Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.10408 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866929629742235648 |
|---|---|
| author | Salazar, Robert Bayona-Roa, Camilo |
| author_facet | Salazar, Robert Bayona-Roa, Camilo |
| contents | In this paper, we explore classical electromagnetic radiation using a dual four-dimensional potential $Θ^μ$ approach. Our focus is on the Planar Dipole Blade Antenna (PDBA), a system consisting of two flat conductive regions on the $xy$-plane, separated by a gap $\mathcal{G}$, with alternating potentials applied to the conductors. This method emphasizes the use of the scalar magnetic potential $Ψ(\boldsymbol{r},t)$ and the electric vector potential $\boldsymbolΘ$, which generates the electric field $\boldsymbol{E}(\boldsymbol{r},t)=\nabla\times\boldsymbolΘ(\boldsymbol{r},t)$ in free space. These potentials replace the standard magnetic vector potential $\boldsymbol{A}$ and the scalar electric potential $\boldsymbolΦ$ in our analysis. For harmonic radiation, the electromagnetic field can be expressed in terms of the electric vector potential $\boldsymbolΘ(\boldsymbol{r},t)$. We derive a corresponding retarded vector potential for $\boldsymbolΘ$ in terms of a two-dimensional vector field $\boldsymbol{\mathcal{W}}(\boldsymbol{r},t)$, which flows through the gap region $\mathcal{G}$. This dual analytical approach yields mathematically equivalent expressions for modeling Planar Blade Antennas, analogous to those used for ribbons in the region $\mathcal{G}$, simplifying the mathematical problem. In the gapless limit, this approach reduces the two-dimensional radiator (PDBA) to a one-dimensional wire-loop-like antenna, significantly simplifying the problem's dimensionality. This leads to a dual version of Jefimenko's equations for the electric field, where $\boldsymbol{\mathcal{W}}$ behaves like a surface current in the gap region and satisfies a continuity condition. To demonstrate the utility of this approach, we provide an analytical solution for a PDBA with a thin annular gap at low frequency. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_10408 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Modeling of Electromagnetic Radiation using a Dual Four-Potential Representation: From Dipole Blade Radiators to Ribbon Loop-like Antennas Salazar, Robert Bayona-Roa, Camilo Classical Physics In this paper, we explore classical electromagnetic radiation using a dual four-dimensional potential $Θ^μ$ approach. Our focus is on the Planar Dipole Blade Antenna (PDBA), a system consisting of two flat conductive regions on the $xy$-plane, separated by a gap $\mathcal{G}$, with alternating potentials applied to the conductors. This method emphasizes the use of the scalar magnetic potential $Ψ(\boldsymbol{r},t)$ and the electric vector potential $\boldsymbolΘ$, which generates the electric field $\boldsymbol{E}(\boldsymbol{r},t)=\nabla\times\boldsymbolΘ(\boldsymbol{r},t)$ in free space. These potentials replace the standard magnetic vector potential $\boldsymbol{A}$ and the scalar electric potential $\boldsymbolΦ$ in our analysis. For harmonic radiation, the electromagnetic field can be expressed in terms of the electric vector potential $\boldsymbolΘ(\boldsymbol{r},t)$. We derive a corresponding retarded vector potential for $\boldsymbolΘ$ in terms of a two-dimensional vector field $\boldsymbol{\mathcal{W}}(\boldsymbol{r},t)$, which flows through the gap region $\mathcal{G}$. This dual analytical approach yields mathematically equivalent expressions for modeling Planar Blade Antennas, analogous to those used for ribbons in the region $\mathcal{G}$, simplifying the mathematical problem. In the gapless limit, this approach reduces the two-dimensional radiator (PDBA) to a one-dimensional wire-loop-like antenna, significantly simplifying the problem's dimensionality. This leads to a dual version of Jefimenko's equations for the electric field, where $\boldsymbol{\mathcal{W}}$ behaves like a surface current in the gap region and satisfies a continuity condition. To demonstrate the utility of this approach, we provide an analytical solution for a PDBA with a thin annular gap at low frequency. |
| title | Modeling of Electromagnetic Radiation using a Dual Four-Potential Representation: From Dipole Blade Radiators to Ribbon Loop-like Antennas |
| topic | Classical Physics |
| url | https://arxiv.org/abs/2412.10408 |