Level of treatment In this treatment of energy storage and power flow, some results will be advanced by inductive generalisation of formulae which can be established readily only in simple geometries. In this aspect the present chapter may appear to differ from earlier chapters, where an attempt...
Line charging waveforms The solution defined by equation 2.26 has the graph shown in Figure 2.10. The following observations may be made about the diagram. • There is no activity at the load until the time T for a one-way propagation of signals on the line has elapsed. • The initial step at tha...
Line open circuit at load end and fed from a low impedance source There are many reflections from both the load and source ends of the line. The reflection factor at the load end is unity, and there is thus no attenuation of the wave reflected from the load end. The reflection factor at the sourc...
Linear crystalline dielectric If a dielectric medium is in the form of a single crystal, it will generally exhibit different polarisation responses to electric fields in different directions. This behaviour is described by the equation P = ²0 χ≈ · E (5.6) where χ≈ is called the dimensionles...
Linear electrostatic case In the simple case of a distribution of point charges which are assembled from infinitely separated points into a final position in a linear homogeneous dielectric medium of dielectric permittivity ², it is possible to show from a study of the mechanical work done that ...
Linear lossless dielectrics In most non-crystalline dielectrics, at least for electric field strengths below that of dielectric breakdown, the polarisation is proportional to and in the direction of the internal electric field. This is expressed by the equation P = χe ²0 E (5.1) where χe is a d...
Linear lossy dielectric In some dielectric materials, losses involved in changing the state of polarisation cannot be entirely neglected. In these materials, we can sometimes write a linear differential equation relating the polarisation and its time rate of change, and the corresponding quantiti...
Linear lossy ferromagnet If we are prepared to consider small signals, and the sinusoidal steady state, we canmodel the behaviour of a material in which the magnetisation lags somewhat behind a sinusoidal magnetic field excitation by the equations M = (χ0 m − jχ00 m) H (5.15) B = (μ0 − jμ00) ...
Linear magnetostatic case A not entirely parallel examination of the work done, perhaps by mechanical or perhaps by electrical means, to create a magnetic field leads to the result Um = 1 2 μ Z vH·Hdv (7.4) for the total energy stored. Of course in the case of a linear medium this result ha...
Linear soft ferromagnet In polycrystalline ferromagnets and for small values of internal field strength we may write to a reasonable level of approximation M= χm H (5.10) where χm is a dimensionless parameter called the magnetic susceptibility. The same relation may be expressed in the alternat...
