sistance and conductance). These cause high fre- original amplitude. At plane 3, which is three times as far quency components to travel at a different velocity from from the source as plane 1, the reduction is 0.8 or 0.512 low frequency components. The variation of velocity with of the original amplitude. frequency is called the frequency dispersion of the line. More generally, at a distance equal to l times the dis- tance from the source to plane 1, the height is reduced by 2.2.9.3 Phase and group velocities (0.8) Because l is the exponent in this expression this type of amplitude variation is called exponential. It can As a pulse consists of sinusoidal components of different also be expressed in the form (e) or ead, where e rep- frequencies, each component will therefore be altered resents the loss per unit length and is 0.8 in this particular differently. Distinction must be made between the ve- example. In fact a is the natural logarithm of the locities of the sinusoidal components which are called 10 This is because dB = 20 Log (Ratio) = 20 Log (e) = 20 a X Log (e) = 20 X a 0.4343 = 8.686a. CHAPTER 2.2 Transmission lines phase velocities, up. The phase velocity (B) is defined as is a common condition for a transmission line to behave the change in radians over a wavelength and since there is electrically as though it was of infinite length. a phase change of 2 radians in every wavelength, it If a transmission line is to be used for signals with follows that B = 2 radians/wavelength (2) or a wide range of frequency components, it may be difficult to terminate it properly. In general, the characteristic (2.2.22) impedance of a transmission line will vary with frequency and if the matching load fails to match the line at all The velocity of the complete waveform is called the frequencies, then the line will not be properly terminated and reflections will occur. group velocity, Ug. The apparent velocity of the pulse in Figure 2.2-11 is called its group velocity. In practice, it is usual to properly terminate b