Di ff erential form In free space the laws of electrodynamics take the following differential form. They were first correctly formulated by J.C. Maxwell, and are known as Maxwell's equations. These equations imply Faraday's law of induction, Coulomb's law for a static electric field, Amp`eres la...
Gauss law for the electric fl ux The total electric flux (defined in terms of the D vector) emerging from a closed surface is equal to the total conduction charge contained within the volume bounded by that surface. In a mathematical formula this law takes the form In the above equation we are e...
Gauss theorem Consider a closed surface S, of which ds, sensed outward, is a vector element of surface area, enclosing a volume v, as shown in Figure 1.5. If F is an arbitrary vector field, it has been shown by Gauss that This theorem states in words that the net flux of a vector F emerging from ...
Helmholz equation If we combine the two curl equations we find curl curl E = ω2²μE. The vector identity curl curl = grad div−∇2 gives, in view of the fact that div E = 0, ∇2E = −ω2²μE . (8.6) This equation is known as the three-dimensional wave equation and we will be concerned with various of ...
Laws we can use When a structure has a significant degree of symmetry, it is usually possible to guess the shape of the field distribution, and obtain its funtional form from Amp`ere's Integral Law I H· dr = I (2.89) or Gauss' Integral Law I...
Linear conductor In many media the free electric charges can move in response to the internal electric field. Over a wide range, the forces opposing that motion are proportional to the drift velocities of the charge carriers. The result is the linear conduction relation J = σ E (5.19) which is ...
MATCHING OF TRANSMISSION LINES In this chapter we will continue the development of transmission line theory in the important context of transforming impedances so that source impedances can be conjugately matched to load impedances. We will introduce the important concept of the Smith Chart whic...
Maxwells equations We will suppose the medium we are studying is either free space or a homogeneous lossless linear medium, i.e. it is characterised by a constant μ and ², and that μ and ² are real, and the conductivity σ is zero. We assume also that there are no free charges or currents. Then M...
Normalised admittance We define the normalised admittance y as y = Y Y0 . (2.73) We find that y = 1/z. The relations between y and Γv are found to be of the form −Γv = y − 1 y + 1 (2.74) and y = 1 − Γv 1 + Γv . (2.75) These do not quite correspond in form to the impedance relations 2...
PROPERTIES OF TRANSMISSION LINES Having noted in the previous chapter the inadequacy of lumped circuit theory for the description of the properties of real electronic circuits, particularly at higher frequencies, we now proceed to the development of the first of the higher level theories that are...
