Input impedance of lossy transmission line¶
Knowing the length of the transmission line, the loss factor of the transmission line and its surge impedance, as well as the propagation constant and load resistance, it is possible to determine the input impedance of the transmission line.
- input_impedance¶
Input
electrical_impedanceof 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_impedanceof the transmission line.
- Symbol:
Z_S- Latex:
\(Z_\text{S}\)
- Dimension:
impedance
- Symbol:
l- Latex:
\(l\)
- Dimension:
length
- propagation_constant¶
- Symbol:
gamma- Latex:
\(\gamma\)
- Dimension:
1/length
- law¶
Z_in = (cosh(gamma * l) * Z_L + Z_S * sinh(gamma * l)) / (Z_L * sinh(gamma * l) / Z_S + cosh(gamma * l))- Latex:
- \[Z_\text{in} = \frac{\cosh{\left(\gamma l \right)} Z_\text{L} + Z_\text{S} \sinh{\left(\gamma l \right)}}{\frac{Z_\text{L} \sinh{\left(\gamma l \right)}}{Z_\text{S}} + \cosh{\left(\gamma l \right)}}\]