Admittance matrix equation¶

The admittance matrix is one of the ways to describe a microwave device. The \(Y\)-parameters of the device act as elements of this matrix. The matrix equation relates the input and output currents to the input and output voltages.

Links:

Wikipedia.

input_voltage¶: Input voltage.

Symbol:: V_i
Latex:: \(V_\text{i}\)
Dimension:: voltage

output_voltage¶: Output voltage.

Symbol:: V_o
Latex:: \(V_\text{o}\)
Dimension:: voltage

input_current¶: Input current.

Symbol:: I_i
Latex:: \(I_\text{i}\)
Dimension:: current

output_current¶: Output current.

Symbol:: I_o
Latex:: \(I_\text{o}\)
Dimension:: current

input_input_admittance¶: Ratio of input_current to input_voltage in case of a short circuit at the output. See admittance.

Symbol:: Y_ii
Latex:: \(Y_\text{ii}\)
Dimension:: conductance

input_output_admittance¶: Ratio of input_current to output_voltage in case of a short circuit at the output. See admittance.

Symbol:: Y_io
Latex:: \(Y_\text{io}\)
Dimension:: conductance

output_input_admittance¶: Ratio of output_current to input_voltage in case of a short circuit at the output. See admittance.

Symbol:: Y_oi
Latex:: \(Y_\text{oi}\)
Dimension:: conductance

output_output_admittance¶: Ratio of output_current to output_voltage in case of a short circuit at the output. See admittance.

Symbol:: Y_oo
Latex:: \(Y_\text{oo}\)
Dimension:: conductance

law¶

[I_i, I_o] = [[Y_ii, Y_io], [Y_oi, Y_oo]]*[V_i, V_o]

Latex:: \[\begin{split}\begin{pmatrix} I_\text{i} \\ I_\text{o} \end{pmatrix} = \begin{pmatrix} Y_\text{ii} & Y_\text{io} \\ Y_\text{oi} & Y_\text{oo} \end{pmatrix} \begin{pmatrix} V_\text{i} \\ V_\text{o} \end{pmatrix}\end{split}\]