## 2 Materials and Methods
### Antenna II  
The structure of this antenna is based on the meander geometry. In this design, similar to the previous design, the method of adding vertices and bending points to the path of the antenna is utilized. However, there is a significant difference in the implementation of this idea compared to the previous design; in this method, periodic units with an odd number of lines are used to reduce the occupied area by the antenna. As seen in Figure 1c, each periodic cell has three current paths; two forward-going paths and one backward-going path, which practically increases the effective length of the antenna three times in the same  
Figure 1: Geometry of Antenna I based on Hilbert design (**a**) top view, (**b**) side view; Antenna II based on the meandered structure (**c**) top view, (**d**) side view; Antenna III based on so called comb structure (**e**) top view, (**f**) side view; and (**g**) Side view of implanted antenna inside multi-layer tissue model.  
occupied area, with a minimal negative effect on the antenna's radiation pattern and gain. This idea can be expanded to higher numbers of current paths in each periodic unit cell. However, it should be noted that the number of the current paths in each unit cell needs to be an odd number because when the forward-going and backward-going current paths with opposite directions are placed close to each other on the antenna's structure, they can cancel each other's radiation and decrease the gain. Therefore, by having an odd number of current paths in each unit cell, we will have one complete effective radiating current path, which has a minimal effect on the radiation and gain but the required area for the antenna is considerably decreased. Finally, the number of the antenna's main branches, which is also periodic, needs to be an odd number as well for similar radiation consideration. As you can see in Figure 1, the number of main branches is 5 in Antenna II and 3 in Antenna I for this reason. Furthermore, the reason that Antenna II has more major current branches compared to Antenna I is that the substrate's relative dielectric constant is 10.2 in Antenna I and 3 in Antenna II. Therefore, Antenna I needs less length to have the effective length of a quarter wavelength (\(\lambda/4\)) due to the higher dielectric constant of its substrate. It should also be noted that, in the design of Antenna II, having a lower substrate dielectric constant and a thicker substrate thickness can reduce the effective capacitance to the ground and consequently achieve a better radiation gain and bandwidth. At the end, similar to the previous design, after the main body and dimensions of the antenna are determined for 400 MHz resonance frequency, other branches are added to some of the high-current nodes to create quarter-wavelength current paths to obtain higher resonance frequencies at 2.4 GHZ and 5.7 GHz bands. Consequently, by using the T-shape branches, three resonant frequencies can be tuned almost independently. The inverted F method is also incorporated to tune the input impedance by changing the input port location. The use of periodic unit cells in this design helped to miniaturize the structure by approximately 40% and to reduce the dimensions of the antenna to 3.04 mm \(\times\) 10 mm \(\times\) 17.25 mm.