CHAPTER 2 - Conveying Power at Radio Frequency
118
2.14.2 Transmission lines
Plane waves may propagate in free space or be guided along transmission lines. The
principles are very much the same and we will now make this connection and see how plane waves,
propagating in a TEM mode, form the basis of transmission line theory.
2.14.2.1 Ideal Model
In section 2.3 we saw how a transmission line may be modelled by a network of series
inductors and parallel capacitors (Figure 2.3-4). This is a simplified model and does not account for
losses. We will look at how to make it more realistic in section 2.14.2.2 but for now let's keep it
simple and lossless. The model for a short segment of transmission line is shown in Figure 2.14-2,
where L and C represent inductance and capacitance per unit length respectively.
Figure 2.14-2 A short section of lossless transmission line
From basic circuit analysis we may write
( ) ( )
( )
( ) ( )
( )
Now taking the limit for in equation (2.14-7), we can obtain the differential form for the
voltage along the line as shown by eq.(2.14-8)(a). Following a similar procedure we can obtain an
analogous expression for the current as shown by eq.(2.14-8)(b).
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
(2.14-7)
Conquer Radio Frequency
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