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...
The conservation equation The equation expressing the fact that charge cannot be created or destroyed, but can merely be moved around in the form of an electric current, which if of suitable nonuniformity in space might cause a change of charge density to arise, is in integral form ∂ ∂t Z v ...
The interior fi eld Inside the material all the fields propagate as the attenuated plane wave Ex(x, y, z) = E−αz 0 e−jβz = E0e−(1+j)z/δ Thus in terms of the original tangential magnetic field Ex(x, y, z) = (1+j)RsH0e−(1+j)z/δ (9.17) The volu...
The Laws of Electrodynamics We provide for reference below compact but complete statements of the four fundamental laws of electrodynamics which are embodied in what are known as Maxwell's equations. In the form stated below the laws are of full generality, and apply both to empty space and to r...
Twin lines We state without proof that for twin lines of the type illustrated in Figure 2.27 Again we note that the velocity is independent of frequency, and equal to velocity of light in the medium. The characteristic impedance is Z0 = 1 π r μ0 ε loge μ 2s d ¶ for s À d (2.101) Comm...
