Page 327 - Solutions Manual to accompany Electric Machinery Fundamentals

 t
 
vt A B e 1 R C
C
where A and B are constants depending upon the initial conditions in the circuit. Since v (0) = 0 V and
C
v () = 100 V, it is possible to solve for A and B.
C
A = v () = 100 V
C
A + B = v (0) = 0 V  B = -100 V
C
Therefore,

 t
 100 100 e
vt  0.50 V
C
The time at which the capacitor will reach breakover voltage is found by setting v (t) = V BO and solving
C
for time t :
1

100 V 30 V
t  0.50 ln  178 ms
1
100 V
Once the PNPN Diode fires, the capacitor discharges through the parallel combination of R and R , so
2
1
the time constant for the discharge is
RR 500 k 1.5 k 
 1 2 C     1.0 F  0.0015 s
R  1 R 2 500 k   1.5 k 
2
The equation for the voltage on the capacitor during the discharge portion of the cycle is
t

 
vt A B e 2 
C
t

 V
vt BO e 2 
C
The current through the PNPN diode is given by
V  t
 
it R BO e 2 
D
2
If we ignore the continuing trickle of current from R , the time at which i (t) reaches I is
H
1
D
IR 0.0005 A 1500  
t  R C ln H 2   0.0015 ln  5.5 ms
2
2
V 30 V
BO
Therefore, the period of the relaxation oscillator is T = 178 ms + 5.5 ms = 183.5 ms, and the frequency of
the relaxation oscillator is f = 1/T = 5.45 Hz.
S1-9. In the circuit in Figure S1-4, T 1 is an autotransformer with the tap exactly in the center of its winding.
Explain the operation of this circuit. Assuming that the load is inductive, sketch the voltage and current
applied to the load. What is the purpose of SCR ? What is the purpose of D 2? (This chopper circuit
2
arrangement is known as a Jones circuit.)

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