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2.11 Transmission lines – Design and Practical Realisation 105 (2.11-4) We must also remember that, when a dielectric is present, the velocity of propagation is also affected and it usually becomes a fraction of the speed of light, . Such a fraction may be determined by means of the dielectric constant , as shown by equation (2.11-2). √ A reduced speed of propagation of the signal also affects the wavelength as you may recall from section 2.2 and equation (2.2-4). The effective wavelength for the signal travelling along our coaxial line therefore becomes √ We will not show the derivation of equation (2.11-1) however this equation is very useful to understand how the characteristic impedance of the coaxial line is affected by the various parameters. The first thing to notice is that it is not just or that affects the impedance value, but their ratio! Now let us try to reason a little. If we increase the radius of the inner conductor (thereby decreasing ⁄ ) we will facilitate the flow of electrons by providing a larger cross sectional area. The resistance to current flow will therefore be lower which translates into a lower . Also, increasing reduces the distance between the surface of the inner conductor and the inner surface of the outer conductor. A shorter distance between the facing surfaces of inner and outer conductors reduces the voltage between them and hence decreases the impedance. Remember that such a voltage may be expressed as shown in equation (2.11-4) since the electric field 19 is radial as illustrated in Figure 2.11-3. is the charge density per unit length. ( ) ( ) ∫ ( ) Figure 2.11-3 Electric field inside a coaxial line. The line is effectively a cylindrical capacitor. 19 The electric field may be easily calculated in this case by using Gauss's Law: (2.11-2) (2.11-3) Conquer Radio Frequency 105 www.cadence.com/go/awr