Question

For equivalent $\mathrm{\pi }$ circuits of lossless lines, the A and D parameters are pure_____, whereas B and C parameters are pure______.

Short answer

Therefore, parameter A and D are pure real and parameters B and C are pure imaginary.

Step-by-step solution

Determine A,B,C and D parameter of the π network.

The parameter A and D are equal for the lossless line and it is given by,

$\begin{array}{l}A\left(x\right)=D\left(x\right)\\ A\left(x\right)=cos\left(\beta x\right)pu\end{array}$ …… (1)

Here, $\beta$is the phase constant.

The parameter B is given by,

$B\left(x\right)=j\sqrt{\frac{L}{C}}sin\left(\beta x\right)\Omega$ …… (2)

Here, L is the inductance and C is the capacitance.

The parameter C is given by,

$C\left(x\right)=\frac{jsin\left(\beta x\right)}{\sqrt{\frac{L}{C}}}S$ …… (3)

Determine the nature of A,B,C and D parameter of the transmission line for π network.

By observing the equation (1), It clear that the imaginary part is zero. Therefore, the parameter A and D are purely real.

By observing the equation (2) and (3), it is clear that the real part is zero both the equation. Therefore, the parameter B and C are purely imaginary.

Hence, the parameter A and D are purely real and parameters B and C are purely imaginary.