## 1 Introduction  
In recent years, novel medical devices, such as wearables and patches, have been receiving a lot of attention in the field of biomedical research and the healthcare industry, providing solutions to a host of applications. Especially, the current global COVID-19 pandemic has led to a critical demand for person-centered healthcare instead of the conventional hospital-centered manner to reduce unnecessary contact as well as to relieve the burden on the healthcare system. The possibility of collecting vital data from a body and reprogramming in-body sets through wireless communications made implantable devices unique. Implantable antennas have been discussed since 2004, and they have reduced the need for further surgeries [1, 2, 3, 4]. These wireless implantable products are widely used for clinical diagnosis and treatment applications, such as implantable medicine, nerve stimulation, and reprogramming of pacemakers or drug delivery, without the need for multiple surgeries [5, 6, 7]. To design implantable antennas, many parameters should be considered, including specific absorption rate (SAR) [8], dimension limits, biocompatibility, and sufficient bandwidth. For the safety of the human body, the maximum power transmitted by the implantable antenna should not exceed certain levels that are imposed by regulations to avoid adverse health effects by electromagnetic emissions. For this purpose, the IEEE C95.1-1999 standard restricts specific absorption rate (SAR) averaged over 1 g of tissue to be less than 1.6 W/kg [8]. SAR is primarily dominated by electric fields in the tissue, and it is given by the following formula:  
\[\text{SAR}=\int\frac{\sigma(r)|E(r)|^{2}}{\rho(r)}dr \tag{1}\]  
where \(\sigma(r)\) is the conductivity of the tissue, \(\rho(r)\) is the mass density of the tissue, and \(E(r)\) is the rms electric field. Therefore, in the design of implantable antenna, the maximum averaged E-field in the tissue should be kept low, while increasing BW, miniaturizing the dimensions, and improving other parameters. To determine the maximum allowable input power for an implantable antenna, maximum SAR averaged over 1 g of tissue is typically calculated first for 1 W of input power to the antenna and then maximum allowable input power is calculated to satisfy the maximum SAR of 1.6 W/kg limit in the human body. Consequently, implantable antennas with a lower SAR can benefit from using a higher allowable input power. Implantable antennas also need to be biocompatible with the host body to ensure patient safety and to also prevent rejection of the implant. Specifically, the human body is conductive, and a short-circuit can be caused if the implantable antenna is not properly isolated from the human body. There are three methods commonly used to approach biocompatibility in implantable antennas: (1) Use of biocompatible substrate or superstrate, which is fabricated in the antenna's structure; and (2) encapsulation, which is achieved by covering the antenna in an insulating dielectric material with low loss. For each of these methods, the radiation pattern, SAR, BW, gain, and other parameters of the antenna need to be studied after the addition of the biocompatible material to ensure that performance metrics are met [9]. Antennas' performance parameters are strongly related to the dimension of the antenna [10; 11; 12]. The physical dimension of the antenna determines the current distribution over the antenna's structure and consequently affects radiation pattern, input impedance, and bandwidth. In order to have appropriate current distribution with constructive radiation and a good performance, the antenna usually needs to be at resonance and has its size comparable to the wavelength or quarter wavelength, which means the implantable antennas need to be quite large at MICS (402-405 MHz) and ISM (902-928 MHz, 2.4-2.4835 GHz, and 5.725-5.825 GHz) bands.