# Partial Discharge Wideband Full-Band High-Gain Resonant Cavity UHF Sensor Research
## 2 Principle of Antenna
### The Basic Principle of Fabry-Perot Resonant Cavity Antenna  
The Fabry-Perot resonant cavity is a multi-beam optical interferometer that can be used to accurately measure the wavelength and refractive index of light, invented by French physicists [PERSON] and [PERSON] in 1897 [16]. The interferometer consists of two parallel mirrors and the space between them forms a resonant cavity. Under certain conditions, the light rays in the resonant cavity can form a series of beams that interfere with each other [17]. This principle can be used in optical sensors to improve filtering performance and increase gain [18]. Later, research scholars discovered that a similar principle could be applied to the field of antenna sensors, leading to the invention of the Fabry-Perot resonant cavity antenna. In the literature [19], [PERSON] loaded a Fabry-Perot resonant cavity on an LTCC microstrip antenna [19], and the resulting resonant cavity gathers the radiated energy inside the cavity to realize the radiation and reception of the signal at the resonant frequency, which improved the strength of the electromagnetic field and achieved the advantage of high gain at low profile. In the literature [20], [PERSON] designed a partially reflective surface unit structure [20] showing a rising phase, which is loaded above the feed antenna to form a Fabry-Perot resonant cavity antenna, overcoming the narrow band of the conventional Fabry-Perot resonant cavity antenna. The principle of the Fabry-Perot resonant cavity antenna is described in detail below:  
The Fabry-Perot resonant cavity configuration is shown in Figure 2 and consists of a partially reflective cladding, a feed antenna and its floor. Part of the reflective cladding is parallel to the feed antenna at a distance of \(l\), between which multiple reflections of electromagnetic waves occur. The feed antenna and its floor are a fully reflective plate with a reflection coefficient of \(e^{i\varphi_{1}}\), the amplitude of the reflection coefficient is 1, and the phase is \(\varphi_{1}\). The partially reflective cladding is a partially reflective plate with a reflection coefficient of \(pe^{i\varphi_{2}}\), the amplitude of the reflection coefficient is \(p\), and the phase is \(\varphi_{2}\). Assuming no transmission loss of the electromagnetic wave, the amplitude of the transmitted beam 0 is proportional to \(\sqrt{1-p^{2}}\); after one reflection, the amplitude of the transmitted beam 1 is proportional to \(p\sqrt{1-p^{2}}\); after two reflections the amplitude of the transmitted beam 2 is proportional to \(p^{2}\sqrt{1-p^{2}}\). After \(n\) reflections, the superposition of the electric field intensity of all transmitted waves transmitted through the partially reflected layer gives:  
\[E=\sum_{n=0}^{\infty}F(\alpha)E_{0}p^{n}\sqrt{1-p^{2}}e^{i\varphi_{n}} \tag{6}\]  
where \(F(a)\) is the feed antenna radiation direction function, \(E_{0}\) is the maximum radiation field strength, \(\theta_{n}\) is the phase difference between the transmitted wave beam n, and the transmitted wave beam 0  
\[\theta_{n}=n\varphi=n\left[\frac{4\pi}{\lambda}l\cos\alpha-\varphi_{1}-\varphi _{2}\right] \tag{7}\]  
as \(p<1\), we can obtain:  
\[\sum_{n=0}^{\infty}\left(pe^{i\varphi}\right)^{n}=\frac{1}{1-pe^{i\varphi}} \tag{8}\]  
substituting Equation (8) into Equation (6) yields the modal value of the electric field:  
\[|E|=|E_{0}|f(\alpha)\sqrt{\frac{1-p^{2}}{1+p^{2}-2p\cos\varphi}} \tag{9}\]  
substituting Equation (7) into Equation (9) yields the energy density in the \(\alpha\) direction:  
\[S=\frac{1-p^{2}}{1+p^{2}-2p\cos\left(-\varphi_{1}-\varphi_{2}+l\frac{4\pi}{ \lambda}\cos\alpha\right)}f^{2}(a) \tag{10}\]  
Figure 2: Fabry–Perot resonant cavity antenna structure.