FreddyOfMaule

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I hope you enjoy editing here and being a Wikipedian! Again, welcome! Constant314 (talk) 20:54, 13 January 2023 (UTC)

Loop Antenna

Copied from Talk:Loop antenna

Both articles use "electromagnetic field" to designate an electric field and a magnetic field which satisfy Maxwell's equations, and define a decomposition of an arbitrary incident time-harmonic electromagnetic field ${\mathcal {F}}_{i}=(\mathbf {E} _{i},\mathbf {H} _{i})$ into four elementary time-harmonic electromagnetic fields ${\mathcal {F}}_{A}=(\mathbf {E} _{A},\mathbf {H} _{A})$, ${\mathcal {F}}_{B}=(\mathbf {E} _{B},\mathbf {H} _{B})$, ${\mathcal {F}}_{C}=(\mathbf {E} _{C},\mathbf {H} _{C})$ and ${\mathcal {F}}_{D}=(\mathbf {E} _{D},\mathbf {H} _{D})$. The important point is that each of the elementary time-harmonic electromagnetic fields could exist independently of the others. ${\mathcal {F}}_{A}$ is the mirror-symmetric part of the transverse electric component of ${\mathcal {F}}_{i}$, ${\mathcal {F}}_{B}$ is the mirror-symmetric part of the transverse magnetic component of ${\mathcal {F}}_{i}$, ${\mathcal {F}}_{C}$ is the mirror-antisymmetric part of the transverse electric component of ${\mathcal {F}}_{i}$, and ${\mathcal {F}}_{D}$ is the mirror-antisymmetric part of the transverse magnetic component of ${\mathcal {F}}_{i}$. The decomposition is the basis of formula (70) of the new paper that gives the open-circuit voltage of an arbitrary planar wire loop antenna used for reception as a function of only $\mathbf {H} _{A}$, $\mathbf {E} _{A}$ and $\mathbf {E} _{B}$. This formula is applicable to any planar wire antenna (circular, square, polyhedral, etc), any incident field configuration, and valid at any frequency at which the thin wire approximation applies. It is possible, especially at low frequencies, to consider that ${\mathcal {F}}_{A}$ causes the intended response of the antenna, while ${\mathcal {F}}_{B}$ may cause an unwanted response. In formula (70) of the new paper, the effect of ${\mathcal {F}}_{A}$ is subdivided into a surface integral of $\mathbf {H} _{A}$, which may be viewed as the intended response of the antenna, and a line integral of $\mathbf {E} _{A}$, which can be viewed as a correction term for the gap width and the nonuniformity of the high-frequency current distribution, since this line integral vanishes if the current is uniform over the integration path. ${\mathcal {F}}_{C}$ and ${\mathcal {F}}_{D}$ have no effect on the antenna. This analysis explains the characteristics and limitations of a planar wire loop antenna used as a measuring antenna or as a direction finder, and is an accurate answer to the "receiving predominantly the magnetic component of the electromagnetic wave" discussion.

Hi Fred, that is exactly what your paper said, but my old brain isn't as flexible as it used to be. I don't absorb large dumps of information like I used to. I would like to understand what it says. With your indulgence I would like to lead off with a few questions that can be mostly answered with a yes or no. These may sound trivial, but I would like to be sure we agree on the basics and terminology etc., so we don't waste time discussing the meaning of words. So here is the first few questions:

• Does your paper assume that the incident field is a propagating plane wave, or is it more complicated than that?
• For convenience can be agree on a system of units where E and H have the same units and the permittivity and permeability of free space are unity? That makes the discussion a whole lot easier since we write E+H without fussing with conversion constants. For those who doubt, this is accomplished by strategically placing the constant c (the speed of light) a few places into Maxwell's equations and the other equations of EM.
• Do we agree that the electromagnetic field at a point can be represented as a set of six coordinates, three of which are designated as the $E_{i}$ or the electric field and three or which are designated as the $H_{i}$ or the magnetic field?
• Assuming that, do we further agree that if there are two observers in the same inertia reference frame who agree on the axis system, ground potential, units, Maxwell's equations and the other laws of electromagnetics will agree on those six numbers? In other words, will two observers sitting side by side and measuring the EM field at the same point and time get the same results for $E_{i}$ and $H_{i}$ even though they use different methods, providing they made no mistakes (ignoring instrument noise)?
• Getting that far, you represent $(E_{i},H_{i})$ as a linear combination of four fields $(E_{A},H_{A})$, $(E_{B},H_{B})$, $(E_{C},H_{C})$ and $(E_{D},H_{D})$. Do we agree that in general, none of $E_{A},H_{A},E_{B},H_{B},E_{C},H_{C},E_{D},H_{D}$ is the magnetic field, or $H_{i}$ or a simple scalar multiple of $H_{i}$?
• Assuming we agree up to here, you we agree that $H_{A}$ must be expressible as a linear combination of $E_{i}$ and $H_{i}$? I'll stop here because I think that there might be some discussion at this point.

Constant314 (talk) 22:05, 13 January 2023 (UTC)

@Constant314:@Evemens: Before answering your questions, please allow me to say that I welcome questions and discussions, and that you do not need to worry too much about the validity of the theory since the "old paper" was peer-reviewed and published by the IEEE, and the "new paper" is only an improved, expanded and open-access version of the old one.

Regarding your first question: As said in the introduction of the purpose of the paper is "to investigate some general properties of a planar wire loop antenna (which need neither be electrically small, nor circular) used for receiving an incident electromagnetic field (which need not be a uniform plane wave), to better understand its characteristics and limitations as a measuring antenna or as a direction finder".

Regarding your questions 2, 3 and 4: yes, but you must keep in mind that, as said in the introduction of the new paper "electromagnetic field" designates the ordered pair ${\mathcal {F}}=(\mathbf {E} ,\mathbf {H} )$ of an electric field $\mathbf {E}$ and a magnetic field $\mathbf {H}$ which satisfy Maxwell's equations in a specified region. In the case of the incident electromagnetic field ${\mathcal {F}}_{i}$, this region is homogeneous and without field sources, since ${\mathcal {F}}_{i}$ is produced by some external field source, in the absence of the loop antenna. In this context, ${\mathcal {F}}_{i}$ is completely defined by $\mathbf {E} _{i}$ or $\mathbf {H} _{i}$, because we are considering a region in which we can use Maxwell's equations, at a nonzero frequency. In your questions you consider that ${\mathcal {F}}_{i}$ at a given point in space is given by 6 scalars. This is correct. But, in the region that we are considering, you only need the distribution of $\mathbf {E} _{i}$ or the distribution of $\mathbf {H} _{i}$, that is 3 scalar distributions.

Regarding your question 5, the computation of $\mathbf {H} _{A}$ in the plane of the loop antenna is very simple, because it is given by equation (63) of the new paper. Elsewhere in the region, the computation of $\mathbf {H} _{A}$ is much more complex. The computation of ${\mathcal {F}}_{A}$, ${\mathcal {F}}_{B}$, ${\mathcal {F}}_{C}$ and ${\mathcal {F}}_{D}$ is treaded in Section VIII of the new paper for the general case, and in Section VI of the new paper for the (much simpler) special case where ${\mathcal {F}}_{i}$ is a plane wave.

In the region that we are considering, wondering if the loop antenna "receives predominantly the magnetic component of the electromagnetic wave" or not makes no sense, because the distribution of $\mathbf {H} _{i}$ completely determines the distribution $\mathbf {E} _{i}$ (and vice-cersa). In contrast, the electromagnetic fields ${\mathcal {F}}_{A}$, ${\mathcal {F}}_{B}$, ${\mathcal {F}}_{C}$ and ${\mathcal {F}}_{D}$ are independent. This is why we can meaningfully express our conclusion using these electromagnetic fields. However, equations (63) and (70) of the new paper tell us that ${\mathcal {F}}_{A}$, which comprises a magnetic field and the associated electric field, somehow plays the role of the "magnetic component" in your "receiving predominantly the magnetic component of the electromagnetic wave" discussion. FreddyOfMaule (talk) 09:35, 14 January 2023 (UTC)

@FreddyOfMaule:@Constant314: O.K. FreddyOfMaule, I have looked at the article according to which the open circuit voltage of the loop antenna is

$e=e_{AH}+e_{AE}+e_{BE}$

where $e_{AH}$ corresponds to the surface integral of $\mathbf {H} _{A}$ in equation (70), $e_{AE}$ corresponds to the contribution of $\mathbf {E} _{A}$ to the line integral in equation (70), and $e_{BE}$ corresponds to the contribution of $\mathbf {E} _{B}$ to the line integral in equation (70). I agree that "receives predominantly the magnetic component of the electromagnetic wave" does not make much sense, as you explained. We can nevertheless wonder if the loop antenna can be used to measure $e_{AH}$, which represents an average value of the $z$ component $\mathbf {H} _{A}\cdot \mathbf {u} _{z}$ of $\mathbf {H} _{A}$. The article also provides an answer to this question (see the conclusion of the article), because $e_{AE}+e_{BE}$ can in this context be viewed as a measurement error, in which $e_{AE}$ is caused by ${\mathcal {F}}_{A}$ and therefore connected to $e_{AH}$, and $e_{BE}$ is caused by ${\mathcal {F}}_{B}$ and therefore independent from $e_{AH}$. Evemens (talk) 12:57, 22 January 2023 (UTC)