Читать книгу RF/Microwave Engineering and Applications in Energy Systems - Abdullah Eroglu - Страница 50

Let's assume we have a sinusoidal function that changes in position and time. This function can be expressed as

(1.116)

Equation (1.116) can rewritten as

(1.117)

In (1.117), is defined as the phasor form of the function g(r,t) and expressed as

(1.118)

This can be applied for vectorial function as

(1.119)

The representation of the time harmonic functions in phasor form provides several advantages. They convert the time domain differential equations to frequency domain algebraic equations. This can be better understood by studying the derivative property as follows. Let's take derivative function g(r,t) with respect to time as

(1.120)

As a result of (1.120), it can be seen that the time derivative of a harmonic function means multiplying the same function by jω in the frequency domain. This can be shown as

(1.121a)

(1.121b)