinuity

1. Use the same structure as in the previous experiment.
2. Using the same excitation and simulation data as in Experiment 1.10, observe the scattering of the sine wave at the air-dielectric interface situated halfway between z = 39Dl and z = 40Dl. Note both the reduction of the wavelength and the reduction in velocity of the wave inside the dielectric, as well as the continuity of the voltage across the interface at all times. In the air section the wave behaves similar to that on a line with a partially reflecting load.
3. By terminating the line in a short or open circuit instead of an absorbing wall, you can observe repeated scattering resulting in a resonance inside the dielectric section.

1.13 Additional Experimentation

The number of similar experiments that can be carried out with this structure is limited only by your imagination. However, when trying other waveforms and frequencies, keep in mind that the discrete TLM mesh behaves like a continuum only for frequencies at which the guided wavelength is long compared with the cell size. For field animation we thus recommend that you choose only band-limited signals as excitation functions. As soon as the wavelength corresponding to their highest frequency component becomes shorter than about 15Dl, distortion of waveforms becomes noticeable.