816 BASIC CONTROL SYSTEMS
feed the information to the microcomputer. Actuators and sensors may be either analog or digital.
Digital-to-analog (D/A) converters are used to convert the digital signals to analog form so as to
suit the analog actuators, where as analog-to-digital (A/D) converters are employed to convert
the analog sensor signals to digital form so as to suit the microcomputer.
One can think of so many systems in daily practice controlled or monitored by microcom-
puters. Some examples include monitoring patients in intensive cardiac-care units of hospitals,
nuclear-reactor controls, traffic signals, aircraft and automobile instrumentation, chemical plants,
and various manufacturing processes.Problems
16.1.1(a) Consider a diode circuit withRCload as
shown in Figure P16.1.1. With the switch
closed att=0 and with the initial condition
att =0 thatvC=0, obtain the functional
forms ofi(t) andvC(t), and plot them.
(b) Then consider a diode circuit with anRLload
with the initial condition att=0 thati=0.
With the switch closed att=0, obtain the
functional forms ofi(t) andvL(t).
(c) In part (b), ift >> L/R, describe what hap-
pens. If an attempt is then made to open switch
S, comment on what is likely to happen.
(d) Next consider a diode circuit with anLCload
with the initial condition att=0 thati= 0
andvC=0. With the switch closed att=0,
obtain the waveforms ofi(t) andvC(t).
16.1.2(a) Figure P16.1.2(a) contains afreewheeling
diode Dm, commonly connected across an in-
ductive load to provide a path for the current
in the inductive load when the switchSis
opened after timet(during which the switch
was closed). Consider the circuit operation in
two modes, with mode 1 beginning when the
switch is closed att=0, and mode 2 starting
when the switch is opened after the currenti
has reached its steady state in mode 1. Obtain
the waveforms of the currentsi(t) andif(t).
(b) Consider the energy-recovery diode circuit
shown in Figure P16.1.2(b), along with afeed-
back winding. Assume the transformer to have
a magnetizing inductance ofLmand an ideal
turns ratio ofa=N 2 /N 1. Let mode 1 begin
when the switchSis closed att=0, and mode
2 start att=t 1 , when the switch is opened.
Lett 1 andt 2 be the durations of modes 1 and 2,
respectively. Develop the equivalent circuits
for the two modes of operation, and obtain
the various waveforms for the currents and
voltages.
16.1.3(a) Consider a full-wave rectifier circuit with a
center-tapped transformer, as shown in Figure
P16.1.3, with a purely resistive load ofR. Let
vs=Vmsin ωt. Determine: (i) efficiency,
(ii) form factor, (iii) ripple factor, (iv) TUF,
and (v) PIV of diodeD 1. Compare the perfor-
mance with that of a half-wave rectifier. (See
Example 16.1.2.)
(b) Let the rectifier in part (a) have anRLload.
Obtain expressions for output voltagevL(t)
and load currentiL(t) by using the Fourier
series.t = 0VSvRvCRC+ +−
+− −S DI Figure P16.1.1