De fi nition of the Smith Chart The Smith Chart provides a graphical method for the visualisation of conditions on a transmission line and for the solution of transmission line problems. The method rests on the fact that the voltage reflection factor Γv defines the conditions on the line, and tha...
Design of stubs Practical reasons, will be discussed in lectures, make it more convenient in many transmission line problems to work in admittance terms. Thus when we design a stub, we are seeking to find the stub length which will provide a part...
Detail of the procedure The details of the procedure are illustrated in Figure 3.13 and the discussion below. As indicated in Figure 3.12, the length 3λ/8 length of line, the two stubs and the main line to be matched all have a characteristic admittance Y0. This is the normal case but the proced...
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
