RF/Microwave Engineering and Applications in Energy Systems. Abdullah Eroglu

      (1.14b)

      (1.15a)

      (1.15b)

      (1.16a)

      (1.16b)

      (1.16c)

      (1.16d)

      1.2.2 Coordinate Systems

      Three coordinate systems are defined in this section: the rectangular or Cartesian coordinate system, the cylindrical coordinate system, and the spherical coordinate system.

      1.2.2.1 Cartesian Coordinate System

Unit vector representation for a Cartesian coordinate system is shown in Figure 1.3.

A vector representation in a Cartesian coordinate system is given by (1.17).

(1.17)

      The magnitude of vector is found from

      (1.18)

The vector can be illustrated in the coordinate system, as shown in Figure 1.4. The base vector properties can be given by

      (1.19)

      (1.20)

Figure 1.4 Representation of vector

in a Cartesian coordinate system.

Figure 1.5 Representation of vector

in a cylindrical coordinate system.

      The vector operations for dot and cross products for vectors and are given by

      (1.21)