Introduction To Modern Planar Transmission Lines. Anand K. Verma

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      (2.1.57)equation

      The phasor line voltage and line current are written as follows:

      The constants A1 and B1 are determined by using the boundary conditions at input x = 0 and output x = ℓ.

       At x = 0, the line input voltage is , giving the value of A1:(2.1.59)

      At the receiving end, x = ℓ, the load end voltage and current are

       At x = ℓ, i.e. at the receiving end, the voltage across load ZL is(2.1.61)

      (2.1.62)equation

      Similarly, the line current at the location P is obtained as follows:

      At any location P on the line, the load impedance is transformed as input impedance by the line length d = (ℓ − x):

      images, where images.

      (2.1.67)equation

      Likewise, from equations (2.1.64) and (2.1.66), an expression for the line current is obtained:

      (2.1.68)equation

      The above equations could be reduced to the following equations for a lossless line, i.e. for α = 0, γ = jβ, cosh(jβ) = cos β and sinh(jβ) = j sin β:

      (2.1.69)equation

      (2.1.70)equation

      Equation (2.1.65c), for the input impedance, could be obtained from the above two equations. The sending end voltage and current are obtained at the input port – aa, x = 0:

      (2.1.71)equation

      (2.1.72)equation

      Likewise, the expressions for the voltage and current at the output port – bb, i.e. at the receiving end for x = ℓ, are obtained:

      (2.1.73)equation

      (2.1.74)equation

      Two

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