Voltage standing wave ratio A quantity of considerable practical importance is the Voltage Standing Wave Ratio (VSWR) denoted by S. S = Vmax Vmin = |Vf | + |Vr| |Vf | − |Vr| . (2.84) If we divide by |Vf | and obtain the relations |Γv| = S − 1 S + 1 (2.85) and S = 1 + |Γv| 1 − |Γv| ...
Voltage standing wave ratio We recall from Chapter 2 the results S = Rmax Z0 = rmax (3.7) S = Z0 Rmin = 1 rmin (3.8) and the fact that the point of maximum voltage on the line occurs as the point of maximum impedance and the point of minimum voltage on the line occurs at the point of ...
Voltage Standing Wave Ratio We now begin the study of a parameter, namely the voltage standing wave ratio, of considerable theoretical and practical importance in transmission line theory. Its theoretical importance lies in the fact that it sharply illustrates the complexity of the variation and ...
Voltage variation along a line We look at the way the total voltage V(z) varies along the lossless line. We have from equation 2.42, with γ = jβ V(z) = Vfe−jβz +Vre+jβz (2.82) where Vf and Vr are complex numbers. As we go along the line, we will have in equation 2.82 the two terms moving in and...
Additional remarks Some additional remarks on the procedure now follow. • The stubs and the main line can be of different characteristic impedances. We should then use three different charts, and work in normalized admittances on each. But to transfer values from one chart to another, e.g. trans...
Derivation of Poynting Vector Analysis Maxwell's equations convert the above equation to ∂W ∂t = E · (curlH− J) −H· (curl E − 0) (7.10) where the absence of free magnetic charges is emphasised by the placement of a zero in the second bracket. Using the vector identity div(A× B) = B · curl A −...
Di ff erential form In free space the laws of electrodynamics take the following differential form. They were first correctly formulated by J.C. Maxwell, and are known as Maxwell's equations. These equations imply Faraday's law of induction, Coulomb's law for a static electric field, Amp`eres la...
Gauss law for the electric fl ux The total electric flux (defined in terms of the D vector) emerging from a closed surface is equal to the total conduction charge contained within the volume bounded by that surface. In a mathematical formula this law takes the form In the above equation we are e...
Gauss theorem Consider a closed surface S, of which ds, sensed outward, is a vector element of surface area, enclosing a volume v, as shown in Figure 1.5. If F is an arbitrary vector field, it has been shown by Gauss that This theorem states in words that the net flux of a vector F emerging from ...
Helmholz equation If we combine the two curl equations we find curl curl E = ω2²μE. The vector identity curl curl = grad div−∇2 gives, in view of the fact that div E = 0, ∇2E = −ω2²μE . (8.6) This equation is known as the three-dimensional wave equation and we will be concerned with various of ...
