Boundary Conditions The complete solution is known when Vf and Vr are known. We need two equations to find them; these can come from any two of the below quantities 1. Sending end voltage. 2. Sending end current. 3. Receiving end voltage. 4. Receiving end current. 5. Receiving end impedance. ...
Charging a fi nite length line through a resistor In the first example we will consider what happens when an initially uncharged line is suddenly connected to an excitation voltage source through a resistance which it is common to call ZS but which might have been more properly known as RS. This ...
Co cordinates and notation again We consider the behaviour of a transmission line terminated as shown in Figure 2.6 in a resistance ZL. It might appear incongruous that we have chosen to represent what is a resistance by the symbol ZL which is normally an indication of an impedance. The reason f...
Co ordinate system It is worth studying this diagram as it represents particular choices among many which are possible and the details of the equations to be developed depend upon these choices. We have followed in this diagram the majority but by no means universal tradition followed by writers...
Con fi guration In the normal arrangement, the stubs are separated by a distance of L = 3λ/8 as shown in Figure 3.12, but other separations are possible, with appropriate variations to the procedure described below. In Figure 3.12 we see that the load admittance YL and a stub known as S2 are bot...
Con fi guration The matching system is shown in Figure 3.9. For the reasons described in a later paragraph we are working in admittance terms. At the right of the diagram is shown is shown a load admittance YL. A line of characteristic admittance Y0 and length l connects the load to a junction p...
Consequences at a boundary As said above we make medium 1 the perfect conductor. This is so that the vector ˆn points out into the adjacent space, as shown in Figure 6.3. For d.c. fields we would have the forms already quoted as equation 6.1 to 6.4 with Et1 and Dn1 set to zero, viz Et2 = 0 (6.13)...
Conservation of Charge Concept As our first major concept we begin with the notation that there is a thing called charge which is conserved. It can be stationary or in motion. It can be used to probe an electromagnetic field; it is discrete but in such small amounts as not to concern us at the m...
Constitutive Parameters Having generalised in Section 4.4 Maxwell's Equations to take into account the effects of polarisation and magnetisation within media, we find we are left with too few equations in the number of unknowns now involved, to obtain a solution. The number of equations in the e...
Current re fl ection factor The current reflection factor Γi is defined by Γi = Ireγz If e−γz . (2.76) This definition is the obvious dual of the previously given definition in equation 2.52 for voltage reflection factor. Substituting for If and Ir in terms of Vf and Vr from equations 2.48 an...
