Tutorial Example File: tut3_mlf.tlm

 
3.1. Preliminary Considerations

The file tut3_mlf.tlm contains data for a microstrip lowpass filter modeled by its equivalent parallel-plate waveguide model with magnetic sidewalls and non-dispersive effective permittivity. (This model has, of course, certain limitations but works well at low frequencies, in this case several GHz).

Several empirical formulae have been developed over the years to calculate the properties of the equivalent parallel-plate waveguide from the microstrip charactristics. Figure 1 shows the cross-sections of a microstrip line and its equivalent model that can be implemented in 2D since all field quantities are independent on the vertical direction.

Figure 2-10:	(a)	Cross-section of a microstrip line.
	(b)	Its equivalent parallel plate waveguide model with magnetic sidewalls.

For convenience, such formulae have been implemented in the Microstrip Wizard that you can find under the Wizard menu. Simply key in the substrate thickness d, the relative dielectric constant of the substrate, e_r , followed by either the strip width W, the normalized strip width W/d, or the microstrip characteristic impedance Z_0m. The Wizard then yields the effective width and effective dielectric constant that you can implement in the TLM model.

The topology of the filter appears on the screen as soon as the file tut3_mlf.tlm is opened. Magnetic walls (blue) define the geometry of the filter. The filter is terminated at both ends by reflection walls (green); the reflection coefficient of these walls has been chosen such that the input and output ports of the filter are matched. Note that the impedance of the absorbing walls is not equal to the microstrip characteristic impedance but rather the TEM wave impedance in the medium that fills the parallel plate waveguide, namely h ₀/Ö e_eff . A reference section with the same electrical properties as the input section is needed for the extraction of the S-parameters of the filter. This reference section appears below the filter input. Both the filter and the reference section are filled with dielectric or computation boxes, as indicated by the darker color.

Figure 2-11:

Microstrip lowpass filter implemented as a parallel-plate waveguide structure with magnetic sidewalls, and reference structure for the extraction of scattering parameters.

3.2 Define and Input the Structure

If you want to re-create the geometry of the lowpass filter, follow this recommended input sequence so that the program generates the proper values for the reflection coefficients of the reflection walls.

3.2.1 Create a new mesh

• In the File menu, select New,
• In the Mesh New dialog box, enter

Number of cells in Z-direction: 52
Number of cells in X-direction: 15
Cell size Delta L in [mm]: 1

• Click OK. The new mesh appears.

3.2.2 Draw the magnetic walls

• In the Draw menu, select Magnetic Wall,
• Draw the magnetic wall sections using the counter in the Coordinate Area. The coordinates of the wall sections can be extracted from the Graph window of file tut3_mlf.tlm

3.2.3 Define the computational domain

• In the Draw menu, select Computation Region,
• Fill all rectangular subareas of the filter and the reference structure with contiguous Computation Regions. In each dialog box, set Relative dielectric constant = 8.22146, Conductivity [S/M] = 0. 

Note:

If you do not want to redraw the structure, you can at least check the property of each element of .the filter. Proceed as follows:

• In the Draw menu, choose Select Element.
• Point and click on any element or area of the filter. The selected element turns purple, and the name of the element appears in the Status Bar.
• In the Right-Mouse-Button menu, select Property. A dialog box displays the properties of the element, if these properties have previously been specified through a dialog box.
  

3.2.4 Draw the reflection walls

• In the Draw menu, select Reflection Wall,
• Draw a Reflection Wall at both ports of the filter and the reference structure. In each dialog box, accept the default value TEM wave reflection coefficient = 0, which characterizes an absorbing boundary or matched termination for a TEM plane wave incident normally on the boundary.

Note:

The Relative dielectric constant is by default the value specified when creating the last Computation Region. It is thus recommended to draw the Computation Region adjacent to an absorbing wall before drawing the wall itself. However, the dielectric constant can be changed at any time. Note that the local impulse reflection coefficient (G i =-0.604351) is different from 0 as predicted by 2D-TLM Theory.

3.2.5 Draw the source regions

• In the Draw menu, select Source Region,
• Draw a narrow vertical box around the left-most column of nodes inside the filter and the reference structure. In the dialog box, accept the default value of 2.02749 which is the scaling factor required to launch a voltage wave of 1 V in the input ports. The source distribution is constant in x-direction.

3.2.6. Place the probes

Up to three probes can be implemented in MEFiSTo-2D. The probes are numbered by the computer in the order in which they are have been created (1 to 3). If one of them is removed, the order is changed in a complicated manner due to internal stack manipulation. In this example, Probe 1 is the probe in the reference section. Probe 2 and Probe 3 are placed in the input and output ports of the filter. (Verify the numbering of the probes by clicking on them after activating Select Element in the Draw menu. The Status Bar indicates the number of the probe.

Note: The reference planes for the S-Parameters are defined by the position of the probes.
 

3.3. Perform the Simulation

3.3.1. Select a Source Waveform

As in the first tutorial example we inject a signal of maximum bandwidth to be certain that all relevant frequencies are excited. This signal will be a single voltage impulse.

• In the Source Waveform menu, select Impulse (T).
• In the dialog box, accept the default value (Magnitude = 1). A graph showing the source waveform appears on the screen.

3.3.2. Select a Sampling Mode

Again, we choose to sample the same component that we have injected, namely the node voltage V_y (equivalent to the field component E_y in the structure.

• In the Sampling Mode menu, select Vy == Ey.
  

3.3.3. Set Simulation Control Data

• In the Simulation Control menu, select Control Data. The Simulation Control Data dialog box appears.
• In the Time Domain Data group box, select the total duration of the simulation (2048 time steps) and the update interval (50 time steps).
• In the Frequency Domain Data group box, enter the number of frequency points (101), the lower frequency (0 GHz), and the upper frequency (6 GHz).

Note:

Since the structure under test is a lowpass filter, we include the low frequency range down to DC. The source waveform (impulse) has a DC component as well.

• In the TLM Mesh Data group box, verify the value of the mesh parameter Dl. The time step is automatically computed and cannot be changed. It guaranties unconditional stability of the algorithm.
• In the TLM Dispersion Error in Percent group box, note that the error in the attenuation content is zero since the dielectric in the waveguide is lossless. The maximum error in the phase constant is the upper bound of the dispersion error, calculated for the value of the Upper Frequency entered above. It is 0.52% in this case.
• Confirm the dialog box content by clicking OK.

You are now ready to start the simulation and to observe its progress. The screen should look as in Figure 2-12.

3.3.4 Start Simulation

• In the View menu, select Graph.
• In the Graph menu, select Probe Responses. You see three columns of graphs for displaying the responses of Probes 1, 2, and 3. The upper row of graphs will be the time response, the middle row will be the magnitude of the frequency response (discrete Fourier Transform), and the lower row the phase response. Note that the horizontal scales correspond to the values set previously in the Simulation Control Data window.
• Start the simulation by clicking on the button in the Simulation Bar. The time response (upper row of graphs) is displayed in bursts of 50 time steps, and the magnitude and phase of the Fourier Transform are updated at the same rate. The whole simulation is completed within a few seconds.

Note:

The frequency response of Probe 3 shows already the characteristics of a lowpass filter from 0 to 1.5 GHz, with a second passband centered around 4 GHz. The spectrum of the voltage in the reference section is almost flat.

Figure 2-12:

Display of the probe responses after 2048 time steps. . Top row: Time responses of probes 1 to 3. Middle row: Frequency responses (Discrete Fourier Transform) of the probes 1 to 3. Bottom row: Phase responses of the same.

• In the Graph menu, select Probe 1 , 2, or 3 to inspect each of the nine windows in greater detail.

Note:

The frequency domain responses are not smooth but show a pronounced ripple (Gibbs effect), particularly towards the higher frequencies. This is due to the following reasons: a) The number of time steps chosen (2048) is insufficient. b) The spectrum of the source waveform contains frequencies above the range of interest (0 - 6 GHz).

1.4. Extract Scattering Parameters

Before extracting scattering parameters we must verify that the three probes are assigned to the correct ports of the structure.

• In the Graph menu, select Port Attributes.
• Verify in the dialog box that

Probe 1 is assigned to the Reference Port,

Probe 2 is assigned to the Input Port, and

Probe 3 is assigned to the Output Port of the filter..

• Verify also that TEM mode propagation is selected for all ports, and that they all have the same width. (If all ports have the same width and carry the same mode, the value entered for the width is immaterial, provided it is the same for all ports.)
• In the Graph menu, select S11 > Magnitude. The magnitude of S₁₁ is displayed. Note again the ripple.
• In the Graph menu, select S11 > Phase. The phase of S₁₁ is displayed.
• In the Graph menu, select S21 > Magnitude. The magnitude of S₂₁ is displayed. Note again the ripple.
• In the Graph menu, select S21 > Phase. The phase of S₂₁ is displayed.
• To change the title, axes or scales of these graphs, select Graph Display Attributes under the Graph menu. You may also display the S-parameters in dB and as a Bar Graph by checking the appropriate boxes.

1.5. Simulation with a reduced bandwidth source

To smoothen the S-parameter curves, we will repeat the simulation with a source waveform tailored to the frequency range of interest. Proceed as follows:

• Reset the simulator by clicking the Reset button.
• In the Source Waveform menu, select Gaussian (f),
• In the dialog box, enter Magnitude = 1, Bandwidth = 12, and Gaussian-Modulated Carrier = Constant. Click OK, and inspect the resulting Gaussian waveform. It is a signal with a bandwidth ranging from -6 GHz to + 6 GHz, centered about DC.

Note:

Even though the properties of the signal have been defined in the frequency domain, the time domain waveform will be displayed. You can verify the spectral characteristics of the signal by computing its Fourier Transform. Simply create a short section of TEM transmission line, match it at both ends, and enter a source point and a probe. Then perform a TLM simulation for a sufficient number of time steps and look at the frequency response of the probe. In this way you can use MEFiSTo-2D as a spectrum analyzer for any discretized signal

• In the Graph menu, select S21 > Magnitude,
• Start the simulation by clicking the button.
• Observe the convergence of the S21 graph. The curve is smoother at lower frequencies, but the ripple at higher frequencies still persists. We must increase the number of time steps further.
• In the Simulation Control menu, select Control Data,
• In the Time Domain Data field, set the Total number of time steps to 3000 and click OK.
• Start the simulation. The curve becomes smooth.

You can now refine the resolution of all graphs and study all aspects of the filter response in greater detail by repeating the steps discussed in Tutorial 1. However, we will explore one more feature of MEFiSTo-2D, namely its capability to dynamically display and visualize the fields in the filter. 
 

1.6. Visualize the Electromagnetic Fields in the Filter.

If we want to observe the behavior of the filter at a certain frequency, we can excite the filter with a sinusoidal waveform at that frequency and visualize the field as it propagates through the structure. Suppose we are interested in the filter behavior at 1.6 GHz, which is the upper edge of the first passband.

• Reset the simulator,
• In the View menu, select Draw,
• In the Draw menu, select Animation Region,
• Draw a box from point (2,1) to point (51,9).
• In the Source Waveform menu, select Sin (f). In the dialog box, set Magnitude = 1 and Frequency [GHz] = 1.6. Click OK. The waveform appears on the screen.
• In the Sampling Mode menu, select Vy == Ey.
• In the Simulation Control menu, select Control Data. In the dialog box, set Total number of time steps = 1000, and Time steps between updates = 1. Disregard the Frequency Domain Data group box and click OK.
• In the View menu, select Field. A three-dimensional view of the filter in its TLM mesh appears on the screen.
• In the Field menu, select Field Display Attributes. Keep that command box open on the side of the screen.
• Start the simulation by clicking on the button.

Figure 2-13:

Visualization of the electric field Ey in the lowpass filter at 1.6 GHz. Note that the field is almost uniform over the wide sections of the structure, indicating that they act essentially as lumped capacitances at that frequency. The Wire Frame option has been de-selected.

• Observe the field as it propagates through the structure. Shift, rotate and scale the display until you like it. . Change the size of the MEFiSTO-2D client window. Continue to modify the 3D View Parameters while the program is running. Adjust the magnification of the field using Magnify Y or Reduce Y. Stop and start the simulation again, or step forward one step at a time using the "+" button.
• You can also change the update interval in the Simulation Control Data box while the simulation is stopped or running. This will change the speed of the field animation at the expense of smoothness. Try also the hidden line removal feature by deselecting the Wire Frame box.
• To visualize the magnetic field components in z- and x-direction, change your selection in the Sampling Mode window.

You have now explored most, but not all features of MEFiSTo-2D. These will be invoked in the following tutorials.