### I. Introduction

### II. Antenna Design and Operating Mechanism

*ɛ*

*= 4.4, tanδ = 0.02) with 1 mm thickness is used as a substrate material. Two C-shaped ground plane sizes are considered. The smaller C-shaped ground plane is 30 mm × 50 mm in size with a 15 mm × 20 mm empty space at the right edge. The larger C-shaped ground plane is 48 mm × 80 mm in size with a 24 mm × 32 mm empty space at the right edge. The geometries of the GradiAnt and the ground planes are shown in Fig. 1. The thickness of the patterns is 0.5 mm. Two GradiAnt locations on the ground plane are evaluated using the characteristic modes of the ground planes. One of the locations (P1) is the middle of the right edge of the ground plane, as shown in Fig. 1(a), and the other location (P2) is the middle of the left edge of the ground plane, as shown in Fig. 1(b).*

_{r}*∫∫∫*(

*E*

*·*

_{i}*J*

*) is the coupling between the impressed field*

_{n}*E*

*and modal current*

_{i}*J*

*, and*

_{n}*λ*

*is the eigenvalue associated with the*

_{n}*n*

^{th}characteristic current mode.

*λ*

*is closely related to the resonance frequency and the radiation performance. The coupling becomes maximum at resonance, when*

_{n}*λ*

*approaches zero, as the denominator term becomes the smallest. According to Eq. (1), maximum coupling will be achieved if the antenna is located at the maximum current of the dominant ground mode. Moreover, the characteristic mode of the ground plane radiates effectively at resonance. Therefore, good radiation performance will be achieved if the antenna is coupled with the characteristic mode of the ground plane that is resonantly close to the operating frequency. The performance of the antenna at locations P1 and P2 is compared for both ground sizes. The characteristic modes of both ground planes are analyzed in a full wave simulator, and the eigenvalues of the first-and second-order modes of both ground planes are presented in Fig. 2. The resonant frequency of the first-order mode is 1.95 GHz at position 1 (P1), and it is close to the operating frequency of the antenna (2.4–2.5 GHz), making the denominator term of Eq. (1) small. The resonant frequency of the second-order mode is 4.79 GHz, which is far from the operating frequency of the antenna at position 2 (P2), thus making the denominator term of Eq. (1) large and the numerator term of Eq. (1) maximum. The performance of the antenna, coupled with the first- and second-order modes, is predicted on the basis of Eq. (1). According to this equation, the coupling of the antenna with the first-order mode is higher than that with the second order mode. Therefore, on the small C-shaped ground plane, the radiation performance of the antenna at location P1 is expected to be higher than that at P2.*

_{n}