General solution The general solution contains forward and reverse travelling waves of arbitrary shape, and has the form It may easily be confirmed that this solution satisfies equation 2.7 when the parameter c, which has the significance of ...
Generalisation Although we have studied the case of normal incidence only, the general picture we have derived is considered to the applicable to a wide range of practical cases. Thus whenever we have a metallic boundary supporting a magnetic field, we will always assume the magnetic field is su...
How We Will Proceed In the early chapters we will focus on the behaviour of transmission lines which will be frequently of the twin line or coaxial line structure. The lines are usually uniform in cross section with respect to the longitudinal d...
Illustration of solution We chose for our first illustration the situation when only a forward wave is present. The wave may be illustrated against a time axis as shown in Figure 2.4. Because the function Vf is of the single argument z − ct, if the voltage observed at the
Integral form Difficulties sometimes arise in using the differential equations when boundaries are introduced and idealized, and some fields become discontinuous at the boundary. In such cases the integral forms of the equations shown below are...
Interpretation Let us examine the relation between complex S and the real N. Since the real electric field is given in terms of the corresponding complex phasor by E(x, y, z, t) = E(x, y, z)ejωt + E∗(x, y, z)e−jωt 2 (7.16) and the real magnetic field is given in terms of the corresponding com...
Interpretation vaves The form of the above expression shows that the power flow is positive in the +z direction, and that the two components of the electric field do not interact. A similar analysis of power flow in the case of two waves propagating in opposite directions leads to the similar an...
Interpretation Now the first term represents the rate of increase of stored energy per unit volume. The second term represents the rate of working per unit volume of the field on the conduction currents J. These currents might result in the dissipation of energy in the resistance of the medium, ...
Kirchho ff s current law Kirchhoff's current law states that the algebraic sum of the currents entering a single node of circuit is zero. There are a number of assumptions underlying this statement. The first is that we know where the currents are in the sense that the currents flow on wires, we...
Kirchho ff s voltage law Kirchhoff's voltage law of lumped circuit theory states that the sum of the voltage rises in traversing any closed path in a circuit is zero. The voltage rises are of course differences in electric potential. The statement above is equivalent to the statement that the lin...
