Additional remarks Some addtional remarks about single stub matching are set out below. • We note that the procedure described above yields two separate solutions, of which we have only developed one, for the matching problem. There is no simple rule for preferring one solution to the other. • ...
Admittance Formulation While some circuit theory problems are easily solved in terms of impedances, others are easily solved in terms of admittances. This difference comes about because the rules for combining impedances in series are simple, but for combining impedances in parallel are complica...
Analysis in the Frequency Domain At the end of we noted that the general equations which describe waves on transmission lines can be usefully solved in two particular contexts, one being transmission lines containing neither of the energy loss producing elements R or G, and the other being trans...
Application to coaxial cabl es Show as an exercise that for the coaxial cable of dimensions shown in Figure 2.26 the inductance per unit length and capacitance per unit length are given by L = μ0 2π loge à b a ! (2.91) C = 2π² loge ³ b a ´. (2.92) Students who cannot produce for t...
Applications of the Smith Chart We have so far developed the Smith Chart as a graphical expression of the voltage reflection factor Γv with impedance contours placed upon it, but the similarity between the relations between the voltage reflection factor and the normalised impedance and between t...
Assumptions In our analysis we make a number of assumptions. The first of these is that the length of the line runs along a z axis and that the line characteristics are uniform with respect to the z axis. This second assumption is made to enable...
Boundary Characterisation We will for simplicity consider plane boundaries, and will regard any smoothly curved boundary as approximately plane at an appropriate scale of viewing. Such a plane boundary is shown in Figure 6.1 and is assumed to lie between region 1, in which the medium is characte...
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...
