Aug 4, 2017 - called plate graphical user interface. (PlateGUI), which calculates and shows electromagnetic (EM) fields inside a parallel-plate waveguide ...
Testing Ourselves
Levent Sevgi
A MATLAB-Based Virtual Tool for Simulations of Wave Propagation Inside a Parallel-Plate Waveguide Gökhan Apaydin and Levent Sevgi
A
MATLAB-based propagation tool called plate graphical user interface (PlateGUI), which calculates and shows electromagnetic (EM) fields inside a parallel-plate waveguide using different analytical and numerical models, was developed and is discussed in this article. PlateGUI can be used in graduate-level courses that deal with guided-wave theory and computational electromagnetics (CEM).
A NEW SIMULATION TOOL EM problems are complex in nature, but wave theory is well established with Maxwell equations. Solution strategies may be grouped into three areas: analytical modeling, numerical simulations, and measurements. Measurement in EM is time consuming, expensive, and, in most cases, extremely difficult to do. A limited number of analytical solutions is available for only a few highly idealized problems, so numerical simulation is the only means for almost all real-life EM engineering problems. This is why modeling and simulation in EM has made significant progress for the last couple of decades [1]–[4]. The philosophy is to keep it as simple as possible so it can be used as a basic CEM tool and supply simple MATLAB codes so even beginners can use them. Digital Object Identifier 10.1109/MAP.2017.2707324 Date of publication: 4 August 2017
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1045-9243/17©2017IEEE
editor’s Note In this issue’s “Testing Ourselves” column, a MATLAB-based education tool that can directly be used for both undergraduate- and graduate-level guided wave theory and computational electromagnetics types courses is introduced. The tool can be downloaded from http://leventsevgi.net/index.php?page=emvirtualtools. The authors are also willing to share this upon request.
Propagation inside a parallel-plate waveguide with perfectly electrical conducting boundaries in two dimensions is one of the most simple and widely used structures to achieve these tasks. In the “Education Corner” column in the April 2016 issue of IEEE Antennas and Propagation Magazine [5], Maaskant and Rosen revisited this problem and presented an analytical problemsolving approach with educational value for EM theory. In their article, they also shared their MATLAB code. This problem has been examined in several studies before [6]–[19], some of which were published in this magazine. The classic paper for the analytical raymode and hybrid formulations was first presented by Kamel and Felsen in [7]. Visualizations of these hybrid ray-mode techniques were discussed in [12], and a free MATLAB package was introduced. Algorithms and codes for the numerical solution of this problem using different models were also presented—e.g., finite difference time domain (FDTD) in [15],
the parabolic equation (PE) method in [16] and [17], the method of moments (MoM) in [18], and so forth. There are also several books that have become classics in the presentation of this problem (e.g., [20]–[26]). Propagation inside a parallel-plate waveguide is an interesting EM problem where both analytical and numerical models can be comparatively tested against each other. ■■ First, the Green’s function solution is exact but requires an infinite number of mode summations. This is a numerical challenge, especially in the near vicinity of the line or Gaussian source. The modes are categorized into two groups: propagating modes and evanescent modes. The number of propagating modes depends on the frequency and the plate width. A tilted directional antenna can also be located inside and modeled in terms of modes, but modal excitation coefficients become complex in this case. This is another numerical challenge,
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IEEE Antennas & Propagation Magazine
START PlateGUI
SPECIFY Plate Parameters
SPECIFY Antenna Parameters
SPECIFY Observer Position
Plate Length Plate Height Number of Height Points Number of Length Points
Polarization Frequency Antenna Height Source (Line, Gaussian)
Observer Height Observer Range
Line Source
Gaussian Source
CALL MoM Analysis
CALL Ray Analysis
CALL Mode Analysis
CALL FDTD Analysis
CALL PE Analysis
Maximum Number of Reflections Number of Reflections
Maximum Number of Reflections Number of Reflections
Maximum Number of Modes Number of Modes
Maximum Time
Wide, Narrow
Horizontal Fields Three-Dimensional Fields Versus Range/Height Vertical Fields
Observer Height
Observer Range
EXIT
FIGURE 1. A flowchart of the PlateGUI algorithms.
■■
■■
especially at high frequencies when the number of propagating modes is high. Ray-based analytical solutions can be also constructed in terms of ray summations by considering a number of reflections. An infinite number of ray summations is required for the line-source excitation. This may be achieved via ray shooting with the image method. The higher the number of images used, the more accurate the results obtained. One-way, fast Fourier transformationbased PE models have been used in propagation modeling in waveguiding environments. The PE models can handle tilted and directed excitation antennas easily; but one needs to use
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FIGURE 2. The front panel of the PlateGUI MATLAB package. (Image courtesy of
PlateGUI.)
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TABLE 1. THE USER-SPECIFIED OPERATIONAL PARAMETERS OF THE PlateGUI PACKAGE. Operational Parameters
Explanation
Plate length (m)
Length of parallel plate
Plate height (m)
Height (width) of parallel plate
Number of height points
Number of vertical points
Number of length points
Number of horizontal points
Height (m)
Height of observer
Range (m)
Range of observer
Source type
Line source/Gaussian source
Polarization type
Horizontal/vertical
Antenna height (m)
Height of antenna
Frequency (MHz)
Operating frequency
Exit
Close the program
Methods
Mode analysis/ray analysis/FDTD analysis/MoM analysis for line source Mode analysis/PE analysis/FDTD analysis for Gaussian source
■■
wide-angle PE models, since narrowangle models suffer paraxial propagation restriction (i.e., it is valid up to 10–15˚ vertical propagation angles). The FDTD method can also be used in modeling propagation inside a parallel-plate waveguide. This method discretizes the physical environment into small cells by replacing partial derivatives with their finite difference equivalents. It is open form and iterative and therefore suffers in terms of stability. Either a line source
■■
or a Gaussian source can be used in the wave excitation in these models, but special care is essential for the tilted and directional transmitter antenna modeling. Finally, the MoM can be used in propagation modeling inside a parallel-plate waveguide. The MoM discretizes the object under investigation into N pieces, called segments or patches, and constructs an N × N system of equations using the Green’s function of the problem.
FIGURE 3. The electric fields inside a 2-m-long, 1-m-wide waveguide at 2 GHz: horizontal polarization, height of line source 0.3 m, mode analysis with 25 modes, and ray analysis and MoM analysis with six reflections. (Image courtesy of PlateGUI.) 102
THE PlateGUI PACKAGE The PlateGUI package has been developed in MATLAB for the analysis and visualization of EM fields inside parallel-plate waveguides with the aid of analytical and numerical methods. The flowchart of the package and the algorithms used there is given in Figure 1. PlateGUI has been designed in such a way that the user first supplies the input parameters (plate parameters, antenna parameters, and observer position); selects the methods (ray, mode, FDTD, the MoM, and the PE); specifies the number of modes, rays, reflections, and so forth; and then comparatively v isualizes the fields. PlateGUI also warns the user if inappropriate input values are entered. The main executable file of the package is PlateGUI.exe. The front panel, displayed in Figure 2, is mainly divided into two parts. The right part is for plotting horizontal, vertical, and two-dimensional field calculations. The left part is reserved for the input parameters and controls. Table 1 shows the input parameters of the package. The left part of Figure 2 is divided into three sections. The plate parameters are supplied in the top section. The length and height (width) of the plate are in meters; the numbers of points are entered here. The middle section is for the antenna parameters, such as source type, polarization, the height of the source in meters, and the beamwidth and
FIGURE 4. The magnetic fields inside a 2-m-long, 1-m-wide waveguide at 2 GHz: vertical polarization, height of line source 0.3 m, mode analysis with 25 modes, and ray analysis and MoM analysis with six reflections. (Image courtesy of PlateGUI.) august 2017
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Height (m)
Height (m)
1 0.8 0.6 0.4 0.2 0 0.5
1 1.5 Range (m) (a)
2
1 0.8 0.6 0.4 0.2 0
Height (m)
Height (m)
0
0
0.5
1 1.5 Range (m) (c)
2
inside the waveguide. EM fields in the time inside the waveguide are recorded as a movie file in .avi format.
1 0.8 0.6 0.4 0.2 0 0
0.5
1 1.5 Range (m) (b)
NUMERICAL SIMULATIONS WITH PlateGUI
2
1 0.8 0.6 0.4 0.2 0 0
0.5
1 1.5 Range (m) (d)
2
FIGURE 5. The ray paths up to (a) one, (b) two, (c) three, and (d) six reflections.
e levation angles in degrees for the Gaussian source. The position of the observer can be chosen to the right of the plate parameters. The bottom section is related to the analytical and numerical methods. If the user chooses the line-source type, then mode analysis, ray analysis, FDTD analysis, and MoM analysis can be used. If the user chooses the Gaussian-source type, then mode analysis, PE analysis, and FDTD analysis can be used. Additional parameters appear on the bottom of the panel for each method, such as the maximum number of modes and the number of modes for mode analysis, the maximum number of reflections and the number of reflections for ray analysis,
the narrow- and wide-angle propagators for PE analysis, the maximum time for FDTD, and the maximum number of reflections and the number of reflections for MoM analysis. The top right panel of Figure 2 shows the horizontal field profile with respect to the observer height. Two vertical field profiles, at the initial and observer points, are displayed in the bottom-left panels. A threedimensional color field map showing the field strength versus range/height is also plotted in the bottom-right panel. For the sake of simplicity, the FDTD method is used only for the visualization of time variations of the fields
FIGURE 6. The electric fields inside a 2-m-long, 1-m-wide waveguide at 2 GHz: horizontal polarization, height of untitled Gaussian source 0.3 m, beamwidth 20˚, mode analysis with 25 modes, and PE analysis (narrow-angle propagator). (Image courtesy of PlateGUI.) IEEE Antennas & Propagation Magazine
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A few examples created w ith the PlateGUI package are presented in this section, and in all of the examples, a 1-m-wide, 2-m-long waveguide is used. The source height is 0.3 m. Figures 3 and 4 show horizontal and vertical polarizations, respectively, with a line source of 2 GHz. The results of mode analysis, ray analysis, and MoM analysis are compared. The number of propagating modes for the sets of parameters of mode summation is 25. Note that increasing the number of modes (such as to 100 modes) improves the results. Six reflections are used for ray and MoM analysis. A different number of reflections is shown in Figure 5. Figures 6 and 7 show horizontal and vertical polarizations, respectively, with an untilted Gaussian source of 2 GHz. The results of mode and narrow-angle PE analysis are compared. The number of propagating modes for the sets of parameters of mode summation is 25. Six reflections are also used in the MoM analysis, as in the previous example. Figures 8 and 9 show the effect of a 10˚ tilted Gaussian source for narrowand wide-angle PE propagators, respectively. Using a wide-angle propagator improves the PE results compared to the mode analysis.
FIGURE 7. The magnetic fields inside a 2-m-long, 1-m-wide waveguide at 2 GHz: vertical polarization, untilted Gaussian source at 0.3 m, beamwidth = 20˚, mode analysis with 25 modes, PE analysis (narrow-angle propagator). (Image courtesy of PlateGUI.) 103
1 0.8 0.6 0.4 0.2 0
1 0.5
0
0.5
1 1.5 Range (m) (a)
2
0 –0.5 –1
1 0.5
0
0.5
1 1.5 Range (m) (c)
2
0 –0.5 –1
Height (m)
1 0.8 0.6 0.4 0.2 0
Height (m)
Height (m)
Height (m)
FIGURE 8. The electric fields inside a 2-m-long, 1-m-wide waveguide at 3 GHz: horizontal polarization, 10˚ down-tilted Gaussian source at 0.3 m, beamwidth = 30˚, mode analysis with 100 modes, PE analysis (narrow-angle propagator). (Image courtesy of PlateGUI.) 1 0.8 0.6 0.4 0.2 0
1 0.8 0.6 0.4 0.2 0
FIGURE 9. The electric fields inside a 2-m-long, 1-m-wide waveguide at 3 GHz: horizontal polarization, 10˚ down-tilted Gaussian source at 0.3 m, beamwidth = 30˚, mode analysis with 100 modes, PE analysis (wide-angle propagator). (Image courtesy of PlateGUI.) 1 0.5
0
0.5
1 1.5 Range (m) (b)
2
0 –0.5 –1
CONCLUSIONS 1 0.5
0
0.5
1 1.5 Range (m) (d)
2
0 –0.5 –1
1 0.8 0.6 0.4 0.2 0
0
0.5
1 1.5 Range (m) (a)
2
0 –0.5 –1
1 0.5
0
0.5
1 1.5 Range (m) (c)
2
0 –0.5 –1
Height (m)
1 0.5
Height (m)
Height (m)
Height (m)
FIGURE 10. The electric fields inside a 2-m-long, 1-m-wide waveguide at 2 GHz: horizontal polarization, a line source at 0.3 m, and FDTD analysis at (a) 1.03 ns, (b) 3.05 ns, (c) 5.06 ns, and (d) 7.08 ns. 1 0.8 0.6 0.4 0.2 0
1 0.8 0.6 0.4 0.2 0
1 0.5
0
1 0.8 0.6 0.4 0.2 0
0.5
1 1.5 Range (m) (b)
2
0 –0.5 –1
1 0.5
0
0.5
1 1.5 Range (m) (d)
2
0 –0.5 –1
FIGURE 11. The magnetic fields inside a 2-m-long, 1-m-wide waveguide at 2 GHz: vertical polarization, a line source at 0.3 m, and FDTD analysis at (a) 1.03 ns, (b) 3.05 ns, (c) 5.06 ns, and (d) 7.08 ns. 104
The last scenario is the electric and magnetic fields inside a parallel-plate waveguide using FDTD analysis. Figures 10 and 11 show the fields for horizontal and vertical polarizations, respectively.
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A MATLAB-based EM field calculator virtual tool that can be used to compare various models has been developed and described. Wave propagation inside a parallel-plate waveguide with nonpenetrable boundaries was chosen for this purpose. The virtual tool uses analytical (in terms of mode and ray summation) and numerical (FDTD, PE, and MoM) models with different source excitations (i.e., line and Gaussian). This tool can be used in CEM lectures.
AUTHOR INFORMATION Gökhan Apaydin (g.apaydin@gmail .com) is an electrical-electronic engineer with Electromagnetic Consulting, Istanbul, Turkey. His research interests include analytical and numerical methods—finite element method, method of moments, finite difference time doman, and splitstep parabolic equation—in electromagnetics (especially on electromagnetic computation of wave propagation, diffraction modeling, scattering, and related areas). He is a Senior Member of the IEEE. Levent Sevgi (levent.sevgi@okan .edu.tr) is a professor in the Department of Electrical-Electronics Engineering, Engineering Faculty, Okan University, Istanbul, Turkey. He is an associate IEEE Antennas & Propagation Magazine
editor of IEEE Antennas and Propagation Magazine and the writer and editor of the “Testing Ourselves” column (since 2007). He has been involved with complex electromagnetic problems and systems for more than three decades. He is a Fellow of the IEEE.
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Turnstile
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