2.14 The dreaded maths
121
The reflection coefficient , which was just mentioned in passing in section 2.8, will feature
extensively in this treatment since it is a very useful measure for RF engineers.
2.14.2.2 A more realistic model
The model analysed in the previous section is a rather simplistic model and in real life we
would need to use the one shown in Figure 2.14-4 (b). In this model a short length of transmission
line is represented by a lumped element circuit where and are
, series resistance per unit length (Ω/m)
, series inductance per unit length (H/m)
, shunt conductance per unit length (S/m)
, shunt capacitance per unit length (F/m)
In particular, is used to account for the finite conductivity of the metal and gives an indication of
the loss in the dielectric material between the conductors.
Figure 2.14-4 Voltage and current definitions (a) and lumped-element equivalent circuit (b) for an incremental length of
transmission line
From basic circuit analysis we may write
( ) ( ) ( )
( )
( ) ( )
( )
( )
z
v(z,t)
i(z,t)
z
v(z,t)
i(z,t)
v(z+ z, t)
i(z+ z,t)
z
z
z
z
z
(a)
(b)
(2.14-17)
Conquer Radio Frequency
121 www.cadence.com/go/awr
