# What is the circuit determinant?

The circuit determinant $$\Delta$$ is the determinant of the matrix description of the circuit. The latter is the matrix form of a general cutset of the circuit. In particular:

• The mesh equations, in which the driving sources are voltages.
• The nodal equations, in which the driving sources are currents.
• The indefinite admittance matrix, defined by Chen.
• ...

The determinant is not invariant among these different formulations, however, each one features the same roots (poles of the circuit) if it describes the same circuit.

References:

1. Wai-Kai Chen. Active network analysis. World Scientific Publishing Co., Inc., 1991. URL

2. HW Bode. Network analysis and feedback amplifier design. D. Van Nostrand Co., Inc., 1945. URL