## 3 Archimedean Spiral Antenna
### Design and Simulation  
Miniaturization plays an important role in the design of the harvesting element. Thus, the dimensions of the Archimedean spiral can be reduced without degrading the operation of the antenna. Multiple miniaturization techniques have been studied to date. The most common ones try to modify either the feed line [18] or the ground plane [19] in the antenna. Furthermore, some newer and more complex techniques use fractal geometries (Koch curve) [20] to increase the electrical length of the antenna. In our design (Figure 3), we simply propose extending the arms of the spiral in a straight line to the end of the antenna. The studies carried out in [11] demonstrate that it is preferable to put an impedance step in the center of the arm extension. Thus, current reflections are softened, and a higher bandwidth can be reached. Some researches [5; 9] have pointed out that the surface current distribution over the Archimedean spiral opens to the end of the antenna at the lowest frequencies and moves to its center at the highest operation frequencies. This fact is visualized in Figure 4. This particular current distribution is frequently used as a rule of thumb in order to initially estimate dimensions of the antenna [9]. The number of turns in the spiral, \(N\), is directly related with the lower cutoff frequency. The higher \(N\) is, the lower the lower cutoff frequency, as the antenna is bigger. On the other hand, the inner radius \(r_{1}\) mainly  
Figure 3: Archimedean spiral antenna. fixes the upper cutoff frequency. The antenna must operate from 400 MHz to up to 5 GHz, in order to capture all frequency bands of interest. Thus, the number of turns \(N\) and the inner radius \(r_{1}\) are chosen to be \(N=6\) and \(r_{1}=1.20\) mm, so the antenna has dimensions of 20.72 cm \(\times\) 19.77 cm. A low-cost FR4 substrate (\(\epsilon_{r}\) = 4.7, \(\tan\delta\) = 0.014 @1 MHz) is used to give mechanical rigidity to the structure and to ease the subsequent placement of a rectifier circuit. The design of a theoretically infinite self-complementary Archimedean spiral (the metallic strip width, \(w\), is equal to the separation between two adjacent strips, \(s\)) ensures that the antenna impedance is constant along the frequency [15]. Its value is calculated according to the Babinet's principle [9] and results in 188 \(\Omega\). Since the size of the antenna cannot be infinite in practice, the values of \(w\) and \(s\) play an important role in controlling the bandwidth of the antenna. An optimization process is carried in commercial software CST Microwave Studio to determine the value of the strip width. For a value of \(w=s=3.9\) mm, the antenna is perfectly matched from 350 MHz to 16 GHz, as Figure 5 shows. A ripple is observed at frequencies below 1.5 GHz, since the antenna becomes electrically short and the impedance starts to move from its constant value of 188 \(\Omega\). However, note that the ripple is mostly below \(-15\) dB. This implies a minimal variation of the impedance, which stands out in Figure 5 due to the decibel scale in the \(y\) axis. Figure 6 shows the farfield radiation pattern at 830 MHz of the miniaturized Archimedean spiral. The antenna presents an omnidirectional radiation pattern, as no ground plane is used. It radiates perpendicularly to the plane of the antenna, with two opposite symmetrical main lobes. The omnidirectional pattern is of great usefulness in RF energy harvesting, since we do not know a priori the direction of arrival of the incoming signals. On the other hand, directional antennas [21] should be used if the location of the main radiating source is known. Figure 6 reveals that the antenna efficiency  
Figure 4: Current distribution over the Archimedean spiral antenna at 0.35 GHz (**a**) and 10 GHz (**b**). Figure 5: Measured and simulated reflection coefficient (with respect to 188 \(\Omega\)) and an inset that zooms the 800–900 MHz band. is quite elevated, at 88%. This way, we ensure the antenna does not waste part of the incoming energy.