Input impedance of lossless transmission line

Knowing the length of the transmission line and its surge impedance, as well as the propagation constant and load impedance, it is possible to determine the input impedance of the transmission line.

input_impedance

Input electrical_impedance of the transmission line.

Symbol:

Z_in

Latex:

$Z_{\text{in}}$

Dimension:

impedance

load_impedance

Load electrical_impedance.

Symbol:

Z_L

Latex:

$Z_{\text{L}}$

Dimension:

impedance

surge_impedance

surge_impedance of the transmission line.

Symbol:

Z_S

Latex:

$Z_{\text{S}}$

Dimension:

impedance

length

length of the transmission line.

Symbol:

l

Latex:

$l$

Dimension:

length

phase_constant

phase_constant.

Symbol:

beta

Latex:

$\beta$

Dimension:

1/length

law

Z_in = Z_S * (Z_L + I * Z_S * tan(beta * l)) / (Z_S + I * Z_L * tan(beta * l))

Latex:

$$Z_{\text{in}}=\frac{Z_{\text{S}}(Z_{\text{L}}+i{Z}_{\text{S}}\tan \left(\beta l\right))}{Z_{\text{S}}+i{Z}_{\text{L}}\tan \left(\beta l\right)}$$