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The Node Equation

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For Δx → 0, the above equations are reduced to

(2.1.52)

The above equations are rewritten below in term of the characteristic impedance (Z0) and propagation constant (γ) of a transmission line:

(2.1.53)

On solving the above equations for the voltage, the following inhomogeneous voltage wave equation, with a current source, is obtained:

(2.1.54)

Away from the location of the current source, i.e. for x ≠ x0, equation (2.1.54) reduces to the homogeneous equation (2.1.37a). The wave equation for the current wave, with a shunt current source, could also be rewritten.

Introduction To Modern Planar Transmission Lines

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