Impedance matrix equation¶

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

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_impedance¶: Ratio of input_voltage to input_current at idle at the output. See electrical_impedance.

Symbol:: Z_ii
Latex:: \(Z_\text{ii}\)
Dimension:: impedance

input_output_impedance¶: Ratio of input_voltage to output_current at idle at the output. See electrical_impedance.

Symbol:: Z_io
Latex:: \(Z_\text{io}\)
Dimension:: impedance

output_input_impedance¶: Ratio of output_voltage to input_current at idle at the output. See electrical_impedance.

Symbol:: Z_oi
Latex:: \(Z_\text{oi}\)
Dimension:: impedance

output_output_impedance¶: Ratio of output_voltage to output_current at idle at the output. See electrical_impedance.

Symbol:: Z_oo
Latex:: \(Z_\text{oo}\)
Dimension:: impedance

law¶

[V_i, V_o] = [[Z_ii, Z_io], [Z_oi, Z_oo]]*[I_i, I_o]

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