254 Integrated circuits
the bilateral Laplace transform of the kernel. It has Since the mid-1960s, integrated circuits have.L'
been shown that the result is correct if, for example, come the primary components Of most electron~,ic y
E(s) is the infinite product in Eq. (10), where c Ž_ 0 tems. Their low cost, high reliability, and spd ba
H 1 - es/ak (1(J) been essential in furthering the wide use ofdigt
ebC, 2bs - 1 s)(0 computers. Microcomputers have spread te j
1 fi (computer
technology to instrumns buinessIn'
and te seiesrea consantschines,o automobiles, and other equipm~
and he eris orel cnstntscommon uses of large-scale integrated circuitsre
pocket calculators and electronic watches. For allj-i
signal processing, integrated subsystems such as FM'-
ak stereo demodulators and switched-capacitor filters a
made. SEE CALCULATORS. DIGITAL COMPUTER; &ELcI,,k.
converges. ICS; MICROCOMPUTER.
For example, if K(x) = e-x, then Eq. (4) is the Integrated circuits consist of the combination of~
Laplace transform. Expressed as a convolution trans- tive electronic devices such as transistors and diode;.
form as in Eq. (3), it becomes Eq. (11), where G is with passive components such as resistors and capac. 1
itors, within and upon a single semiconductor crystW
?F~e) =G~x- y)(e" ~ 11) The construction of these elements within the senmi
(,e)G~x y),~e-' dy 11) conductor is achieved through the introduction of
electrically active impurities into well-definergir
given in the above list as entry K. The bilateral La- of the semiconductor. The fabrication of integrae
place transform of this kernel is the familiar gamma circuits thus involves such processes as vapor-phiu'
function, Eq. (12), whose reciprocal has a well- deposition of semiconductors and insulators, oxida
tion, solid-state diffusion, ion implantation, vacnuuml
e"G~) e'' dt (12) deposition, and sputtering.
F(I S)-"G~) dt e-t- dt 12) Generally, integrated circuits are not straightfor.
ward replacements of electronic circuits assembled
known expansion in the form of Eq. (10). In Eq. (13) from discrete components. They represent an exte D:
sion of the technology by which silicon planar ti~.,
1~)eW s' 13 sistors are made. Because of this, transistors or mod,
E~s = ~ fi -- esk) (3 ifications of transistor structures are the prima7ý::
devices of integrated circuits. Methods of fabrnicating
-y is Euler's constant. In the present example Eq. (9) good-quality resistors and capacitors have been de'
becomes Eq. (14), or if e-' = t, Eq. (15) may be vised, but the third major type of passive component,,
inductors, must be simulated with complex circuitry,
oradded to the integrated circuit as discrete conpi.ý
e-D eD'keF(e) (D(e-) (14) nents. SEE TRANSISTOR.
k=) Simple logic circuits were the easiest to adapt to,
/\ k+ these design changes. The first of these, such as in-
Wi I() (5 verters and gates, were produced in the early 1960s'
k--~ k! t Iprimarily for miniaturization of missile guidance
computers and other aerospace systems. Analog cii
written. This familiar inversion formula also serves to cuits, called linear integrated circuits, did not become
illustrate the operator 0, appearing in Eq. (2). In the commercially practical until several years later beý"
present case the operator is a differential one, and the cause of their heavy dependence on passive comppo-,
parameter t is an integer k which tends to -. SEE CON- nents such as resistors and capacitors. The first good.
FORMAL MAPPING; INTEGRATION, quality operational amplifiers for analog computetiS
David V. Widder and instruments were produced in 1966. SEE AMPLI
Bibliography. M. 1. Akhiezer, Lectures on Integral FIER; ANALOG COMPUTER; LOGIC CIRCUITS.
Transforms, 1988; L. C. Andrews and B. K. Shiva-
moggi, Integral Transforms for Engineers and Ap- TYPES OF CIRCUITS
plied Mathematicians, 1987; 0. I. Marchev, Hand- Integrated circuits can be classified into two group.
book of Integral Transforms of Higher Transcendental on the basis of the type of transistors which they enm
Functions, 1983; K. B. Wolf, Integral Transformns in ploy: bipolar integrated circuits, in which the prifld-
Science and Engineering, 1979. pal element is the bipolar junction transistor, and
metal oxide semiconductor (MOS) integrated circati
in which the principal element is the MOS tranlsistor
IntgraedircitsBoth depend upon the construction of a desired pait
Interate ciruitstern of electrically active impurities withinth semi:l
Miniature electronic circuits produced within and conductor body, and upon the formation of an
upon a single semiconductor crystal, usually silicon, connection pattern of metal films on the surface of d0
Integrated circuits range in complexity from simple semiconductor. ge,
logic circunits and amplifiers, about 1/2o in. (1.3 mm) Bipolar circuits are generally used where hge
square, to large-scale integrated circuits up to about logic speed is desired, and MOS for largest-scale R
1/2 in. (12 mm) square. They can contain millions of tegration or lowest power dissipation. Linear c~CO '
transistors and other components that provide com- are mostly bipolar, but MOS devices are used exttýý
puter memory circuits and complex logic subsystems sively in switched-capacitor filters. Hfigh-perc1i
such as microcomputer central processor units. SEE bipolar transistors and complementary MOS (CM05)
SEMICONDUCTOR; SILICON. transistors have been combined on the salme ~
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