Hybrid parameters matrix equation¶

The hybrid parameters matrix is one of the ways to describe a microwave device. The \(H\)-parameters of the device act as elements of this matrix. The matrix equation relates the input voltage and output current to the input current and output voltage.

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

Symbol:: H_ii
Latex:: \(H_\text{ii}\)
Dimension:: impedance

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

Symbol:: H_io
Latex:: \(H_\text{io}\)
Dimension:: dimensionless

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

Symbol:: H_oi
Latex:: \(H_\text{oi}\)
Dimension:: dimensionless

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

Symbol:: H_oo
Latex:: \(H_\text{oo}\)
Dimension:: conductance

law¶

[V_i, I_o] = [[H_ii, H_io], [H_oi, H_oo]]*[I_i, V_o]

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