Impedances of T-type circuit of transmission line¶
The T-type circuit consists of the first impedance connected in series, the third impedance connected in parallel, and the second impedance connected in series. For a transmission line, these impedances can be calculated for an equivalent replacement circuit by knowing the transmission line parameters.
- first_impedance¶
First
electrical_impedance.
- Symbol:
Z_1- Latex:
\(Z_{1}\)
- Dimension:
impedance
- second_impedance¶
Second
electrical_impedance.
- Symbol:
Z_2- Latex:
\(Z_{2}\)
- Dimension:
impedance
- third_impedance¶
Third
electrical_impedance.
- Symbol:
Z_3- Latex:
\(Z_{3}\)
- 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_1, Z_2, Z_3] = [Z_S * tanh(l * gamma / 2), Z_S * tanh(l * gamma / 2), Z_S / sinh(l * gamma)]- Latex:
- \[\begin{split}\begin{pmatrix} Z_{1} \\ Z_{2} \\ Z_{3} \end{pmatrix} = \begin{pmatrix} Z_\text{S} \tanh{\left(\frac{l \gamma}{2} \right)} \\ Z_\text{S} \tanh{\left(\frac{l \gamma}{2} \right)} \\ \frac{Z_\text{S}}{\sinh{\left(l \gamma \right)}} \end{pmatrix}\end{split}\]