Transmission matrix for parallel load in line¶

Knowing the impedance of the load connected in parallel to the transmission line, it is possible to calculate the parameters \(A, B, C, D\) of the transmission matrix of the load.

Notes:

See Transmission Matrix.

Conditions:

The load is connected to the transmission line in parallel.

voltage_voltage_parameter¶: Ratio of input voltage to output voltage at idle at the output.

Symbol:: A
Latex:: \(A\)
Dimension:: dimensionless

voltage_current_parameter¶: Ratio of input voltage to output current in case of a short circuit at the output.

Symbol:: B
Latex:: \(B\)
Dimension:: impedance

current_voltage_parameter¶: Ratio of input current to output voltage at idle at the output.

Symbol:: C
Latex:: \(C\)
Dimension:: conductance

current_current_parameter¶: Ratio of input current to output current in case of a short circuit at the output.

Symbol:: D
Latex:: \(D\)
Dimension:: dimensionless

load_impedance¶: Load electrical_impedance.

Symbol:: Z_L
Latex:: \(Z_\text{L}\)
Dimension:: impedance

law¶

[[A, B], [C, D]] = [[1, 0], [1 / Z_L, 1]]

Latex:: \[\begin{split}\begin{pmatrix} A & B \\ C & D \end{pmatrix} = \begin{pmatrix} 1 & 0 \\ \frac{1}{Z_\text{L}} & 1 \end{pmatrix}\end{split}\]