Matching RFIC Wireless Transmitters to Small Loop Antennas

These three quantities can be derived from expressions in antenna theory textbooks [1, 2]. Note that the radiation resistance increases as the fourth power of the ratio of the loop dimension (e.g., radius) to the wavelength, which is the same as the fourth power of the loop dimension times frequency. The loss resistance, arising from the skin effect, only increases as the square root of the frequency. This means that any increase in the size of the loop, or equivalently, any increase in frequency, will increase the radiation efficiency of an electrically small loop significantly. A typical printed circuit board loop, whose dimensions are used to derive representative resistive and reactive values for a small loop, is shown in the drawing of Figure 1. It is roughly rectangular, 25 by 32 mm, with a trace width of 0.9 mm. These dimensions lead to the following values for the three quantities above at 315 MHz.