PROBLEMS 817t = 0(a)VS Dm
ifRL+−S Di(b)VS+
+−−− +SDi 1
v 1N 1 : N 2v 2i 2Figure P16.1.2(a)Diode circuit with freewheeling diode.(b)Energy-recovery diode circuit with
feedback winding.vP+++−−−
vD 2vD 1vs+−vsvLiLD 2RD 1Figure P16.1.3*16.1.4Consider a full-wave single-phase bridge rectifier
circuit with dc motor load, as shown in Figure
P16.1.4(a). Let the transformer turns ratio be unity.
Let the load be such that the motor draws a ripple-
free armature current ofIa. Given the waveforms
for the input current and input voltage of the rec-
tifier, as in Figure P16.1.4(b), determine: (i) har-
monic factor HF of the input current, and (ii) input
power factor PF of the rectifier.
16.1.5(a) Consider a three-phase star or wye half-wave
rectifier with a purely resistive loadR. Deter-
mine: (i) efficiency, (ii) form factor, (iii) ripple
factor, (iv) TUF, and (v) PIV of each diode.
(b) Express the output voltage of the three-phase
rectifier in Fourier series.
16.1.6Consider a three-phase, full-wave bridge rectifier,
as shown in Figure P16.1.6, with a purely resistive
loadR. For each diode, determine: (i) efficiency,
(ii) form factor, (iii) ripple factor, (iv) TUF, and
(v) PIV.
16.1.7Consider Example 16.1.2 in the text.
(a) Calculate the firing angle corresponding to
a torque of 35 N·m and a speed of− 1350
r/min, assuming continuous conduction. What
is the quadrant of operation in the torque–
speed relationship?
(b) Find the motor speed at the rated torque and
α=160° for the regenerative braking in the
second quadrant.
16.1.8For a three-phase, fully controlled, rectifier-fed,
separately excited dc motor, corresponding to
ideal no-load operation, find the expression for
the no-load speeds. Comment on whether no-load
speeds could be negative. Compared to the one-
phase case, would you expect a considerable re-
duction in the zone of discontinuous conduction?
*16.1.9Consider the motor of Example 16.1.3 in the text.
Calculate the motor speed for: (a)α =120°,
Ta =25 N·m, and (b)α=60°,Ta=5N·m.
Assume continuous conduction in both cases.
16.1.10Consider Example 16.1.4 in the text. For part (c),
compute the corresponding rms fundamental sta-
tor current.
16.1.11A 60-Hz, six-pole, wye-connected, three-phase
induction motor, with the parametersR 1 =R′ 2 =
0. 025 andXl 1 =X′l 2 = 0. 125 , is controlled
by variable-frequency control with constantV/f
ratio. Use the approximate equivalent circuit of
Figure 13.2.6, withjXmmoved over to the supply