Fundamental Dimension Limits of Antennas Ensuring Proper Antenna Dimensions in Mobile Device Designs

The electronics industry has historically decreased the physical dimensions of their product offerings. In the age of wireless products this drive to miniaturize continues. Antennas are critical devices that enable wireless products. Unfortunately, system designers often choose antenna dimensions in an ad hoc manner. Many times the choice of antenna dimensions is driven by convenience rather than through the examination of fundamental electrical limitations of an antenna. In this presentation the fundamental limits and the trade-offs between the physical size of an antenna and its gain, efficiency and bandwidth are examined. Finally, we examine the difficulty experienced in determining the physical dimensions of an antenna when “non-antenna” sections of a device’s structure may be radiating. “It was the IRE (IEEE) that embraced the new field of wireless and radio, which became the fertile field for electronics and later the computer age. But antennas and propagation will always retain their identity, being immune to miniaturization or digitization. ” – Harold A. Wheeler Electrically Small Antennas Many customers often budget the amount of antenna volume for a given application on an ad hoc basis rather than through the use of electromagnetic analysis. Frequently the volume is driven by customer convenience and is small enough that performance trade-offs are inherent in the antenna solution. Many times the volume allotted may be such that only an electrically small antenna can be used in the application. Early in a design cycle it is important to determine if the physical volume specified is, in theory, large enough electrically to allow the design of any antenna which can meet the impedance bandwidth requirements specified. There is a fundamental theoretical limit to the bandwidth and radiation efficiency of electrically small antennas. Attempting to circumvent these theoretical limits can divert resources in an unproductive manner to tackle a problem which is insurmountable. 2 Fundamental Dimension Limits of Antennas The first work to address the fundamental limits of electrically small antennas was done by Wheeler in 1947. Wheeler defined an electrically small antenna as one whose maximum dimension is less than λ 2π . This relation is often expressed as: ka < 1 (1) k = 2π λ (radians/meter) λ=free space wavelength (meters) a=radius of sphere enclosing the maximum dimension of the antenna (meters) The situation described by Wheeler is illustrated in Figure 1—1. The electrically small antenna is in free space and may be enclosed in a sphere of radius a. ka < 1. Figure 1—1 Sphere enclosing an electrically small radiating element. In 1987 the monograph Small Antennas by Fujimoto, Henderson, Hirasawa and James summarized the approaches used to design electrically small antennas. They also surveyed refinements concerning the theoretical limits of electrically small antennas. It has been established that for an electrically small antenna, contained within a given volume, the antenna has an inherentminimum value ofQ. This places a limit on the attainable impedance bandwidth of an Electrically Small Antenna (ESA). The higher the antenna Q the smaller the impedance bandwidth. The efficiency of an electrically small antenna is determined by the amount of losses in the conductors, dielectrics and other materials out of which the antenna is constructed compared with the radiation loss. This can be expressed as: