An electrically small planar antenna using complementary split-ring resonators

Electrically small antennas have been investigated for more than half a century, and many interesting results and structures have been obtained. Among them, the most important deduction may be the "Chu-limit," which relates the volume occupied by an antenna to its radiation characteristics and bandwidth by introducing the concept of the quality factor. Particularly, the bandwidth-efficiency product of an antenna is limited by its electrical size. The bandwidth here is defined by a specified level of reflection coefficient (|S₁₁|) rather than the half-power bandwidth that is commonly used in the circuit theory. Chu's analysis was based on the spherical wave function expansion of fields radiated by the antenna. Since the spherical eigen-functions are orthogonal, no energy could be coupled among modes, and therefore, each spherical mode can be represented by an individual equivalent circuit, for which the quality factor, or Q_mode, can be calculated. Then, the quality factor of the antenna Q can be expressed as a function of Q_mode's. Importantly, it was also shown that ßmode of the lowest order mode is the lower bound for Q of a single-resonant antenna. Consider the impedance bandwidth defined by |S₁₁| ≤ -10 dB: BW = Δf/f₀, where Δf and f₀ are the absolute bandwidth and the self-resonant frequency of the antenna, respectively. Combining the results yields the upper bound for the bandwidth: BW ≤ l/(√2Q_Chu), where Q_Chu = η/(ka)³, k = ω₀√μ ε η is the radiation efficiency, and a is the radius of the smallest sphere enclosing the antenna. Although nothing has been mentioned about the procedures to design an electrically small antenna, it does imply that such an antenna should have rotationally symmetric structure since the TE₁₀ and TM₁₀ modes have the lowest Q_mode, which correspond to the fields radiated by a short dipole and a small loop, respectively. This also explains why the geometries of many small antennas are highly symmetric. In this paper, the split-ring resonators (SRRs) and the complementary split-ring resonators (CSRRs) are adopted respectively to produce the fields of the TE₁₀ and TM₁₀ modes when self-resonating. Two planar designs of electrically small antennas are thus proposed, and the unbalanced effects on the antenna performance are discussed. Both antennas are designed to be input matched for 50 Ω, and their overall sizes are merely about (λ₀<;/20)×(λ₀/20).