Admittance of rectangular loop coupler¶
The rectangular loop coupler consists of four sections. The admittance of each section can be calculated by calculating the admittance of the transmission line to which the coupler is connected and the power ratio at the outputs.
- first_admittance¶
admittanceof the first section.
- Symbol:
Y_1- Latex:
\(Y_{1}\)
- Dimension:
conductance
- second_admittance¶
admittanceof the second section.
- Symbol:
Y_2- Latex:
\(Y_{2}\)
- Dimension:
conductance
- third_admittance¶
admittanceof the third section.
- Symbol:
Y_3- Latex:
\(Y_{3}\)
- Dimension:
conductance
- fourth_admittance¶
admittanceof the fourth section.
- Symbol:
Y_4- Latex:
\(Y_{4}\)
- Dimension:
conductance
- transmission_line_admittance¶
admittanceof the transmission line.
- Symbol:
Y_0- Latex:
\(Y_{0}\)
- Dimension:
conductance
- power_ratio¶
Ratio of the power at the outputs of the coupler.
- Symbol:
k- Latex:
\(k\)
- Dimension:
dimensionless
- law¶
[Y_1, Y_2, Y_3, Y_4] = [Y_0 / sqrt(k), Y_0 * sqrt((k + 1) / k), Y_0 * sqrt((k + 1) / k), Y_0 / sqrt(k)]- Latex:
- \[\begin{split}\begin{pmatrix} Y_{1} \\ Y_{2} \\ Y_{3} \\ Y_{4} \end{pmatrix} = \begin{pmatrix} \frac{Y_{0}}{\sqrt{k}} \\ Y_{0} \sqrt{\frac{k + 1}{k}} \\ Y_{0} \sqrt{\frac{k + 1}{k}} \\ \frac{Y_{0}}{\sqrt{k}} \end{pmatrix}\end{split}\]