Fields lines and guides - strona 3

Di ff erential equations for a short length We assume the line is characterised by distributed resistance R, inductance L, capacitance C, and conductance G per unit length. Of these elements, the L and C provide energy storage, while the R and G provide energy dissipation Applying Kirchhoff's vo...

Di ff erential Fo rms of Electrodynamic Laws With the aid of Gauss' and Stokes' theorems we may transform the laws of electrodynamics given in integral form in Section 1.6 to the equivalent differential forms below. ∇ × E = −∂B∂t ∇ ×H = J + ∂D∂t ∇ · D = ρ ∇ · B = 0 (1.16) These equations, to...

Distributed circuit theory The first of these is known as distributed circuit theory (which is one step up from lumped circuit theory) and resembles lumped circuit theory to some degree. This level of theory is applicable when we still have • an idea of where the currents are, either on thin wire...

Electric e ff ects The electric effects can be described on a basis of separation of internal charges, to give rise to a polarization vector P = Np (4.6) described as the result of N dipoles, each of strength p, created per unit volume. The charge dq crossing an area ds in the direction of ds i...

ELECTROMAGNETIC ENERGY AND FORCES In this chapter we will consider the storage and transformation of energy in electromagnetic systems. In the evolution of physical theory, two of the most durable principles have been that of conservation of ...

Electromagnetic fi eld theory There are, however, situations when the assumptions of neither distributed circuit theory nor lumped circuit theory are applicable. In these contexts we are obliged to deal directly in terms of the electromagnetic fields. The need for field theory can come about for...

Elementary properties of the Smith Chart We will now develop a number of important properties of the Smith Chart, the first of which is that for lines with passive terminations, the chart is confined to the

Force on Moving Charge The force FF on a charge q moving in a vacuum in which the electric and magnetic fields are E and H respectively is given by F = q (E + μ0v ×H) (4.3) This equation in effect defines E and H in SI units. The corresponding SI units of a number of quantities are as follows. ...

General discussion We look for plane wave solutions of the form e−γ·r, in which γ is the complex vector γ = α + jβ (9.4) It will be recalled from the previous discussion that there exist planes of constant amplitude (⊥ α) and planes of constant phase (⊥ β). It may be shown that in the lossless ...

General Formulae for Energy Change In the light of the results discussed in the last two sections we will postulate that the general expression for the change in stored energy in an electromagnetic system in response to changes in fields is dU = Z v{E · dD +H· dB}dv (7.7) This general result ...