Solution 6.74
RC = 0.01 x 20 x 10-3 sec
secm
dt
dv
2.0
dt
dv
RCv i
o−=−=
Thus vo(t) is as sketched below:
1
vo(t) (V)
2
Solution 6.75
An op amp differentiator has R= 250 kΩ and C = 10
µ
F. The input voltage is a ramp r(t)
= 7 t mV. Find the output voltage.
Solution
Solution 6.76
,
dv
RCv
i
o
−=
RC = 50 x 103 x 10 x 10-6 = 0.5
The input is sketched in Fig. (a), while the output is sketched in Fig. (b).
(a)
vi(t) (mV)
–
10
(b)
vo(t) (V)
Solution 6.77
i = iR + iC
Thus vi is obtained from vo as shown below:
4
-4
3
2
8
1
4
-4
3
2
0
1
–dvo(t)/dt
4
3
2
0
1
– vo(t) (V)
-4
4
vi(t) (V)
-8
Solution 6.78
Design an analog computer to simulate
Solution
Thus, by combining integrators with a summer, we obtain the appropriate analog
computer as shown below, where vo(0) = –6 V:
R
−
−
−
R
R
C
C
R
−
R
R
−
R
R/2
R
vo(0)
Solution 6.79
Design an analog computer circuit to solve for v(t) given the following equation and a
value for f(t) and that v(0) = 0 V.
Solution
are many acceptable solutions, this is just one of them.
100 kΩ
300 kΩ
300 kΩ
100 kΩ
100 kΩ
Solution 6.80
From the given circuit,
Solution 6.81
Design an analog computer to simulate the following equation to solve for v(t) (assume
the initial conditions are zero):
3
3
() ()
3 4()+=
dvt dvt ft
dt dt
.
Solution
As with any design problem there are many acceptable solutions, this is one of them.
Note, the above can also be solved without the integration step and would also be an
accurate solution.
100 kΩ
300 kΩ
100 kΩ
10 µF
Solution 6.82
The circuit consists of a summer, an inverter, and an integrator. Such circuit is shown
below.
10R R
Solution 6.83
Your laboratory has available a large number of 5–µF capacitors rated at 150 V. To
design a capacitor bank of 10-µF rated at 600 V, how many 5-µF capacitors are needed
and how would you connect them?
Solution
Since four 5 µF capacitors in series gives 1.25 µF, rated at 600V, it requires 8 groups in
parallel with each group consisting of four capacitors in series, as shown below:
Solution 6.84
An 8-mH inductor is used in a fusion power experiment. If the current through the
Solution
Solution 6.85
It is evident that differentiating i will give a waveform similar to v. Hence,
dt
di
Lv =
Solution 6.86