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parallel plate transmission line input/characteristic impedance
Posted Jul 9, 2017, 3:51 p.m. EDT 10 Replies
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I am new to COMSOL and I'm trying to model an idealized parallel plate transmission line and determine it's characteristic impedance as well as calculate the input impedance.
In the emw package, I have modeled it as a slab of SiO2 that is w = 100 nm wide, d = 10 nm thick, and L = 20 um long. I then set the upper and lower surfaces (the two 100 nm by 20 um surfaces) to be Perfect Electrical conductors, and I enclosed the entire slab in a box of air, with Scattering Boundary Condition applied to all 6 of the external air surfaces. I then created two user-defined lumped ports (dimensions w x d), one on either end of the transmission line. On one port, I am applying 1 volt across the thickness of the line at f=30 THz (
), with a 
reference impedance. The port at the far end of the line (my load) is set to the same dimensions and has an impedance of with the wave excitation turned off.
Using the dimensions of the SiO2 slab and a relative permittivity of 3.9, the parallel plate transmission line equations predict a characteristic impedance of
. This is the quantity I'm interested in verifying in COMSOL, but there seems to be no way of directly determining it, so I instead use the lumped excitation port impedance (Global evaluation emw.Zport_1) to tell me the input impedance looking down the entire line. This value ends up being 
. I then use the length of the line, the above characteristic and load impedances, and the wavelength of my excitation to compute a theoretical input impedance of 
. Unfortunately, the two results clearly differ greatly.
Is there something wrong with my COMSOL model, perhaps my boundary conditions or the way I'm using the ports? If you could provide any insight as to how I might correctly determine the characteristic and input impedances, I would greatly appreciate it. I have tried varying my line dimensions, wavelength, mesh resolution, port sizes, and changing air from absorbing to PEC and nothing gets me close to the expected input impedance for my line. Thank you!
In the emw package, I have modeled it as a slab of SiO2 that is w = 100 nm wide, d = 10 nm thick, and L = 20 um long. I then set the upper and lower surfaces (the two 100 nm by 20 um surfaces) to be Perfect Electrical conductors, and I enclosed the entire slab in a box of air, with Scattering Boundary Condition applied to all 6 of the external air surfaces. I then created two user-defined lumped ports (dimensions w x d), one on either end of the transmission line. On one port, I am applying 1 volt across the thickness of the line at f=30 THz (
), with a reference impedance. The port at the far end of the line (my load) is set to the same dimensions and has an impedance of with the wave excitation turned off. Using the dimensions of the SiO2 slab and a relative permittivity of 3.9, the parallel plate transmission line equations predict a characteristic impedance of
. This is the quantity I'm interested in verifying in COMSOL, but there seems to be no way of directly determining it, so I instead use the lumped excitation port impedance (Global evaluation emw.Zport_1) to tell me the input impedance looking down the entire line. This value ends up being . I then use the length of the line, the above characteristic and load impedances, and the wavelength of my excitation to compute a theoretical input impedance of . Unfortunately, the two results clearly differ greatly.Is there something wrong with my COMSOL model, perhaps my boundary conditions or the way I'm using the ports? If you could provide any insight as to how I might correctly determine the characteristic and input impedances, I would greatly appreciate it. I have tried varying my line dimensions, wavelength, mesh resolution, port sizes, and changing air from absorbing to PEC and nothing gets me close to the expected input impedance for my line. Thank you!
10 Replies Last Post Jul 10, 2017, 7:56 p.m. EDT
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Posted:
7 years ago
My recommendation: Don't use a lumped port for this. With a lumped port, the code generally assumes you already know the impedance, and that you are specifying things like voltage or current, and that the detailed field distribution in the port region is of minimal interest. But that is NOT your case, since the detailed field distribution at the port is what determines the impedance, Instead, you need to use a "numeric" port. This (when done right) separates the problem into two parts. First, Comsol Multiphysics computes (i.e., numerically solves) for the fields in the port region (a 2D subset of your 3D problem) then applies those fields to the transmission line for the 3D problem. I think if you hunt around you may find an example in the library files. For what it is worth, this trick used to be a lot more difficult to do correctly in older versions of Comsol Multiphysics. In the newer versions, once you set up the port right, you can get the software to set up the solver sequence for you, which is a big help. OK, now I realize that the above notes aren't a detailed step-by-step explanation, but I hope this will at least help you to get going in the right direction. Good luck.
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Posted:
7 years ago
Are you using the free-space lambda in your equation?
That expression only works if you use the guide wavelength, which will be different (by roughly a factor of 1/sqrt(epsilon).
D.W. Greve
DWGreve Consulting
That expression only works if you use the guide wavelength, which will be different (by roughly a factor of 1/sqrt(epsilon).
D.W. Greve
DWGreve Consulting
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Posted:
7 years ago
In the equation I have shown above, yes I am using the free-space lambda of 
. But also in the equation is 
, which already accounts for the wavelength change in SiO2.
. But also in the equation is , which already accounts for the wavelength change in SiO2. Please login with a confirmed email address before reporting spam
Posted:
7 years ago
Updated:
7 years ago
Robert,
Thanks for the reply! I have tried toying with a numerical port but keep getting an error saying "integration lines defining voltage and current are not defined." I will try to pursue this further and find some examples on line if possible.
Thanks for the reply! I have tried toying with a numerical port but keep getting an error saying "integration lines defining voltage and current are not defined." I will try to pursue this further and find some examples on line if possible.
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Posted:
7 years ago
OK a couple more possibilities and a suggestion.
1. Using sqrt (epsilon) is only approximate, as there would be some electric field fringing.
2. Make sure the value for epsilon is correct. Comsol 5.3 has three different things that are similar to SiO2: SiO2, glass(quartz), and silica glass. The permittivity for silica glass is wrong.
The suggestion: draw your geometry in 2D, and use Mode Analysis (only available in 2D). Not Boundary Mode Analysis. See
www.comsol.com/model/finding-the-impedance-of-a-parallel-wire-transmission-line-12403
(Your question made me realize that the way I was doing line impedance calculations in 3D was unnecessarily complex.)
1. Using sqrt (epsilon) is only approximate, as there would be some electric field fringing.
2. Make sure the value for epsilon is correct. Comsol 5.3 has three different things that are similar to SiO2: SiO2, glass(quartz), and silica glass. The permittivity for silica glass is wrong.
The suggestion: draw your geometry in 2D, and use Mode Analysis (only available in 2D). Not Boundary Mode Analysis. See
www.comsol.com/model/finding-the-impedance-of-a-parallel-wire-transmission-line-12403
(Your question made me realize that the way I was doing line impedance calculations in 3D was unnecessarily complex.)
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Posted:
7 years ago
Thank you. The value I'm using for epsilon is 
, which was taken directly from the SiO2 material information in COMSOL, so I know that this is not the issue. I will try to do the 2D mode analysis but then I will still have this problem as I will eventually need to model this as a more complex 3D device.
, which was taken directly from the SiO2 material information in COMSOL, so I know that this is not the issue. I will try to do the 2D mode analysis but then I will still have this problem as I will eventually need to model this as a more complex 3D device. Please login with a confirmed email address before reporting spam
Posted:
7 years ago
I've attached an example of 3D stripline model that you may find helpful. In this case, the substrate is air, but you could certainly modify the model to change that. Also, I have found that integrating to find currents using the local H fields can be more accurate than using Comsol Multiphysics' computed surface current terms. Anyway, see what you think. Good luck.
Attachments:
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Posted:
7 years ago
Robert,
Thank you so much! I will take a look at the file you attached and see if I can work it out for there. I really appreciate it.
Thank you so much! I will take a look at the file you attached and see if I can work it out for there. I really appreciate it.
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Posted:
7 years ago
Did you make this file in version 5.3? Unfortunately I'm running 5.2a and am unable to open the file you attached. Do you know of a way around this issue? Thank you for all of your help!
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Posted:
7 years ago
Yes, I used version 5.3 (I try to always use the latest version). I don't seem to have an easy/fast way to export the file to an earlier version -- it seems I would have to rebuild it mostly from scratch.
If you have a current license/support, you should be able to update your Comsol software to the latest version. I encourage you to do that, if you can.
Meanwhile, although it is not as close a fit to your problem, you may be able to learn something from looking at the Comsol application library file for the "waveguide adapter" in regard to the use of numeric ports. Take a look at it, if you haven't already. Another one (in 2D) in the Comsol library that might help you is the "parallel_wires_impedance" model, which is listed under the "verification examples" in the Application Library.
If you have a current license/support, you should be able to update your Comsol software to the latest version. I encourage you to do that, if you can.
Meanwhile, although it is not as close a fit to your problem, you may be able to learn something from looking at the Comsol application library file for the "waveguide adapter" in regard to the use of numeric ports. Take a look at it, if you haven't already. Another one (in 2D) in the Comsol library that might help you is the "parallel_wires_impedance" model, which is listed under the "verification examples" in the Application Library.