Chapter4.Antennas

Chapter 4. Antennas

William A. Davis and Stanislav Licul

Ultra wideband (UWB) systems are limited by the response capabilities of the antennas used in the systems. This chapter emphasizes the modeling of both the antenna and scattering structures that must be considered in the performance estimates of UWB technology and links.

Classically, communication links have been modeled by the Friis transmission formula [1]

Equation 4.1

The basic concepts of antenna gain, G, and effective antenna aperture, Gl²/4p, are difficult to define in a wideband sense, and new concepts of transmission are needed for understanding the transient behavior of UWB systems. The transient performance may be related to equivalent frequency performance metrics, and insight may be obtained by viewing both time and frequency domain representations.

Because the concepts of power and gain are frequency dependent, it becomes useful to look at the signal performance rather than power transmission, particularly for correlation reception applications. From antenna theory, we can define the effective length of an antenna, shown in Figure 4.1a, in terms of the current distribution on the antenna due to an input current I_t at a given frequency as [2]

Equation 4.2

where the frequency is included in both the current distribution J and the wave number b = 2p/l, while the direction of the radiation is included in the properties of the unit vector . The polarization properties are included in the vector nature of the current J. The typical use of a conjugation of h in (4.2) has not been used to simplify the connection with the transient performance. Normally, effective length is defined for linearly polarized antennas, but the form of (4.2) provides a general form for arbitrary antenna polarization. In the following sections, appropriate definitions are developed for this effective length and are related to commonly used antenna parameters. These definitions are followed by the measured performance of a variety of antennas, as well as a simple characterization for the antennas. Many aspects such as gain, pulse width, pulse amplitude, and a minimal model for the antenna properties are presented.

Figure 4.1. The Three Problems Used in the Reciprocity Development of a Communications Link.

This chapter presents the basic properties of antennas from both frequency and time domain viewpoints. The effective length is developed and related to the need in transient link computations. Section 4.2 presents methods for representing antennas and scatterers in a minimal fashion. The basic concept is a pole-residue representation based on the theory of the singularity expansion method [18]. Several examples are included to demonstrate the modeling for a minimal representation of the antenna and scattering structures.