Difference between revisions of "Talk:Travelling Wave Line Model"
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(Created page with "== Footnotes == === Derivation of Voltage Equation === The general solution to the transmission line wave equations are: : <math> I(x, t) = i^{+}(x - vt) + i^{-}(x + vt) \,...") |
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Latest revision as of 07:41, 22 November 2020
Footnotes
Derivation of Voltage Equation
The general solution to the transmission line wave equations are:
Where is the velocity of propagation (m/s).
- and are arbitrary current functions of time.
- and are arbitrary voltage functions of time.
The Laplace Transform of the above equations are:
- ... Equ. (1)
- ... Equ. (2)
Recall the Telegrapher's equation for current:
Taking the Laplace Transform of this equation, we get:
- ... Equ. (3)
Substituting Equations (1) and (2) into Equ. (3):
We can differentiate the left-hand side:
Equating the and terms on both sides, we get the following pair of equations:
Solving for voltage yields the following:
- ... Equ. (4)
- ... Equ. (5)
Where is the characteristic impedance (Ohms)
We can use the above equations to re-write the voltage equation of Equ. (2) in terms of current as follows:
Finally, taking the inverse Laplace Transform of the equation above, we get: