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Phase of a far-field calculation?
Posted Jun 17, 2016, 12:16 p.m. EDT RF & Microwave Engineering Version 5.1 3 Replies
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COMSOL'ers:
When applying Fraunhofer approximations to field calculations (asymptotic analysis), we ignore small changes in amplitude from the source plane to the observation plane, but we do not ignore changes in phase, as it is much more sensitive to variations. Instead, we expand the exponential phase term and cut off higher-order (non-parabolic) terms in the expansion. To determine the complex field we usually normalize w/r/t the prefactor (usually both magnitude and phase terms as a function of displacement and wavelength).
In this regard, the component far-field amplitude makes sense --> i.e. abs(ewfd.Efarx). My question is, then, is there any value in the value of the phase of Efar --> i.e. arg(ewfd.Efarx)? This explicitly requires a distance to identify the phase, and as I mentioned it is quite sensitive to variation, so it seems we would need a known distance "R" to input.
What I need is to extract phase information from a scatterer in the Fraunhofer region. Currently, given the uncertainty above, this requires me to generate a large air domain above the scatterer and extract the phase using a point probe placed a few wavelengths above along the normal. I would like to reduce the size of the air domain and rely on a far-field calculation, but I do not see how this is possible without specifying a point.
Thanks!
-Bryan
When applying Fraunhofer approximations to field calculations (asymptotic analysis), we ignore small changes in amplitude from the source plane to the observation plane, but we do not ignore changes in phase, as it is much more sensitive to variations. Instead, we expand the exponential phase term and cut off higher-order (non-parabolic) terms in the expansion. To determine the complex field we usually normalize w/r/t the prefactor (usually both magnitude and phase terms as a function of displacement and wavelength).
In this regard, the component far-field amplitude makes sense --> i.e. abs(ewfd.Efarx). My question is, then, is there any value in the value of the phase of Efar --> i.e. arg(ewfd.Efarx)? This explicitly requires a distance to identify the phase, and as I mentioned it is quite sensitive to variation, so it seems we would need a known distance "R" to input.
What I need is to extract phase information from a scatterer in the Fraunhofer region. Currently, given the uncertainty above, this requires me to generate a large air domain above the scatterer and extract the phase using a point probe placed a few wavelengths above along the normal. I would like to reduce the size of the air domain and rely on a far-field calculation, but I do not see how this is possible without specifying a point.
Thanks!
-Bryan
3 Replies Last Post Jun 21, 2016, 3:38 p.m. EDT
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Posted:
8 years ago
Hmm. Well, if you have trouble obtaining meaningful phase values on a virtual sphere using Comsol's formulation of the far-field electric field, you can always try applying the near-field version to specific points (at finite R) of your own choosing, without needing to extend the FE model itself over a large volume. The details of how to do this are contained in my short paper, "Computation of Antenna Radiating Near-Fields," available from the Comsol Model Exchange at:
www.comsol.com/community/exchange/247/
Hope that helps.
www.comsol.com/community/exchange/247/
Hope that helps.
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Posted:
8 years ago
First let me say thank you, Robert, for your reply. My original concern was: what does the phase of the far-field calculation even tell you if you never specify a finite R? And then, of course: if arg(ewfd.Efar) is not useful for accurate far-field phase extraction, what is the most efficient way?
Your paper is quite a helpful contribution to my current solution, which is extending the model to several wavelengths above the radiating aperture and extracting fields in the Fraunhofer region. Your solution directly attacks the hurdle of dealing with large FE volumes, and I shall try it today vs. my solution that ran over the weekend. If I understood it correctly, all I should need to do is create a destination surface at the desired far-field computation point outside the small FE volume of interest containing my aperture. Have you done any comparisons of your solution (using a small FE volume and projecting a finite R) vs. COMSOL's calculation (modeling the entire FE volume which contains R)?
Thank you again, Robert!
-Bryan
Your paper is quite a helpful contribution to my current solution, which is extending the model to several wavelengths above the radiating aperture and extracting fields in the Fraunhofer region. Your solution directly attacks the hurdle of dealing with large FE volumes, and I shall try it today vs. my solution that ran over the weekend. If I understood it correctly, all I should need to do is create a destination surface at the desired far-field computation point outside the small FE volume of interest containing my aperture. Have you done any comparisons of your solution (using a small FE volume and projecting a finite R) vs. COMSOL's calculation (modeling the entire FE volume which contains R)?
Thank you again, Robert!
-Bryan
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Posted:
8 years ago
I'm not sure what to say about the phase. You might want to explore the technical literature concerning the "phase center" of an antenna. The phase center is the geometric center of a virtual (large radius) sphere around the antenna, such that it has a surface of constant phase in the radiated field. Interestingly, not every antenna actually has an unambiguous phase center! So, I suppose that looking at the phase of the far-field could provide you with information about that type of condition.
Regarding the radiating near-field formulation, it is based on the same equations I used decades ago to compute near-fields of various rectangular and conical horn antennas. Back then, this yielded good agreement with experiments, if one was not overly-close to the antenna. Note that there are no reactive near-field terms included. Now, math is math, regardless of the computer and computer language used, so in principle this implementation in Comsol Multiphysics should work just as well. However, I can't speak for much specific validation of it. I've been happy with the results from it and it seems right. There could also, of course, be errors or typos in the expressions that I put into the paper on the Comsol Exchange, but I do try to be careful. That said, if you are going to use this for serious work, you would be wise to run some of your own test/comparison validation cases to build up your confidence in it.
Regarding the radiating near-field formulation, it is based on the same equations I used decades ago to compute near-fields of various rectangular and conical horn antennas. Back then, this yielded good agreement with experiments, if one was not overly-close to the antenna. Note that there are no reactive near-field terms included. Now, math is math, regardless of the computer and computer language used, so in principle this implementation in Comsol Multiphysics should work just as well. However, I can't speak for much specific validation of it. I've been happy with the results from it and it seems right. There could also, of course, be errors or typos in the expressions that I put into the paper on the Comsol Exchange, but I do try to be careful. That said, if you are going to use this for serious work, you would be wise to run some of your own test/comparison validation cases to build up your confidence in it.