Review of Waves and Transmission Lines 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. | RF and Microwave Wireless Systems. Kai Chang Copyright 2000 John Wiley Sons Inc. ISBNs 0-471-35199-7 Hardback 0-471-22432-4 Electronic CHAPTER TWO Review of Waves and Transmission Lines 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 1 2 2-1 where m 2 is the angular frequency f is the frequency is the permeability and u is the conductivity. For copper at a frequency of 10 GHz u x 107 S m and ds x 10 5 cm which is a very small distance. The field amplitude decays exponentially from its surface value according to as shown in Fig. . The field decays by an amount of c 1 in a distance of skin depth 3S. When a wire is operating at low RF the current is distributed uniformly inside the wire as shown in Fig. . 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 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 is given in Table . Transmission lines and or waveguides are extensively used in any system. They are used for interconnecting different components. They form the building blocks of 10 INTRODUCTION 11 FIGURE Fields inside the conductor. Low frequency Medium frequency FIGURE The currrent distribution within a wire operating at different frequencies. Radiated field High frequency many components and circuits. Examples are the matching networks for an amplifier and .
