Question

Surge Impedance Loading (SIL) is the power delivered by a lossless line to the load resistance equal to______

Short answer

Therefore, the surge for the lossless transmission line is $\sqrt{\frac{L}{C}}$.

Step-by-step solution

Determine the formulas to calculate the surge impedance loading.

The equation of the impedance of the transmission line given below,

$\mathbf{z}\mathbf{=}\mathbf{R}\mathbf{+}\mathbf{j\omega L}\frac{\mathbf{\Omega }}{\mathbf{m}}$ …… (1)

Here, R is the resistance, L is the inductance, $\mathit{\omega }$ is the angular frequency.

The equation of the admittance of the transmission line is given below.

$\mathbf{y}\mathbf{=}\mathbf{G}\mathbf{+}\mathbf{j\omega C}\frac{\mathbf{S}}{\mathbf{m}}$ …… (2)

Here, G is the conductance and C is the capacitance.

The formula for the surge impedance is given below,

${\mathit{Z}}_{\mathbf{c}}\mathbf{=}\sqrt{\frac{\mathbf{z}}{\mathbf{y}}}$ …… (3)

Determine the equation for the surge impedance loading.

For the lossless line, the resistance of the transmission line is zero.

Substitute 0 for R into equation (1).

$\begin{array}{l}z=0+j\omega L\\ z=j\omega L\end{array}$

For the lossless line, the conductance of the transmission line is zero.

Substitute 0 for G into equation (2).

$\begin{array}{l}y=0+j\omega C\\ y=j\omega C\end{array}$

Calculate the surge impedance.

Substitute$j\omega L$ for z and $j\omega C$for y into equation (3).

$\begin{array}{l}{Z}_c=\sqrt{\frac{j\omega L}{j\omega C}}\\ Z_c=\sqrt{\frac{L}{C}}\end{array}$

Hence, the surge for the lossless transmission line is $\sqrt{\frac{L}{C}}$.