Impedance Matrix for an Eddy Current Solution

An impedance matrix gives the relationship between AC voltages and AC currents for multiple conductors. In the current loops below, the voltage and current in each loop is:

This can be expressed in matrix form as:

where:

• DV_i and I_i are phasors.
• Z₁₁ = R₁ + jwL₁₁ (the self-impedance of Loop 1).
• Z₁₂ = R₁₂+ jwL₁₂ (the mutual impedance between Loops 1 and 2).
• Z₂₂ = R₂ + jwL₂₂ (the self-impedance of Loop 2).

A device with n current loops would have an n´n impedance matrix.