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CHAPTER 2 - Conveying Power at Radio Frequency 106 When the radius of the outer conductor is increased, the opposite happens: the voltage between inner and outer conductors increases and hence so does the impedance of the line. Remember that ( ) is a positive and monotonically increasing function when . This condition is always verified in this case since is always greater then . There is also another way to look at this. We can think of our coaxial line as a cylindrical capacitor. Much in same way as in the case of parallel plate capacitors 20 , as the distance between the two conductors increases, the capacitance decreases. In the case of a capacitor, a lower means higher impedance as shown by equation (1.5-6). Now, as you may recall from Figure 2.3-4, a transmission line may be represented as a network of capacitors and inductors so, if we reduce the capacitance value, thereby increasing the impedance of the capacitors, we would expect the impedance of the line to increase also. This ties in well with equation (2.11-1) shown in graphical form in Figure 2.11-4 where is plotted versus ⁄ at a fixed . Figure 2.11-4 Characteristic impedance of a coaxial line vs the b/a ratio, Now let us re-examine Figure 2.11-3 and pick up again the analogy with a parallel plate capacitor. Just as in that geometry, as the dielectric constant of the dielectric between the coaxial line conductors increases, so does the capacitance . This in turn means that the impedance of the capacitors which model the line (Figure 2.3-4) decreases and hence so does the characteristic impedance of the line, . This is yet again confirmed by equation (2.11-1) plotted vs at a constant ⁄ in Figure 2.11-5. From a field viewpoint, the dielectric reduces the electric field by the factor i.e. This means that, as the dielectric constant increases, the Electric field decreases and consequently, voltage (equation (2.11-4)) and impedance decrease also. 20 For a parallel plate capacitor ⁄ , where is the distance between the plates 1 2 3 4 5 6 7 8 9 10 0 20 40 60 80 100 Characteristic Impedance of a Coaxial Line b/a Z 0 , () Conquer Radio Frequency 106 www.cadence.com/go/awr

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