Compact Antennas for Wireless Communications and Terminals: Theory and Design

Chapter 5Electrical Equivalent Circuit of a PrintedAntenna ¹

 

 

 

5.1. Energy considerations

Let us consider a medium of permeability μ₀, complex permittivity ε=ε′-jε″, and conductivity σ, containing one or more electrical sources labeled J_i (Figure 5.1). We know that Maxwell's equations for time-harmonic fields notably lead to the following two relationships:

[5.1]

[5.2]

where ω is the pulsation. After some effort, we can extract the energy conservation equation from equations [5.1] and [5.2]]:

[5.3]

in which the volume (V) is contained within the closed surface (S).

Note that:

[5.4]

[5.5]

[5.6]

[5.7]

[5.8]

[5.9]

where P_f is the total power provided by the sources at volume (V), P