elps considerably in the matching of line impedances. 2.2.6 Characteristic impedance (Zo) = 75.810 2/-10.30x10-3 rad by measurement (c) At 15 kHz Occasions often arise when the primary constants of a line are unknown yet it is necessary to find the char- acteristic impedance (Zo). In this case, Z can be obtained R + jwL = = (23 + j11.78)Q km - , by measuring the short- and open-circuit impedance of G + jwC = 4 + j4.52 mS km-1 the line. In Figures 2.2-9 and 2.2-10 as in Figure 2.2-8 let: R represent the resistance per metre (ohms/metre) Hence L represent the inductance per metre (henry/metre) Transmission lines CHAPTER 2.2 (Z,/4) 81 (Z/4) 81 R &I L ol circuit (Z/4) di (Z/4) ol R & L 81 Fig. 2.2-9 Open-circuit equivalent of a short length of transmission line. G represent the conductance per metre (siemen/metre) C represent the capacitance per metre (farad/metre) It follows that for a short length sl, we would obtain Rôl, Lol, Gol and Col respectively. 2.2.6.1 Open-circuit measurement (Zoc) Hence defining Z8l as 1/Yl we have (2.2.20) Using Equation 2.2.16 to substitute for the numerator and Equation 2.2.20 to substitute for the denominator, we have 2.2.6.2 Short-circuit measurement (Zsc) The short-circuit impedance is (Z/4) 81 (Z,/4) ol RSI L81 Short circuit (Z/4) 81 (Z/4) 81 R & I L ll Fig. 2.2-10 Short-circuit equivalent of a short length of transmission line. CHAPTER 2.2 Transmission lines Hence aerials are designed for this impedance and it is almost certain that the cable that joins your TV set to Zo = Z scZoo the external aerial will have this impedance. The comments relating to the different types of 50 S lines also apply to 75 S lines. 140 S - This type of cable is used extensively by the Zo = VZscZoo (2.2.21) telephone industry. The comments relating to the different types of 50 L lines also apply to 140 S lines. Example 2.2.5 300 S - This type of cable is favoured by both the The following measurements have been made on a line at radio and television industry because it provides 1.6 MHz where Zoc = 900 $ 