电基本振子辐射出的电场 (蓝色) 与磁场 (红色)
电基本振子(Electric Short Dipole)又称电流元,指一段理想高频电流直导线,其长度l远小于波长λ并且其半径r远小于l,同时振子沿线的电流I处处等幅并且同相。这样的电流元可构成现实当中更复杂的天线,因而电基本振子的辐射特性是研究更复杂天线辐射特性的基础。[1]
在球坐标当中,电基本振子在无限大自由空间中场强为[2]
![{\displaystyle E_{r}={\frac {Z\,I_{0}\delta \ell }{2\pi }}\left({\frac {1}{r^{2}}}-{\frac {i}{kr^{3}}}\right)e^{i(\omega t-k\,r)}\,\cos(\theta )}](https://backend.710302.xyz/https/wikimedia.org/api/rest_v1/media/math/render/svg/ab04d1b1a7aa5d2a284c767421dfc80272521d1a)
![{\displaystyle E_{\theta }=i{\frac {Z\,I_{0}\delta \ell }{4\pi }}\left({\frac {k}{r}}-{\frac {i}{r^{2}}}-{\frac {1}{kr^{3}}}\right)e^{i(\omega t-k\,r)}\,\sin(\theta )}](https://backend.710302.xyz/https/wikimedia.org/api/rest_v1/media/math/render/svg/5092ef78235fd3407e7a14e3d740d6fd56682697)
![{\displaystyle H_{\phi }=i{\frac {I_{0}\delta \ell }{4\pi }}\left({\frac {k}{r}}-{\frac {i}{r^{2}}}\right)e^{i(\omega t-k\,r)}\,\sin(\theta )}](https://backend.710302.xyz/https/wikimedia.org/api/rest_v1/media/math/render/svg/411ac30450b99ee5a61fee2e58e524fea73c94fd)
![{\displaystyle E_{\phi }=H_{r}=H_{\theta }=0,}](https://backend.710302.xyz/https/wikimedia.org/api/rest_v1/media/math/render/svg/07abff4477872534bca501da284f6bdecaa813d6)
在近区场坡印廷矢量的均值
电基本振子的远区场表达式为:
![{\displaystyle H_{\phi }=j{\frac {Il}{2\lambda r}}sin\theta e^{-jkr}}](https://backend.710302.xyz/https/wikimedia.org/api/rest_v1/media/math/render/svg/c62687641e552b863b185df1f746039603f4a90f)
![{\displaystyle E_{\theta }=j{\frac {60\pi Il}{\lambda r}}sin\theta e^{-jkr}}](https://backend.710302.xyz/https/wikimedia.org/api/rest_v1/media/math/render/svg/9b9d2f807df2e3e7be6db7c652b1342f994836bb)
![{\displaystyle H_{r}=H_{\theta }=E_{r}=E_{\phi }=0}](https://backend.710302.xyz/https/wikimedia.org/api/rest_v1/media/math/render/svg/70655ffc823236c9c5e4c5fa4684e5a507be4493)
电偶极子向自由空间辐射的总功率为
![{\displaystyle P_{r}=\oint _{S}{\frac {1}{2}}Re[\mathbf {E\times H^{*}} ]\cdot d\mathbf {s} =40\pi ^{2}I^{2}({\frac {l}{\lambda }})^{2}\ W}](https://backend.710302.xyz/https/wikimedia.org/api/rest_v1/media/math/render/svg/76192eeeea79e6becde86168ba3fca6f0026ac3a)
- ^ [1] 宋峥. 天线与电波传播[M]. 2. 西安:西安电子科技大学出版社, 2011.
- ^ Silver, Samuel. Microwave Antenna Theory and Design. 1949: 92–94.