Metal Waveguide¶
Problem Description¶
A waveguide is a key component of microwave devices. This example shows a standard WG-340 microwave waveguide operating at \(\nu\)=2.5 GHz ( \(\lambda_0\)=12 cm). The sides are modeled as perfect electric conductors and the waveguide widths are wx = 8.636 cm, wy = wx/2.
Input File Features¶
The simulation setup consists of a rectangular waveguide created as a GridBoundary and set to an impedance of unity. The waveguide edges have perfect electric conductor boundary conditions, which are the default conditions when none are specified in the EmField block. The solver employs the Dey-Mittra version of the finite-difference time-domain algorithm [1].
The input file employs a unidirectional wave launcher, perfectly matched layers, power diagnostics, and feedback histories to launch a specified power.
Unidirectional wave launcher: The superposition of two closely-spaced sources with an appropriate phase can result in a wave propagating in one direction from the source pair. The following are needed to employ this method:
- The spatial profile of the source must match the propagating mode. For this example, this corresponds to factor of cos(πx/wx) in the function drive(x,y,z,t,phase).
- The wavenumber kz of the propagating mode is needed to properly set the phase difference between the two sources. Generally speaking, kz = ±(\(\omega/c)*sqrt(1-(\omega_{co}/\omega)^2\)). The phase difference d\(\phi\) is the product of the wavenumber kz and the spatial separation of the two sources.
In this example, the two sources are separated by one cell in z, a distance DZ apart. One plane gets a temporal factor of sin(\(\omega\)t) while the other plane gets a temporal factor of -sin(\(\omega\)t-kz*DZ). There is also a ramp function, which gradually increases the source intensity so as to create a source with a narrow spectrum. [2]
Perfectly-matched layers: See the section on applyPML in Using Macros section of the Vorpal Reference Manual.
Power diagnostics: The history blocks at the end of the input file allow the user to characterize the performance of the waveguide. The history named “forwardPower” records the integral Poynting vector through a cross-section of the waveguide a few cells after the source. Similarly, the history named “reflectedPower” measures the same quantity traveling in the -z direction behind the source. In this case, the diagnostic characterizes the unidirectional wave launcher. In more complex cases, such as if the width of the waveguide changes, this diagnostic would measure reflected power.
Junction of waveguides with different widths: The input file allows the user to model a junction between waveguides of different widths in the y-dimension. For example, that of a half-height to full-height WR-340 waveguide.
Running the Simulation¶
Start VorpalComposer and select File -> Clone Example. Highlight Solving Classical Physics Problems and then select Next. Highlight Wave Guide Metal and then select Choose. Create a new folder and then select Choose.
Alternatively, save the VORPAL input file, waveguideMetal.pre, and open in VorpalComposer.
The file should be displayed in the right pane of the Setup window. Click on the Save and Process Setup button in the lower right corner. Proceed to the run window as instructed. To run the file, click on the Run button in the lower left corner of the window. You can see the real time output of the run in the right pane.
Viewing the Output¶
Once instructed after the run has completed, proceed to the Visualize window to view the results. Load in the data files as instructed.
To view the electric field, switch to the Field Analysis tab in the Controls pane. From the Field drop down menu, choose the desired component of the ElecField.
Results¶
The figure below shows the forward and reflected power through planes defined by the History blocks in the .pre file. The forward power is measured at a plane two cells in front of the field source, while the reflected power is measured three cells behind it. Note the ramp-up time, which is specified in the .pre file as five periods, or 2 ns. Increasing this ramp time would narrow the spectrum allow the perfectly-matched layer to be more effective.
Forward and reflected power through planes defined by the History blocks in the .pre file.
The next figure shows the y-component of the electric field at the end of the simulation.
Left: Contour plot of Ey as a function of x (horizontal) and z (vertical). Right: Contour plot of Ey as a function of x (horizontal) and y (vertical) at a position z=0.8 inside the waveguide.
References¶
[1] C. Nieter, John R. Cary, Gregory R. Werner, David N. Smithe, and Peter H. Stoltz. 2009. Application of Dey-Mittra conformal boundary algorithm to 3D electromagnetic modeling. J. Comput. Phys. 228, 21 (November 2009), 7902-7916. DOI=10.1016/j.jcp.2009.07.025 http://dx.doi.org/10.1016/j.jcp.2009.07.025
[2] D.N. Smith, “Full-Field/Scattered-Field Formulation Containing a Dielectric Interface,” The Open Plasma Physics Journal, vol. 3, issue 2, pp. 60-72, 2010.
