**Multiply Excited Magnetic Field System:**

Multiply Excited Magnetic Field System – Singly-excited devices discussed earlier, are generally employed for motion through a limited distance or rotation through a prescribed angle.

Electro-mechanical transducers have the special requirement of producing an electrical signal proportional to forces or velocities or producing force proportional to electrical signal (current or voltage). Such transducers require two excitation one excitation establishes a magnetic field of specified strength while the other excitation produces the desired signal (electrical or mechanical).

Also continuous energy conversion devices motors and generators require multiple excitation.

Figure 4.15 shows a magnetic field system with two electrical excitations one on stator and the other on rotor. The system can be described in either of the two sets of three independent variables; (λ_{1}, λ_{2}, θ) or (i_{1}, i_{2}, θ). In terms of the first set

where the field energy is given by

Assuming linearity

Solving for i_{1} and i_{2} in terms of λ_{1}, λ_{2} and substituting in Eq. (4.63) gives upon integration

where

The Self- and mutual-inductance of the two exciting coils are functions are angle θ.

If currents are used to describe the system state

where the coenergy is given by

In the linear case

where inductances are functions of angle θ.