Magnetic Frequency Multipliers

Because of the simple relationships that govern the behavior of a saturable reactor in a frequency multiplying arrangement, the magnetic frequency

Figure 7-2. Basic circuit for frequency multiplier

multiplier is treated here to serve as an introduction to the analysis of saturable reactor operation in wider applications. In the frequency multipliers under consideration, a polyphase circuit with an odd number of m phases, and having a frequency of f cps, supplies m saturable reactors connected in star to provide a single-phase source, operating at a frequency of mf cps. The load is connected between the neutral point of the source and that formed by the common connection of the saturable reactor as shown for the frequency tripler in Fig. 7-4(a). The basic circuit of the frequency multiplier is shown for one phase in Fig. 7-2; the simplified magnetization curve in Fig. 7-1(b) is assumed for the core material. Although the core is represented as a toroid in Fig. 7-2, it may have other shapes as well. The design of the reactor must be such that it saturates at or above a certain angle a_f, known as the firing angle, which is determined by

[7-1]

On the basis of the simplified saturation curve in Fig. 7-1(b), the saturable reactor is an open circuit when unsaturated and a short circuit when saturated, thus operating as a synchronous switching device or a gate. This discussion is confined, for reasons of simplicity, to applications in which the load is noninductive, although inductive loads may be supplied as well.

Wave forms of voltage, flux density, and current are shown in Fig. 7-3(a) with the idealized magnetization curve of Fig. 7-3(b) as a basis. The applied voltage is expressed by

[7-2]

The core saturates at ωt = α_f, the firing angle. The reactor, when the resistance and capacitance of its winding are neglected, becomes a short circuit after having been an open circuit, for 0 < ωt < α_f and full voltage is impressed on the load resistance. The current that results in the non-inductive resistance is then defined by

Figure 7-3. (a) Waveforms of voltage, flux density, and current for noninductive load; (b) idealized magnetization curve for multiplier.

and

[7-3]

The angle α_c represents the interval during the half cycle in which conduction takes place and is called the conduction angle.