2
\$\begingroup\$

In class we've been introduced to two port networks, and I was wondering: Is there a physical significance to a singular matrix in a two port network, or is it simply where the mathematical model breaks down?

\$\endgroup\$
1
\$\begingroup\$

It doesn't mean that the model breaks down, but it is usually a symptom that the model is idealized.

Consider the simplified common-emitter AC model for a BJT:

schematic

simulate this circuit – Schematic created using CircuitLab

It is clear that:

\begin{align*} I_2 &= h_{fe} \cdot I_1 \\ V_1 &= h_{ie} \cdot I_1 \end{align*}

which can be rewritten in matrix form as:

\$ \begin{bmatrix} V_1 \\ I_2 \end{bmatrix} = \begin{bmatrix} h_{11} & h_{12} \\ h_{21} & h_{22} \end{bmatrix} \cdot \begin{bmatrix} I_1 \\ V_2 \end{bmatrix} = \begin{bmatrix} h_{ie} & 0 \\ h_{fe} & 0 \end{bmatrix} \cdot \begin{bmatrix} I_1 \\ V_2 \end{bmatrix} \$

from which you can see the h-parameter matrix is singular, having the second column made up of zeroes, but still the model is valid, although really idealized, since it neglects the output conductance \$h_{oe}\$ and the \$h_{re}\$ coefficient.

| improve this answer | |
\$\endgroup\$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.