VizEM Application Note
Simulation of 2D Microwave Fields in a L-bent Waveguide Using TimeDomain Electromagnetics Wave SolverThis application note illustrates the transient development of microwave field in an air-filled
waveguide with an L-bend geometric feature. The Time-Domain Electromagnetic Wave Solver Moduleof the VizEM Electromagnetics Modeling Software Package developed by Esgee Technologies Inc. is usedfor this problem.
The 2D planar waveguide geometry and thecomputational mesh used for the simulations of
this problem are shown in Figure 1.
Thewaveguide is 100 cm long in the horizontaldirection (x-direction) and 55 cm in the vertical (ydirection). The waveguide channel width is 10 cm
in along the horizontal length and 18 cm along thevertical direction. The geometry comprises a wave
inlet to the right and perfect electric conducting
Figure 1: Geometry and mesh for 2Dside walls along the length of the waveguide. The
waveguide with an L-bend.
waveguide is terminated with a perfect conductor.
The computational mesh has approximately 6,900
cells and comprises a single sub-domain for the wave propagation. The maximum of the mesh size isdetermined by the frequency of the microwave. For this particular simulation, the drive frequency is 1.5
GHz with in a vacuum wavelength of about 20 cm. The mesh resolution is such that about 40 mesh cells(5 mm length) resolve a single wavelength. It is important to note that the problem geometry does notaccommodate a perfect integer number of wave lengths. Hence a true standing wave pattern at thedrive frequency of 1.5 GHz is notexpected for this problem.
For the time-domain solver atime-step of 10-12 sec is used.
Thiscorresponds
toanapproximate CFL number of 0.3
for the time-step.
Thesimulation is run to a final timeof 84 ns.
A wave is launched from theright inlet boundary with a nonzero wave field component inFigure 2: Snapshot of the wave field at 0.6 ns after being
launched at the waveguide inlet at the right.

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the y-direction. The wave travels down the waveguide (in the -x
direction) and negotiates the L-bend and further propagates up
the waveguide in the +y direction. Finally the wave interacts
with the perfect electric conductor termination and is reflectedback down the waveguide to form a standing wave in thewaveguide. As mentioned above the geometry is such that astationary (steady) standing wave can never be achieved in thisgeometry. Figure 2 shows a snapshot of the wave at 0.6 ns
after the wave is launched at the inlet (the initial conditions
being a wave-free domain). The wavelength is observed to beabout 20 cm and is exactly the vacuum wavelength for the 1.5
GHz excitation. At a perfect electric conducting wall thetangential component of the wave field is zero while the normalcomponent is non-zero. This feature is clearly seen in the wave
at this time.

6.6 ns7.92 ns

13.53 ns

Figure 3 shows the transient development of the wave fieldat various times after the wave is launched at the inlet. At 6.6
ns the wave has reflected off the termination boundary andformed a standing wave pattern within the wave guide. Notethat the perfect conducting waveguide wall in the verticalsection of the waveguide dictates that the y-component of thewave field is zero, which results in a wave pattern that looks
different from the horizontal section of the waveguide.

34.32 ns

40.26 ns

As seen in Figure 3, the amplitude of the standing wave
grows in time until about 13 ns following which the amplitudedecreases to reach a minimum at about 60 ns. After 60 ns theamplitude of the standing wave starts increasing again and thepattern repeats itself. Essentially the transient snapshots inFigure 3 show the occurrence of a lower frequency modulationof the standing wave indicating that a stationary (steady)standing wave is not established in this geometry as mentioned
earlier.
This problem demonstrates the importance of using a timeaccurate (time-domain) simulation of the electromagnetic wave
phenomena and ability to capture higher and lower harmonictransients that are not resolved by a frequency-domain solution.

61.05 ns

66 ns

82.5 ns

Figure 3: Development ofstanding wave pattern andoccurrence of a low frequency
modulation of the standing wave
in the waveguide.

The VizEM software package provides a very robust
environment to solve such problems with quick turnaround.
The VizEM software is available through the Overviz framework.
This framework features an easy-to-use interface that provides utilities for problem set-up, problem
solution, and post-processing of the solution. Once a mesh is available, the problem discussed in thisCopyright © Esgee Technologies Inc.

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VizEM version 1.8 (Feb 2012)note can be set-up within a matter of a few minutes. The Overviz framework provides “intelligent”
default options that the user can trust and use in the absence of additional information.
The different modules within the VizEM software package are used seamlessly within the othersoftware packages offered by Esgee Technologies. For example the Time-Domain Electromagnetic Wave
Solver Module used in the above problem can be called by the VizGlow Plasma Modeling Software
Package to solved coupled electromagnetic wave—plasma problems, such as in high-frequency
capacitively coupled plasma (CCP) reactors. Examples of such coupled problems are discussed in other
Application Notes.
For further information on this application note or details about the VizEM and other software
packages you may contact us atEsgee Technologies Inc.
14, North PeakAustin, Texas 78746, USA
info@esgeetech.com
www.esgeetech.com

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VizEM version 1.8 (Feb 2012)