Magnetic Amplifier - Example

Control Reactors for Single-Phase Rectifier.

Assume the following conditions:

Power supply 400 cycles.

Center-tap d-c circuit per Fig. 217(c).

Control current available = 40 ma d-c.

Plate transformer E = 125 volts per side.

At full output I_dc = 2 amp in R_L.

Per cent reduction in E_dc = 33 per cent at minimum output.

Assume grain-oriented nickel-steel core with A_c = 0.1 sq in., l_c = 5.5 in., and B_s = 14,700 gauss.

Core-case dimensions 1 1/4 in. I.D., 2 3/16 in. O.D., 15/32 in. high.

Each reactor must be capable of absorbing the voltage-time integral corresponding to 33 per cent voltage reduction, or 0.33 · 125 = 41 volts. From equation 34,

With full output, load winding current = 2π/(2 · 2) = 1.57 amp rms. From Fig. 219(a) this can be controlled with H = 0.5 oersted

This will be increased to 276 turns to allow for rectifier reverse current, variations in slope of the core B-H loop, and effective core gap. Using 650 cir mils per ampere, and single enameled wire, yields 1.57 · 650 = 1,020 cir mils or No. 20 wire for N_L, and 0.040 · 650 = 26 cir mils or No. 35 wire for N_c. With an average winding area space factor of 60 per cent, the coil winding areas required are, from Table V (p. 37), 244/(860 · 0.60) = 0.48 in.² for N_L and 276/(24,500 · 0.60) = 0.019 in.² for N_c. If Nc turns are wound concentrically over Nl, the load winding inside diameter is, from equation 124,

N_c turns occupy but a single layer. Then, for N_c, d₁ = 0.955 - 2(0.0064) = 0.94 in. With 10-mil insulation over N_c, the hole diameter becomes 0.94 - 0.02 = 0.92 in. Space required to insulate the ends of the windings and space for additional control windings reduce the hole diameter further. Winding mean turn lengths are, for a core-case periphery of 1.88 in.,

Load winding IR = 0.71 volt. PR = 1.12 watt.

Control winding IR = 0.76 volt. PR = 0.0305 watt.

with no external series resistance in the control circuit. With feedback applied to the control winding, this rectifier can be made self-regulating. If the feedback is further refined by comparison with a voltage reference, a stable voltage regulator results.