## 2 Design and Implementation of On-Line PD Monitoring System
### Partial Discharge Detectors
#### 2.2.2 Ultra-High Frequency Antenna
The results of tests and simulations showed that the highest performance and possibility of relatively easy bandwidth regulation is offered by the modified constructions of a conventional PIFA. It is currently the most popular antenna in the world applied in mobile devices [60; 61; 62]. This is due to its numerous advantages such as compact size compared to monopole antenna, high gain in both vertical and horizontal states of polarization, close to omnidirectional radiation pattern, and low manufacturing cost. Figure 4 presents a schematic diagram of the conventional PIFA, which consists of a ground plane, a rectangular radiating element of length equal to the quarter-wave, feeding pin and shorting plate (or pin) to connect the ground plane with the top patch. Resonant frequency \(f_{r}\) of conventional PIFA may be approximately estimated with the use of Equation (1), in which \(c\) is the speed of light in vacuum, \(\varepsilon_{\textit{eff}}\) is the effective permittivity of the dielectric substrate, \(L_{I}\) and \(L_{2}\) are the width and length of the rectangular radiating element, \(H\) is the thickness of  
Figure 4: Schematic diagram of the conventional planar inverted-F antenna (PIFA). the substrate, and \(W\) is the width of shorting plate, assuming that \(L_{I}>W>0\)[63; 64]. In order to more accurately estimate the resonant frequency of PIFA, some authors propose more complex formulas [65]. \[f_{r}\ =\ \frac{c}{4\sqrt{\varepsilon_{\text{eff}}}(L_{1}+L_{2}+H-W)} \tag{1}\]  
The major limitation of standard PIFA is the narrow bandwidth. Simple methods for widening the bandwidth of PIFA are based on reducing the size of the ground plane and the use of a substrate with the low value of dielectric constant [64]. Another technique is the employment of specially designed slits in front patch [66; 67; 68; 69; 70], ground plane [71], or in both these structures [72; 73; 74]. A more advanced method of bandwidth widening is based on the use of stacked patches, often also equipped in slits [75; 76; 77; 78; 79]. Other tuning techniques are based on varying the position of feeding pin, changing the capacitance value of the shorting plate, or changing the widths of feed and shorting plates [80; 81]. By applying a properly selected chip resistor or chip capacitor load in place of the shorting plate one may reduce the resonant frequency of the antenna [82]. For the needs of the monitoring system, it was decided to apply PIFA construction with the meandered radiating structure loaded with chip resistor [83]. Meandering the radiating patch allows to reduce the dimensions of the conventional PIFA and obtain large gain [84; 85; 86; 87; 88]. In turn, applying the chip resistor causes not only lowering of the resonant frequency but also widens the bandwidth (even several times compared to standard PIFA) [83]. A schematic diagram of a meandered PIFA is presented in Figure 5.  
In the initial stage of designing, the necessity to adjust the antenna to the dielectric window dimensions was taken into account (Figure 2) of internal diameter equal to 15 cm and the need to equip the antenna in a protective housing. Since the gain of PIFA increases as the ground plane size increases [89], it was assumed that the largest possible diameter equaled 14 cm. The remaining dimensions of the prototype meandered PIFA (Table 3) were optimized through iterative simulations performed in CST Microwave Studio 2016 (Dassault Systemes SE, Velizy-Villacoublay, France). The results of the simulation proved that the application of chip-resistor in place of the shorting pin allows to increase the bandwidth (Figure 6), whereas by changing the distance between the patch and ground plane one may regulate the resonant frequency of the antenna (Figure 7). Satisfying results were obtained for chip-resistor with resistance \(R=5.4\)\(\Omega\) and distance \(H=5\) mm, for which the simulated voltage standing wave ratio was VSWR = 1.038 (S\({}_{11}\) = -36.34 dB), resonant frequency \(f_{r}=347\) MHz, and the \(-6\) dB bandwidth was 73 MHz.