A coaxial line 5.6 m long has distributed parameters R=6.5 Ω/m, L=3.4 μH/m, G=8. mS/m and C=21.5pF/m. if line operated at 2 MHz, Calculate the characteristic impedance and end-to-end propagation time delay
Question
A coaxial line 5.6 m long has distributed parameters R=6.5 Ω/m, L=3.4 μH/m, G=8. mS/m and C=21.5pF/m. if line operated at 2 MHz, Calculate the characteristic impedance and end-to-end propagation time delay
Solution
To solve this problem, we need to calculate two things: the characteristic impedance (Z0) and the end-to-end propagation time delay (t).
- Characteristic Impedance (Z0)
The characteristic impedance of a transmission line can be calculated using the formula:
Z0 = sqrt((R + jwL) / (G + jwC))
where: R = resistance per unit length = 6.5 Ω/m L = inductance per unit length = 3.4 μH/m = 3.4 x 10^-6 H/m G = conductance per unit length = 8 mS/m = 8 x 10^-3 S/m C = capacitance per unit length = 21.5 pF/m = 21.5 x 10^-12 F/m w = angular frequency = 2πf, f is the frequency = 2 MHz = 2 x 10^6 Hz
First, calculate w: w = 2πf = 2π(2 x 10^6) = 4π x 10^6 rad/s
Then, substitute R, L, G, C, and w into the formula:
Z0 = sqrt((6.5 + j4π x 10^6 x 3.4 x 10^-6) / (8 x 10^-3 + j4π x 10^6 x 21.5 x 10^-12))
Solving the above equation will give you the characteristic impedance Z0.
- End-to-End Propagation Time Delay (t)
The propagation time delay can be calculated using the formula:
t = L / v
where: L = length of the line = 5.6 m v = velocity of propagation = 1 / sqrt(LC)
First, calculate v: v = 1 / sqrt((3.4 x 10^-6)(21.5 x 10^-12)) = 1 / sqrt(7.31 x 10^-18)
Then, substitute L and v into the formula:
t = 5.6 / v
Solving the above equation will give you the end-to-end propagation time delay t.
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