Mutual reactances

Mutual reactance between windings in the d-axis. Mutual reactance between windings in the g-axis. Leakage reactance of a stator winding. 

A synchronous generator (and a synchronous motor) can be represented by many inductances and reactances to account for transformer-type induction, rotational induction, mutual coupling between windings, leakage and self-induction, magnetising and excitation induction and the effects of the pole-face damper windings. Extremely complex equivalent circuits have been developed for synchronous machines, see References 1 and 2 as examples. 

The absence of the field winding can be used to convert the mathematical model of the synchronous machine into one for an induction machine. In addition the mutual inductance in the < -axis is made equal to mumal inductance in the d-axis, i.e. the machine becomes symmetrical in both axes. The matrix equations (20.6) to (20.16) are modified as shown below. In these equations the mutual inductances Mj and become M, Lim and Lihq become L/j., Rjut and R/aj become Rk. All the derived reactances and time constants for an induction machine are equivalent to those appUcable to the g-axis of the synchronous machine. 

The MMW electrical properties of the cavity and the oscillator at resonance are effectively fixed in their manufacture. This treatment addresses the coupling between those two circuit elements to achieve optimal performance. It considers only the circuits at resonance that is, under the working condition of the spectrometer. Recall that the capacitive and inductive reactances in a tuned circuit at resonance cancel each other yielding a purely resistive circuit element. Nonetheless the reactances both still remain and are manifest in the property Q. The treatment will yield the reflection coefficient p of the coupling interface between the cavity and oscillator in terms of their gs and the mutual inductance coupling coefficient M of the impedance transformer that the interface represents. Optimum performance will be when the two circuit elements are critically coupled to each other and that will be shown to occur when p = 0. 

---