Ayodeji Alalade Abiola LAB 7

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Lambton College *

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Electrical Engineering

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Apr 3, 2024

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LAB 7 Estimation of the Transmission Line Characteristic Impedance Objective To estimate the characteristic impedance for a number of typical transmission line sections through measuring the physical dimensions of them. Equipment Required  8 sections of typical transmission lines  Digital Vernier caliper Introduction Transmission lines are manufactured with some different standard characteristic impedance levels such as 50, 75 or 300 Ohms. The characteristic impedance of the coaxial cable shown in figure (1) can de estimated from: Z ο ≈ 138 √ ε r log D d Figure (1) Where “D” is the diameter of the outer conductor, “d” is the diameter of the inner conductor and “ ε r ” is the relative permittivity of the dielectric between the two conductors. The characteristic impedance of the two parallel lines shown in figure (2) can be estimated from:

Z ο ≈ 276 √ ε r log 2 D d Figure (2) Where “D” is the distance between the centers of the two parallel lines, “d = 2r” is the diameter of each line and “ ε r ” is the relative permittivity of the dielectric that separates the two lines. Typical Dielectric Constants The polyethylene dielectric is clear and reflective with ε r = 2.3 . The foam dielectric is cloudy and non reflective with ε r = 1.5 . The Teflon dielectric (cable marked with H and has silver plated conductors) has ε r = 2.1 . The relative permittivity for air =1 Vernier Caliper Figure (3) shows an image of a typical vernier caliper. The following parts of which are numbered from (1) to (8): (1) Outside jaws (2) Inside jaws (3) Depth probe (4) Main scale in cm (5) Main scale in inch (6) Vernier scale in cm (7) Vernier scale in inch (8) Retainer

Figure (3) Digital Caliper To measure the diameter of a conductor encloses it between the outside jaws of the vernier caliper. Read the diameter on the screen. You can choose either mm or inch as a unit. Procedure Based on the measured values of the diameters of the inner and outer conductors, calculate the estimated characteristic impedance for each of the eight coaxial transmission line sections designated with letters “A” to “H”. Fill in table (1). The dielectric material in these samples are as follows: A – Air, B, C , D, E, G – Foam, F - polyethylene , H - Teflon Cable d (mm) D (mm) ε r Workings Z ο (Ω) A 28.87 68.03 1 138 log 2.3564= 51.370 51 B 15.14 45.69 1.5 112.676 log 3.0178= 54.050 54 C 4.14 19.03 1.5 112.676 log 4.5966= 74.640 75 D 3.52 12.22 1.5 112.676 log 3.4716= 60.904 61 E 4.98 13.64 1.5 112.676 log 2.7390= 49.306 49 F 2.33 8.57 2.3 90.995 log 3.6781= 51.468 51 G 4.10 12.72 1.5 112.676 log 3.1024= 55.402 55

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H 1.19 3.62 2.1 95.229 log 3.0420= 46.011 46 From samples above, which one has Zo equal to 75 ohms? Answer: Cable C is equal to 75 ohms. Table (1)

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