Question

The propagation constant, which is a complex quantity in general, hasunits of ______, and the characteristic impedance has units of ______.

Short answer

The propagation constant, which is a complex quantity in general, has units of $m^{-1}$, and the characteristic impedance has units of $\Omega$.

Step-by-step solution

Determine the formula of propagation constant and characteristics impedance.

Write the formula of propagation constant.

$\mathit{Y}\mathbf{=}\sqrt{\mathbf{z}\mathbf{y}}{\mathit{m}}^{\mathbf{-}\mathbf{1}}$……. (1)

Here, $z$ is series impedance and $y$ is shunt admittance.

Write the formula of characteristics impedance.

role="math" localid="1653155336937" ${\mathit{Z}}_{\mathbf{c}}\mathbf{=}\sqrt{\frac{\mathbf{z}}{\mathbf{y}}}\mathit{\Omega }$ ……. (2)

Here, $Z_c$ is a characteristics impedance.

Determine the units of propagation constant and characteristics impedance.

From equation (1), the unit of propagation constant is $m^{-1}$.

From equation (2), the unit of characteristics impedance is$\Omega$.

Therefore, the answer is:

The propagation constant, which is a complex quantity in general, has units of$m^{-1}$, and the characteristic impedance has units of$\Omega$.