RF and Microwave Wireless Systems

CHAPTER TWO

Review of Waves and Transmission Lines

2.1   INTRODUCTION

At low RF, a wire or a line on a printed circuit board can be used to connect two electronic components. At higher frequencies, the current tends to concentrate on the surface of the wire due to the skin effect. The skin depth is a function of frequency and conductivity given by

where ω = 2πf is the angular frequency, f is the frequency, μ is the permeability, and σ is the conductivity. For copper at a frequency of 10 GHz, σ = 5.8 x 10⁷ S/m and δ_s = 6.6 x 10^–5 cm, which is a very small distance. The field amplitude decays exponentially from its surface value according to e^–z/δ_s as shown in Fig. 2.1. The field decays by an amount of e^–1 in a distance of skin depth δ_s. When a wire is operating at low RF, the current is distributed uniformly inside the wire, as shown in Fig. 2.2. As the frequency is increased, the current will move to the surface of the wire. This will cause higher conductor losses and field radiation. To overcome this problem, shielded wires or field-confined lines are used at higher frequencies.

Many transmission lines and waveguides have been proposed and used in RF and microwave frequencies. Figure 2.3 shows the cross-sectional views of some of these structures. They can be classified into two categories: conventional and integrated circuits. A qualitative comparison of some of these structures ...