How Do You Calculate the Characteristic Impedance of a Transmission Line?

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SUMMARY

The characteristic impedance of a transmission line can be calculated using the formula Z = √(L0/C0), where L0 is the self-inductance and C0 is the capacitance per unit length. In this discussion, L was given as 7.0x10^-7 Hm^-1 and the signal speed was 70% of the speed of light (c = 3x10^8 ms^-1). The correct calculation for C0 yielded 5.77x10^-8 F, leading to a characteristic impedance Z of 3.4 Ω after resolving an initial calculation error involving squaring. The final result aligns with the expected theoretical framework.

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Roodles01
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Homework Statement


Transmission line is designed so it has selfinductance, L = 7.0x10^-7 Hm^-1 & signal speed 70% of c
Find characteristic impedance


Homework Equations


Z = √L0/C0 Ω
also
v = 1/ √L0C0



The Attempt at a Solution


So
L = 7.0x10^-7 Hm^-1
v = 0.7c
(c = 3x10^8 ms^-1)

7(3x10^8)/10 = 1/√7.0 * C0
so
C0 = √((10(7.0x10^-7))/(7*3x10^8))
C0 = √ 3.33x10^-15
C0 = 5.77x10^-8 F

Z = √L0/C0
Z = √7.0x10^-7/5.77x10^-8
Z = 3.4 Ω

Which isn't in the park as far as expected result goes, so AGAIN, please could you show me where I went wrong.
 
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OK, OK I get it.
Forgot to square, but square rooted instead.
All sorted.
 
Last edited:

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