ons because in these regions, 8 The Zo term in the centre fraction on the right-hand side of the equation is present because the short section of line (81) is terminated by an additional line which presents an input impedance of Zo. CHAPTER 2.2 Transmission lines frequency dispersion and waveform distortion tend to be minimal. These statements can also be verified by the following practical example. (d) At 5 MHz Example 2.2.4 A transmission line has the following primary constants: R + jwL = (23 + j3926.99)Q km , R = 23 S G = 4 mS L = 125 H C = 48 nF Calculate the characteristic km-1 km-superscript(1) km-1 impedance, km-1 and G + jwC = (4 j1508) mS km-1 Zo, of the line at a frequency of (a) 100 Hz, (b) 500 Hz, Hence (c) 15 kHz, (d) 5 MHz and (e) 10 MHz. Given: R = 23 O km-superscript(1), G = 4 mS km-1 L = 125 H = 50.03 Q - 0.00 rad km and C = 48 nF km-superscript(1). Required: Z at (a) 100 Hz, (b) 500 Hz, (c) 15 kHz, (d) 5 MHz and (e) 10 MHz. (e) At 10 MHz Solution R + jwL = (23 + j7853.998)9 km , Use Equation 2.2.17 in the calculations that follow, G + jwC = (4 + j3016) mS km-1 (a) At 100 Hz Hence R + juL = (23 + j0.08)Q.km~ = G + jwC = (4 + j0.030)mS km-superscript(1) = 50.03 Q - 0.00 rad Hence Conclusions from Example 2.2.4. At low frequencies, i.e. 100-500 Hz, the line impedance Z o tends to remain at about 75 S with very little phase shift over a wide = 75.830 - 2.06 x 10-3 rad frequency range. For most purposes, it is resistive and constant in this region. See cases (a) and (b). At high frequencies, i.e. 5-10 MHz, the line impedance Zo tends (b) At 500 Hz to remain constant at about 50 S with little phase shift over a wide frequency range. For most purposes, it is R + juL = (23 + j0.39)Q km T = resistive and constant in this region. See cases (d) and G + jwC = (4 + j0.15)mS km-1 (e). In between the above regions, the line impedance Z o varies with frequency and tends to be reactive. See case Hence (c). For radio work, we tend to use transmission lines in the 'lossless' condition (Equation 2.2.19) and this h