0195136047.pdf

256 ANALOG BUILDING BLOCKS AND OPERATIONAL AMPLIFIERS

−

+ +

vo

+ xy

−

vi

+

−

vi R

Ri

−

+

kvi

−

Rf

Rf

A =

A

y = −Ax

(a)

(b)

Ri

−

+ −

+

+

vo

+ xy

−

vi

Ri

−

VC(0)

y(0)

Cf

y(t) = −^1 ∫t

0 x(τ) dτ^ +^ y(0)

(d)

RiCf

−

+

+

vo

x 2 a 2 y

xn an

... x 1 a 1

v 1

R 1

−

v 2

R 2

vn

Rn

Rf

1

y = −a 1 x 1 − a 2 x 2 − ... −anxn

(c)

k

1

Figure 5.4.18Analog computer components.(a)Basic op amp to provide integer multiplication.(b)Po-

tentiometer for providing noninteger gains of less than 1.(c)Summer. [Note:y=x 1 +x 2 +···+xn,by

choosingRf/R 1 =Rf/R 2 = ··· =Rf/Rn=1.](d)Integrator. [Note: Cfis charged to an initial value

VC(0) to provide the initial condition ony; withRiCf= 1 ,y=−

∫t

0 x(τ)dτ+y(^0 ).]

The coefficients may simply be scaled by the appropriate factors to change the solution time of

the analog computer. For example, ifα=20, thent=20 s corresponds toτ=1 s, and thus the

solution time may be reduced.

5.5 Learning Objectives

Thelearning objectivesof this chapter are summarized here, so that the student can check whether

he or she has accomplished each of the following.