Series-connected rectenna associations are proposed to improve the harvesting performance of conventional rectenna circuits by recovering power from different directions. With an available input power of -20 dBm, post-layout simulations evaluated the total output power of four series-connected rectennas designed in Complementary Metal Oxide Semiconductor Fully Depleted Silicon On Insulator (CMOS FD-SOI) 28 nm technology, to 14 μW at maximum power point (MPP), while the post-layout simulation of a single rectenna yields 5 μW at the same input power level. However, the rectenna association performance may be significantly degraded when dealing with different input power levels among rectennas. Therefore, a passive bypass circuit has been added at the output of the series association to short-circuit the weakest rectenna. The proposed design is cost-effective since there is a negligible silicon penalty and no additional power losses. In the designed four series-connected rectenna association, the total output power is 7 μW at MPP with the bypass circuit when the strongest and the weakest rectennas receive -20 and -35 dBm, respectively. Also, thanks to the bypass circuit, the efficiency of the rectenna association and the ratio of maximum achieved power are improved by, respectively, 10 and 20%.