document73

Technovation, 18(6/7) (1998) 439457 1998 Elsevier Science Ltd. All rights reservedPergamon

Printed in Great Britain0166-4972/98 $19.00 + 0.00PII: S0166-4972(98)00021-2

Performance analysis of technologyusing the S curve model: the caseof digital signal processing (DSP)

technologiesMariano Nieto*

Department of Management, Universidad Complutense de Madrid, Madrid, Spain

Francisco LopezDepartment of Signal and Communication Theory, Universidad de Alcala de Henares,

Alcala de Henares, Spain

Fernando CruzDepartment of Circuits and Systems Engineering, Universidad Politecnica de Madrid,

Madrid, Spain

AbstractThe purpose of this paper is to analyse the evolution of the technologyperformance of Digital Signal Processing components (DSPs) using the Scurve model. In the first part, the theoretical base of this model is establishedthrough a comparative study between the S curve model and other conceptswith which it is closely related: innovation diffusion models and life cyclemodels. The purpose of this study is to use the solid analytical foundation ofthese models to increase the theoretical consistency of the S curve model. Inthe second part of the article, a methodology that facilitates the applicationof this model is proposed. At the same time, the usefulness of the S curve asa strategic analysis tool is discussed as well as the problems that can arisewhen the model is put into practice. This methodology is used in the analysisof the technology of DSPs. 1998 Elsevier Science Ltd. All rights reserved

1. INTRODUCTIONThe progressive acceleration that technological

changes have experienced in recent decades has dem-

*Author for correspondence.

Technovation Vol. 18 Nos 6/7 439

onstrated the need to consider the incidence of suchtechnological advances in all areas of enterprise. Ithas been demonstrated that technology determines, toa large extent, the competition level, and the need toincorporate technological analyses in the process offormulating strategies has been emphasized. In the

M. Nieto et al.

literature of technology management, numerousmethodologies that facilitate the link between tech-nology and strategy have been proposed. One modelthat has been widely published, is the so-called Scurve, which enables the analysis of the evolution ofthe performance of any technology. The majority ofmanuals about the strategic management of tech-nology (Betz, 1993; Dussauge et al., 1992; Goodmanand Lawless, 1994; Twiss, 1986) use this model andsuggest its use to make predictions about the evol-ution of the rate of technological change, to detectpossible technological ruptures, or to determine thelimits of a particular technology.

In the first part of this paper, the model of the Scurve is examined by establishing links with othersimilar concepts with which it is closely related. Tra-ditional separation, existent in the fields of economyand management, has brought about a proliferation ofequivalent concepts and has consolidated methodol-ogical differences that undoubtedly impede orobstruct terminological normalization and the trans-mission of knowledge. This fact justifies the need(before presenting the empirical work in the followingsection) to reflect upon the existing relationshipsbetween the concept of the S curve and other dif-fusion of innovations models (used in the fields ofindustrial economy and marketing) and life cyclemodels (used in the literature of strategy, productionand marketing).

In the second part, the technology performance ofdigital signal processors (DSPs) is analyzed by meansof the S curve model. DSPs constitute a new familyof semiconductors that have numerous applications inthe scope of information and communication techno-logies (ICTs). DSP components will become a majorgrowth area in the semiconductor components marketover the next few years (Price Waterhouse, 1994).The S curve model will allow evolution of the tech-nology performance of DSPs to take place as well asestimate the limits of its growth potential. This analy-sis is achieved by following an original methodologywhich enables it to overcome the problems that mayappear when this model is put into practice. Inaddition, the possibilities of the S curve model as astrategic analysis tool and its usefulness in the designof strategic technologies will be discussed.

2. THEORETICAL FOUNDATIONS OF THE S CURVEMODEL

Before presenting the results of the analysis of thetechnology performance of DSPs using the S curvemodel, it is important to reflect upon its theoretical

440 Technovation Vol. 18 Nos 6/7

foundations. In spite of the fact that the S curve modelhas been studied extensively in recent years,especially since the publication of Fosters book(Foster, 1986a), there are no studies that establish thebasis of its theoretical foundation. The primary objec-tive of this paper is to make every attempt to increasethe theoretical consistency of this concept using thesolid theoretical and empirical groundwork of othermodels (which appear in the field of economy andmanagement) to which it is related. It seems appropri-ate to analyze its antecedents before exposing themain characteristics of this model. Therefore, twomodel families that are closely related to the conceptof the S curve are identified below:

(1) diffusion models, and(2) life cycle models.

Diffusion models attempt to analyse the process bywhich an innovation is diffused throughout a determ-ined social system (Rogers, 1993). Most of theresearch regarding diffusion processes has been car-ried out by scholars from the field of industrial econ-omy and marketing. Therefore, in these models, vari-ables that are related to the structure of the industrialmarket in which the innovation is diffused and othercharacteristics of the overall economic environmentplay a relevant role. The first studies that were carriedout in the 1960s and 1970s were concerned primarilywith predicting the diffusion speed of the innovations.In general, the models that were proposed were quiterigid and incorporated very restrictive hypotheses:innovations with constant technology performancesover time, constant market potentials, etc. During the1980s and 1990s, new models have appeared. Theyreduce these hypotheses and include new explicatoryvariables: price, advertising, etc. These recent studies(Mahajan et al., 1993) emphasize the role of diffusionmodels as analysis instruments to formulate stra-tegies.

The life cycle models have been used in differentmanagement fields (strategy, marketing, production)in order to represent the evolution of industries, pro-ducts, brands, etc. The most widespread among themis the one that describes the different stages in thetemporal evolution of the sales of a product. Using theconceptual framework of the life cycle model, someauthors have defined different models that are rep-resentative of the evolutions of technologies(Abernathy and Utterback, 1975; Ford and Ryan,1981; Roussel et al., 1991). These models assume thatthe life cycles of technologies, industries and productsfollow similar patterns to that of the biological cycleof living beings and therefore are easily predictable.

Because the S curve model represents the evolution

Performance analysis of technology using the S curve model

of technology performance, it is as clearly related todiffusion models as it is to life cycle models. Itscapacity to analyze technological performance poten-tial makes this model a useful tool for designing tech-nological strategies. However, like many other mod-els that are developed in the management field, itslimited analytical base diminishes its theoretical con-sistency. This fact makes it difficult to achieve empiri-cal contrasts and their application in the analysis ofconcrete cases. Continuing with what constitutes thefirst part of this paper, existing relationships betweendiffusion models and life cycle and S curve modelswill be analyzed. This analysis will clearly demon-strate the common link between these models and theS curve. In addition, it allows for the demarcation ofthe theoretical foundations of the S curve model,increasing its consistency by using the solid analyticalbase of the diffusion and life cycle models.

2.1 Diffusion models

Studies of technological change, attained under theperspective of industrial economy, have paid specialattention to the processes of innovation diffusion. Inlarge part, these works (Baldwin and Scott, 1987;Davies et al., 1991; Stoneman, 1983, 1995) gatherand synthesize different analytical models thatdescribe the evolution patterns of existing techno-logies and their substitution for newer ones, both inproducts as well as processes. In general, these analy-ses have centered on the speed of diffusion of thetechnologies in different sectors, and they have triedto identify the factors that determine it.

Kuznets (1930) was among the first to recognizethat technological change was able to evolve by fol-lowing the known model of the S curve. Sub-sequently, the highly revealing research of Griliches(1957) on the diffusion of hybrid corn seeds in differ-ent geographical areas of the United States, and ofMansfield (1961) on the diffusion of 12 technologiesamong the largest enterprises of four sectors(bituminous coal, iron and steel, beer, and railroads)confirm this regularity in the diffusion process ofnew technologies.

Mansfield (1961) suggests that the representationof the temporal evolution of firms that have adopteda technology in an industry approaches logisticalgrowth function, known as Pearls law (Pearl, 1925).This function is symmetrical and in the shape of apositive S gradient. This is a growth function whichis frequently used in biology and social sciences tosupply models for every kind of diffusion process(epidemics, rumors, etc.). The underlying hypothesisin diffusion models that are based on the logistical


function is very simple: the speed to which the totalnumber of firms that adopt a new technologyincreases, depends on the number of firms that havealready assimilated it and the potential number offirms that have not yet incorporated it. Intuitively, thissame idea can be expressed in epidemiological terms:the speed with which a contagious disease is spreadis directly proportional to the number of peopleinfected to date and the size of the city that is poten-tially exposed to the disease.

Mansfield, after a series of manipulations andapproximations, transformed the function into ausable expression:

mij(t) = nij[1 + exp{ - (lij + wij t)}] - 1where:mij(t) number of firms that

have introducedinnovation up to theinstant t

nij total number of firmslij integration constantwijt rate of imitation

The form of this function will depend solely onthe parameter wijt that represents the rate of imitationwhich, in accordance with the adopted hypotheses, isa lineal function of: (1) the profitability of the instal-lation: pij; (2) the investment volume required for itsinstallation: Sij; and (3) the contingent variable withan expected null value that obtains the effect of othernon-specified variables: zij.

wij t = ai1 + ai2pij + ai3Sij + zij

In this representation of the diffusion process of atechnology in an industry (Fig. 1), there are threeclearly defined phases:

Fig. 1. Diffusion model.

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(1) There is great uncertainty in the results and theinvestment is risky. The number of firms thatincorporate the new technology is reduced. Thediffusion process is slow. The learning processbegins and the rate of technological performanceinnovation increases slowly.

(2) In the course of time the technology demonstratesits utility and achieves success. The diffusion pro-cess accelerates. The accumulated understandingaccelerates the increments in technological per-formance.

(3) As long as the proportion of firms that have notadopted it is less and/or the ones that lag behindopt for another new technology, the speed of dif-fusion is reduced. The technology approximatesits performance limit and its productivity dimin-ishes.

Since Mansfields research, countless empiricalworks have been offered. In them, other functionalexpressions of logistical growth function are sug-gested. Fisher and Pry (1971) employ a hyperbolictangent function to analyze the substitution process oftechnologies that were competing in the same indus-try. Lal et al. (1988) proposed a model in differentialterms that takes into consideration the time intervalthat the innovative potential uses to study and adoptnew technology. Meade (1989) and Oliver and Yang(1988) suggest that the diffusion process be analyzedin terms of probability by incorporating the likelihoodof market deciders adopting the new technology.

This logistical growth function has been utilizedprofusely in the modeling of diverse diffusion pro-cesses of new product technologies/processes in dif-ferent markets/industries: tractors and agriculturalmachinery (Oliver, 1981); household appliances andcolor televisions (Meade, 1988); industrial robots(Mansfield, 1989); new telecommunication techno-logies (Campisi and Tesauro, 1992); and oxigen-steeltechnology (Kumar and Kumar, 1992). Nonetheless,some works have indicated that this model, whichuses the diffusion of information or epidemics by con-tact as a paradigm, is analytically inadequate forexamining the diffusion of innovations, since thereare radical differences in the nature of these pro-cesses. Thus, it has been indicated that the static nat-ure of the diffusion model does not allow for increas-ing improvements in the performance of differenttechnologies (Metcalfe, 1981); nor does it establish,when considering each technology separately, inter-relations between the diffusion of different techno-logies that are integrated into the same technologicalsystem (Freeman et al., 1982).

In addition, diffusion of and access to information


about the characteristics of a new technology is onlythe first step in a complex, decision-making processthat will conclude with its incorporation into the firm.These criticisms seem to give direction to the searchfor factors which determine the diffusion speed ofinnovations towards other scopes that are closer to theprocess of making decisions at enterprise level. It willbe necessary to describe the mechanisms that deter-mine the diffusion of a technology, by relating themto their capacity to generate new products and/or cre-ate new markets; a capacity that, as a last resort, willbe determined by its technical performance.

Along the same lines, some studies have consideredexplicatory variables that reflect certain character-istics of the adopting firms and the nature of the tech-nology. Therefore, using the ideas proposed by Rog-ers (1993), Bass (1969) developed logistical modelthat could reflect different strategic behaviors of theagents. Bass distinguishes the innovative firms which,at the beginning of the process adopt the innovationautonomously, from the imitative firms which littleby little incorporate it after becoming influenced bythe contagion of the innovators. The logistical func-tion has also been employed by Mansfield (1968) toanalyze the intra-firm diffusion process. In this modelMansfield incorporates a series of commercial (sizeand cash-flow) and technological (performance andrisk associated with the adoption of a newtechnology) variables that are not ordinarily gatheredin the inter-firms diffusion models. Davies (1979) haspointed out that size is the commercial variable thathas greatest explicatory power, as it is usually corre-lated to other commercial variables such as: (1) learn-ing capacity to acquire and assimilate new techno-logies; (2) attitude towards risk; and (3) long-termobjectives of the firm.

Nonetheless, the majority of the research recog-nizes that the diffusion of innovation technologiesevolves by following average behavior patterns(identifiable by means of sinusoidal functions) similarto the one described by the S curve. The diffusionmodels are useful for studying the process of techno-logical change on a macro-level. On the contrary, itsapplications in the field of management are limited.At a commercial level, it is more important to modelthe evolution of the technological performance of aspecific innovation than to know the speed of dif-fusion.

Similarly, in the literature pertaining to manage-ment other concepts, closely related to diffusion mod-els, have come forth: life cycle models. These modelshave a fundamentally practical orientation. They areanalysis tools that help the adoption of strategic


decisions. In the following section, their principalcharacteristics will be described, as we point out theirsimilarities with the S curve model.

2.2 Life cycle concept

In different works in the field of management, theterm life cycle has been used to describe some genericmodels. These models represent the evolution ofindustrial sectors, products, technologies, etc. Themost widespread among them, initially formulated byLevitt (1965), is the one that refers to the life cycleof a product and describes the evolution of the volumeof sales over time.

Just as in the biological cycle of living beings, inthe life of a product, four stages can also be dis-tinguished: introduction, growth, maturity and decline(Fig. 2). Some research (Cox, 1967; Swan and Rink,1982; Tellis and Crawford, 1981) has demonstratedthat not all products go through a vital theoreticalcycle that is represented in the form of an S. However,numerous empirical studies have contrasted the val-idity of the model that adapts itself to a logistic func-tion in its first three stages:

(1) Introduction: a new product is introduced into themarketplace. Only one or two firms have enteredthe market, and the competition is limited. Therate of sales growth depends on the newness ofthe product. Generally, a product modificationgenerates faster sales than a major innovation.The technology performance of the innovationincreases slowly.

(2) Growth: a new product gains wider consumeracceptance and the objective is to expand therange of available product alternatives. Industrysales increase rapidly as a few more firms enterthe marketplace. To accommodate the growingmarket, modified versions of basic models areoffered. Successive incremental innovations

Fig. 2. Product life cycle model.


increase the technology performance rate of theproduct.

(3) Maturity: industry sales stabilize as the marketbecomes saturated and many firms enter to capi-talize on the still sizable demand. The possi-bilities of increasing product contributions arelimited. Innovations are less frequent. The tech-nology performance rate stabilizes.

It has been recognized that these models are basedon the theory of diffusion and adoption of innovations(Ansoff, 1984; Kotler, 1994) and that they are con-sidered to be conceptually derived from the diffusionmodels that were described previously. In large partthey complement the diffusion models in that, whilethese models enable us to predict the speed of techno-logical changes, life cycle models reveal their impacton markets and products (Betz, 1993).

One problem that has traditionally been associatedwith the use of these models is the definition of unitanalysis. Thus, depending on how branded products,product forms, product categories or industries aretreated, different life cycles can be developed. Theprocess of diffusing innovations is underlying all ofthese models. However, the intensity of the relationmay vary depending upon which analysis unit is chos-en.

The technological factor affects the product formsand brands to a lesser degree than the product categor-ies. The effects of fashion and other commercial vari-ables become watered down by the similarities withinthe total offering of manufacturers (product category).The duration of the different stages and the total lifeof the product depend on factors of a technologicalnature. When the diffusion speed of new technologiesis increased, product performance improves and/orthe efficiency of the processes increases. In Fig. 3 the

Fig. 3. Relationship between the technology life cycle and life cycles of pro-ducts.

M. Nieto et al.

existing relationship between the life cycles of thetechnology and that of the products is shown.

The life cycle model at the industry level has beenused profusely in the field of strategic management.Porter (1980) characterizes the evolution of an indus-trial sector by using the curve in the shape of an Swith which he distinguishes four defined stages bythe inflection points on the growth rate of total sales.Although this model acceptably describes the evol-ution of the majority of sectors, Porter recognizes itslimitations, and therefore, suggests that it is necessaryto consider all of the forces that condition the lifecycle of the sectors. These forces, known as evol-utionary processes, are of a dynamic nature and differwhen they are in divergent sectors. Of the evolution-ary processes analyzed by Porter (1980), at least fourhave a clear technological component: diffusion ofpatented knowledge, accumulation of experience, pro-duct innovation and process innovation.

Therefore, the link between technology and lifecycle at the industrial level seems far narrower thanat product or brand levels. Thus, the appearance ofnew technologies in many cases can create the emerg-ence of new sectors or the revitalization of alreadyexisting ones. In addition, the maturity and decline ofold technologies can induce the restructuring of somesectors, and in extreme cases, cause their disappear-ance (Dussauge et al., 1992). Keeping in mind thatthe life cycle of technology and the life cycle of sectoroften reveal the same phenomenon, some authors donot differentiate and integrate them into what hasbeen named industrial technology life cycle.

Although life cycle models may represent the mostfrequent standard of product and industrial evolution,some conceptual inconsistencies have been pointedout. The two most significant objections are: (1) theirquasi-tautologic nature (sales define the phases of theproduct life cycle that, at the same time, explain thesales); and (2) their large determinist component (ittries to describe a pattern of evolution that willinvariably occur) (Porter, 1980). According to this,the explanatory and predictive capacity of these mod-els is limited in so far as they do not incorporate vari-ables that determine the evolution of the cycle.

2.3 Technology life cycle and the S curve model

It has been noted that the concepts of sector lifecycle and technology life cycle are, in practice,closely related, as technological changes determine, toa great extent, the evolution of the industry. However,some authors have proposed life cycle models thatdifferentiate between technology and industry.


Since Abernathy and Utterbacks research (1975)about the evolution of product and process techno-logies, Ford and Ryan (1981) have defined the con-cept of technology life cycle. They propose a concep-tual standard that allows the base level oftechnological development to the application level ofdifferent technologies to be revealed. With this find-ing, they claim to guide the adoption of strategicdecisions, particularly as far as the sale of technologyis concerned.

The consulting firm Arthur D. Little (1981) hasdeveloped a technological life cycle model that rep-resents the evolution of the technologies with a sys-tem that is similar to the one used to reveal the lifecycle of an industry, but it utilizes, on the verticalaxis, some qualitative measure of technologicaladvancement. However, some of their consultants(Roussel, 1984) have recognized the need to quanti-tatively express the concept of technological perform-ance, as both upper management and engineersrequest more concrete data. According to its develop-mental phase (or technological maturity), the techno-logies are described as embryonic, growth, matureand aging (Roussel et al., 1991). Since this classi-fication, there tend to be recommendations for thestrategic management of technology.

Another way of creating a technology life cyclemodel which may resolve this problem is by usingthe S curve model. This is a function that relates theaccomplished effort in the development of a tech-nology with the results that are obtained. It is calledS curve because, when the results are graphicallydemonstrated, the curve that is usually obtained is asinusoidal line that resembles an S (Fig. 4). This func-tion is similar to the one used in models of innovationdiffusion. This model, initially conceived by RichardFoster (1986a), director of the consulting firm McKin-sey, has received widespread acclaim in the field oftechnology management.

Fig. 4. The S curve model.


Consistency and similarity between the differentphases of the S curve and the characterization of thestages in the life cycle of a technology in previousmodels are evident. In Fig. 5 the close relationshipbetween the technological categories, as proposed inArthur D. Littles model, and the S curve are indi-cated. Furthermore, the objective of these models isthe same: to verify the rationality of technologicalstrategies. In fact, by means of these models a firmcan know the situation in which a specific technologyis found at a particular point in time, as well as fore-see its future evolution and its developmental limits.

There is a great deal of empirical evidence that theS curve reveals the general evolution process of theperformance of technologies and that this finding sys-tematically repeats itself in all industrial sectors. Inaddition to the original works of Foster (1982a, b,1986a, b, c) other authors have developed theorieswith effective data. Becker and Speltz (1983, 1986)have proved that the technological performances ofinsecticides for agricultural use evolve in accordancewith patterns that are defined by the S curve. Lee andNakicenovic (1988) have analyzed substitutionphenomena among different technologies as they areemployed in the transportation sector (air, railway)and in the energy sector (gas, petroleum, electricity).Roussel (1984) has used the S curve to study derivedplastics and their application to the automobile indus-try.

Foster (1986a) pointed out that the progress of anew technology must never be represented in termsof time, but rather in terms of the actual investmentin its development (measured in monetary units, num-ber of researchers, hours worked, workers per year,etc.). If, on the contrary, it were represented in termsof time, no extrapolation could be carried out becausein the diagram, implicit assumptions about appliedforce would remain hidden. In this way, if the rateof investments changed, the time necessary for the

Fig. 5. Technological maturity and the S curve model.


performance of the technology to improve wouldincrease or decrease. Nonetheless, the difficultiesassociated with obtaining data about the investmentthat is made by different firms in the development ofa specific technology are often irreparable. Conse-quently, many empirical studies (Roussel, 1984;Becker and Speltz, 1983, 1986; Lee and Nakicenovic,1988) have modeled the technology performancesaccording to the time.

On the other hand, the parameter of the global per-formance value of a technology can be created uponestablishing a carefully measured sum of differentelements that reveal technical aspects as well as com-mercial ones. That is to say, two requirements shouldbe met (Foster, 1986a, b, c): It should express some-thing valuable for the client, and it should do so interms that make sense to the scientists and engineersof the company. If the performance parameter isdefined in a way that acceptably reflects all the tech-nological improvements that may affect the contri-bution (quality, safety and cost of the products), theS curve model would facilitate the understanding ofthe process of technological change. In this way,when the S curve is used as a performance model ofevolution of a specific technology, what it is demon-strating in reality is the speed at which incrementalinnovations in a given technology are produced.Therefore, if the performance parameter is definedadequately, the S curve model would provide reliableanalyses from which significant recommendations forthe design of technological strategies could bederived.

The gradient of any point of the curve reveals theproductivity of the investments in R&D (Fig. 6). On

Fig. 6. S curve and R&D productivity.

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the upper half of the S curve, past the point of inflec-tion, the productivity of R&D is decreasing. From thatpoint on, the productivity of technological invest-ments will only increase by abandoning the presenttechnology to adopt a new one. It is at that momentwhen it is most difficult to make this decision, as thetechnology is at its maximum performance and thereis little reason to risk investing in new technologies(Becker and Speltz, 1986). Likewise, it has beenpointed out that company management tends tounderestimate the speed with which the progress of atechnology takes place when it is found in the middleof the exponential growth phase (Twiss, 1986).

Representing the S curve of two or more alternatingtechnologies can be especially revealing. On manyoccasions there are different technologies which com-pete amongst themselves, each one with its own Scurve. When one of them successfully imposes itselfon another, a discontinuity appears: a rupture in theS curve is produced and a new one is now formed.Identifying a discontinuity at the moment in whichthe facts are being produced can be very difficult, butextremely useful.

Gathering all the information that is necessary toconstruct an S curve requires time and can be costly.Foster (1986a, b, c) recommends constructing thecurve only in those cases in which there are markeddifferences of opinion about which strategy to choose.In these cases, the value of the response can compen-sate for the cost of gathering information. In othercases, creating a collection of S curves that mayreveal different parameters of one technology can bemore useful than a single S curve (Lee and Nak-icenovic, 1988).

In addition, the S curve can be used in making pre-dictions. In fact, if it is possible to define reliable per-formance parameters, relating the early advances ofthese parameters to the realized investment and esti-mating what their limits are, a basis for evaluating towhat extent current technologies may improve and atwhat cost will be established. Likewise, when a com-pany foresees that a technology is near its perform-ance limit, it will no longer invest in it, as only smallimprovements will be achieved in exchange forcostly investments.

In general, the firm bases its strategic decisionsregarding the adoption of innovations inproducts/processes on analysis and foresight of theperformance of the technologies that they incorporate.The S curve model and life cycle models of tech-nology can, in general, be useful in designing stra-tegies, since they allow for the analysis and foresight


of performance potential of technologies. However, itis necessary to keep in mind that the S curve modelis a typical product of consultation. It was conceivedexclusively as a practical tool and therefore presentscertain inadequacies of a theoretical nature. This lim-ited theoretical base makes its application in theanalysis of concrete cases rather difficult.

As a theoretical conclusion, the existing linksbetween the previously described models are emphas-ized. On the one hand, the similarity between analyti-cal expressions that are used is evident: logisticalfunctions, Gompertz curve, etc. On the other hand,they all attempt to model some aspect of the processof technological change. Some emphasize the evol-ution of the performance technology, others the dif-fusion process or the effects on life cycle productsand industries. With these conclusions, our intentionis to use the solid theoretical and analytical foun-dation and the diffusion models of innovation toincrease the theoretical consistency to the S curvemodel and justify the methodology that is employedin the empirical studies.

2.4 Relations between the three types of models

These three types of models come from differentstudies and strive to use different phenomena as mod-els. Among them, it is possible to establish distincthierarchies in terms of their generality level, theirstage of formulation and their explicative capacity(Table 1). However, among them it is possible todetect certain similarities. These originate in the com-mon bond that connects all of these concepts: thetechnological factor.

In the field of industrial economy, models thatallow the analysis of the diffusion of innovations ata sectorial level have been proposed. The diffusionspeed of a technology will depend on the proportionof companies that have already adopted it, therequired investment volume, its profitability, thedegree of market concentration, the size of enterprisesthat do business in the sector, etc. These models areuseful at an additional level for making decisionsabout the design of industrial and technological poli-cies. However, they do not describe the nature of thedecision-making mechanism that induces the dif-fusion of innovations at firm level: increase of invest-ment in R&D in terms of the expectations of techno-logical performance increase.

Life cycle models describe the evolution of pro-ducts and/or markets at different levels (industry, pro-duct, brand). Emerging from studies in the fields ofmarketing and strategy, they have been employed


TABLE 1. Comparison of models

Model Phenomenon analyzed Analysis unit Main field Origin

Diffusion Diffusion and substitution Economic system History of technical change Griliches (1957); Mansfieldprocess of a technology over Industry Industrial economy (1961); Fisher and Pry (1971)

time MarketingProduct life cycle Evolution of sales of products Firm Marketing Levitt (1965)

based on the same technology Business unit Strategic managementover time

Industry life cycle Effects that the technological Industry Industrial economy Porter (1980)change has on the production Strategic managementvolume of an industry over

timeTechnology life cycle Effects that the evolution of the FirmBusiness unit Production management Abernathy and Utterback

technology has on the firm Strategic management (1975); Ford and Ryan (1981);strategy Technology management Roussel and Arthur D. Little,

Inc. (1981)S curve Technology performance over Industry Technology management Foster and McKinsey and Co,

time (or effort expended) Firm Inc. (1986)Business unit

intensively in support of strategic decision-making.Although in some cases these models may reveal theeffects of technological changes on markets and/orproducts, they do not provide information about thecauses that create them (variations of the performanceof the technologies).

Life cycle technologies strive to explain the evol-ution of technologies in exclusively technologicalterms. This family of models clearly reveals the evol-ution of the performances of the technologies. Theevolution of the performances of a technology is thevariable that explains its speed of diffusion, and thatconditions the life cycle of the products/industries thatincorporate it. Of all the technological life cycle mod-els, the S curve, which connects the investment oftechnology with the performances that it generates, isthe one that shows a greater usefulness in formulatingtechnological strategies. However, the S curve modeldoes present difficulties of a practical nature in sel-ecting and evaluating the performance parameter andin calculating the total cost of the investment.

In spite of the fact that they come from differentareas of study and represent different phenomena,these families of models have a common nexus. Onthe one hand, the S curve models variations in theperformance of a technology based on the effort inR&D which is realized in its development and/ortime. On the other hand, the diffusion process of inno-vations has been modeled as a consequence of thetechnological performance explicatory variable.Along these lines, Betz (1993) has identified someconnections between the technological performancevariable and the diffusion process of new techno-logies:


I If the new technology brings forward a non-exist-ent functional capacity, it will create new marketsand its speed of diffusion will depend on theincreases in the technical performance that it gener-ates. These increases in performance will contrib-ute to the widening of the markets, by means ofnew products and/or cost decreases.

I If the new technology does not create a new func-tional capacity and only substitutes an alreadyexisting one, its speed of diffusion will depend onthe relationship between performance improve-ments and costs.

I The speed of diffusion will depend on the characterof the new technology, whether it deals with radicalinnovation followed by increasing improvements,or it deals exclusively with a series of increasingimprovements that, through accumulation, provokea radical change within time.

These three relationships emphasize the role oftechnology performance as an inductor mechanism ofthe diffusion process of innovations. This explainswhy the technological performance variable of a spe-cific technology (modeled by the S curve) follows abehavior pattern which is similar to the one describedby the diffusion models of innovations.

Consistent arguments can also be found to relatethe life cycles of products/industries to the life cyclesof their principal technologies. On the one hand, theevolution of the technological performance of a tech-nology conditions the life of the products that incor-porate it. If the increases in technological perform-ance are perceived by the market, they will betranslated into increases of volume in sales (Ansoff,1984). On the other hand, the performances of princi-

M. Nieto et al.

pal technologies that characterize an industry, deter-mine the life cycle and define the competition. In fact,the transition between the principal phases in theevolution of an industry (birth, development,maturity, decline or revitalization) have beenexplained according to the performance of their tech-nologies (Porter, 1980).

3. ANALYSIS OF THE TECHNOLOGY OF DSPS

The S curve allows for the evolution model of theperformance of any technology. In spite of not beinga very precise tool of technological foresight (Lee andNakicenovic, 1988), the S curve can be very usefulin orienting the technological strategies of firms. Infact, this model supplies information: (1) about themagnitude of effort necessary to obtain a determinedincrease in the productivity of a technology; and (2)about the existence of natural limits in its perform-ance.

The use of the S curve model to analyze a particulartechnology poses diverse difficulties of a practicalnature. The literature has recognized: (1) the difficultyof estimating the parameter of technology perform-ance; and (2) the near impossibility of obtainingreliable information about investment that is made inthe development of different technologies. Theempirical research that has been published hasresolved these problems in different ways. Generallyspeaking, in these studies the adopted solutions havenot been justified in relation to existing scientificliterature, nor have they been articulated in an operat-ive methodology.

Having established the theoretical basis of the Scurve model, the second part of this paper will bedevoted to the problems that arise when putting it intopractice. The structure of the operative methodologydeveloped to analyze the technology performance ofDSPs will be discussed. This methodology can be out-lined in three phases:

(1) selection of the technology to be analyzed;(2) definition of the technology performance indi-

cator; and(3) construction of the S curve.

In the following section, the principal problems thatarise in each of these phases will be described andpossible solutions will be suggested. At the sametime, the analysis results of the technology of DSPswill be presented.


3.1 First phase: selection of the technology to be analyzed

Little attention has been given to this phase in mostof the empirical research that has been carried out todate. In our opinion, this aspect is critical, as an incor-rect selection of the technology to be studied can cre-ate errors in the strategic analyses and lead to the for-mulation of inconsistent technological strategies.

The selection of the technology poses three differ-ent problems. In the first place, it is necessary toidentify the technology in a precise way in order todifferentiate it from others that have similar character-istics or that perform the same functions. Secondly,it is necessary to evaluate the role of the technologyin relation to the technological system in which it isimmersed. No technology can be analyzed in an iso-lated way without taking into account the interactionsof other technologies within its technological system(Metcalfe, 1981; Freeman et al., 1982). Finally, it isnecessary to evaluate the impact of the technology onthe present and future activities (products/processes)of the firm. These aspects are closely related andtherefore should be analyzed together. In all certainty,if in this first phase a faulty selection of the tech-nology to be analyzed is produced, the S curve modelwill lead to erroneous and irrelevant conclusions.

The selection of a technology of DSPs was madeas a result of two complementary analyses: (1) theidentification of the technology to analyze; and (2)the evaluation of its impact on the technological sys-tem. On a commercial level, the impact of DSPs onthe activities was not evaluated, as this was not anobjective of our study. If this analysis had presenteditself for a specific firm, the impact of the technologyon its activities would have had to be analyzed.

3.1.1 Identification of the technology of DSPsIdentifying a technology consists of differentiating

it from others that have similar characteristics or thatperform the same functions. In our case, the DSPs aremicroprocessors which belong to the extensive familyof digital devices. The basic function that DSPs per-form is to digitally process the signal. As an alterna-tive, the signal can also be processed analogicallyusing other semiconductor components. Therefore,the first step in our analysis consists of clearly ident-ifying the DSPs so as not to confuse them with othermicroprocessors with similar characteristics or withother semiconductor components that perform thesame function analogically (Table 2).

Up until the end of the 1970s, signal processingwas achieved, in large part, by using analogic techno-


TABLE 2. Semicondutor devices and components

logies. The appearance of the first DSPs in approxi-mately 1979 provoked a discontinuity in the tech-nology of signal processing, shifting all analogicsystems towards digital systems. The main problemsthat arise with signal processing systems based onanalogic electronics are their low versatility and lim-ited capacity for processing complex algorithms. Ver-satility depends on the programming possibilities ofthe device. In spite of the fact that analogic processingsystems can incorporate the characteristic of pro-grammability, they are not comparable to what a DSP,designed specifically for signal processing, can offer.In fact, a DSP enables the programming of any algor-ithm that will determine the desired signal treatment.The DSPs are essentially high speed microprocessorsdesigned to develop signal processing algorithms withelevated calculations.

In a DSP, the limitation at the time of executing analgorithm for signal processing is its velocity. Digitalprocedures are found to be disadvantageous in appli-cations where great speed is required. Therefore, it isessential to realize them by using analogic techniques.It is important to point out that, due to technologicalimprovements and the optimization of informal struc-tures, the speed of DSPs has been increasing dramati-cally in recent years. Nonetheless, analogic signalprocessing is not likely to disappear. Currently a grad-ual transition in signal processing technologies is tak-ing place. It is necessary to consider that the firstDSPs were quite slow and although they solved theproblem of complicated assembly, when the demandfor greater velocity increased, it was necessary to turnto analogic technology.


3.1.2 Incidence of DSPs in information andcommunication technologies (ICTs)

In order to complete the selection of the technologyof DSPs, it is necessary to evaluate the role that DSPsplay in relation to the technological system in whichthey are immersed. It is quite clear that DSPs and allsemiconductor devices are the foundation ofmicroelectronic technologies and the support of theentire technological system of information and com-munication technologies (ICTs). This system includesall techniques that are related to the generating, trans-mission, reception, storage and processing of infor-mation, as much for human communication as for thatamong machines. The spectrum of technologies thatembraces this definition is extensive as it includesvery concrete applications (automatic, robotic, arti-ficial intelligence) that can be used in differentenvironments as well as support technologies(microelectronic, optoelectronic). Therefore, ICTs canbe characterized as a technological system whosemodules constitute a chain in which each link uses,out of necessity, the previous one until the final appli-cations are realized. This concept is visualized in Fig.7, in which the different elements that form the tech-nological system of ICTs are defined: support techno-logies, information and communication technologiesin the strictest sense, derived technologies, and comp-lementary technologies.

DSPs are the base of this technological chain andfulfill the task of supporting the functional develop-ment of ICTs. The technologies that are incorporatedinto the DSPs have no utility themselves if they arenot applied in their natural area of incidence. There-

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Fig. 7. Information and communication technologies system.

fore, DSPs, being typical support technologies, facili-tate the realization of the majority of functions thatare required in the equipment and the systems that areused by ICTs.

The large growth of these devices that the marketis experiencing and the optimistic expectationsregarding their development in the future can beexplained by their multiple applications in the scopeof ICTs. In addition, DSPs using digital techniqueshave made processing possible in real time of signalsof elevated width band and have provoked a clearbreaking-off with the analogic technologies used todate. It has been confirmed that the revolution thatthese devices have provoked can be compared to theone that the first microcomputers caused in the 1970s.

Digital computing tasks can be divided into twoclasses. Data processing operates on numbers thatrepresent textual and numerical information. Signalprocessing operates on numbers that represent real-world signals such as speech and vision. Data pro-cessing applications have dominated the computermarket and the semiconductor components marketover the past decades. DSPs components will becomea major growth area in the semiconductor componentsmarket over the next few years for two reasons (PriceWaterhouse, 1994):

I Applications pull such as digital audio for enter-tainment (Compact Disc, Digital Audio Tape),digital telecommunications (ISDN), digital TV,video-conferencing, speech input and output tocomputers, and computer vision.

I Technology push such as increased processingspeeds, greater storage capacities and new algor-ithms.


3.2 Second phase: definition of an indicator of the technologyperformance

After having identified the technology of DSPs andevaluated its impact on the system of ICTs, it isnecessary to define a parameter that allows for thetrue evaluation of its performance. This second phasehas transcendental importance, as one incorrect defi-nition of the performance parameter could invalidatethe analysis results. The definition of this parameterposes some problems which, in research done to date,have been resolved in different ways.

In some studies the technology performance hasbeen estimated based on scientific/technical efficiencyindicators, without taking into account commercialaspects. In this way, Roussel (1984) modeled the rateof performance increase of the resilient foam cushion-ing technology based on the number of related scien-tific articles that were published. In his study, Rous-sels underlying hypothesis is that increments in thenumber of significant publications about a determinedtechnology reflect increments in the level of under-standing of it, which normally is converted intoimprovements in the products that incorporate it.Nonetheless, this is often not the case. Progress inscientific understanding about a determined tech-nology does not always translate into identifiableimprovements for the marketplace.

On the contrary, other studies have measured thetechnology performance with criteria and variables ofa commercial nature. In this way Becker and Speltz(1983, 1986) estimated the performance incrementsof different chemical compounds for the productionof insecticides based on the number of new productsthat were introduced into the marketplace. These


authors maintain that a new chemical compound rep-resented some improvement in terms of cost, spec-trum, market niche and the like over those productsalready in the marketplace. The problem with thisindicator is that the degree of newness of a productdoes not necessarily reflect an increase in technicalefficiency. It is true that consumers often associate themodification of certain product qualities with techno-logical improvement. Nonetheless, defining a para-meter based exclusively on commercial criteria is oflittle use when making technological decisions. Itmust be understood that researchers and engineers inthe R&D department can only quantify their findingsin the development of a determined technology byusing physical/technical units.

Foster (1986a) emphasizes that the parameter mustreflect technical characteristics which are easilymeasurable and, at the same time, recognizable by theclients. On the one hand it should reflect theexpressed performance in physical/technical units. Itis highly recommended that it be defined by engineersfrom the firm using variables that are easily quantifi-able by the personnel of R&D. At the same time, itshould reflect perfectly identifiable attributes or qual-ities which synthesize the most significant propertiesand characteristics of the technology in accordancewith their impact on the marketplace. In this way, anyincrement in the physical/technical performance of atechnology will also reflect an improvement in thecontributions of the products that incorporate it.

Additional difficulties can arise when defining theindicator. The main problem is related to the selectionof the most adequate performance parameter for eval-uating a specific technology. In this way, Lee andNakicenovic (1988) have suggested elaborating awide range of alternative indicators using a processof trial and error to reject the most ineffecient.

Another problem has to do with the engineerstendency to define performance parameter on thebasis of fundamental physical variables instead ofconsidering physical variables of configuration. Thisdifficulty has been pointed out by Ayres (1994) afteranalyzing the performances of different technologies(vacuum technology, semiconductors, computers, par-ticle accelerators). According to Ayres, the tech-nology performance should be defined using variablesthat reflect intrinsic properties of the materials thatare employed and in the configurations in which theyare used (configuration variables). On the contrary, ifthe parameter is defined on the basis of variables thatare used in the enunciation of fundamental physicslaws (fundamental variables) they would producebiases in estimating performance. In fact, the factors


that limit performance increases of a technology arerelated to the physical properties of the materials thatconfigure it at that moment. It is obvious that the fun-damental laws of physics establish a definite limit tothe development of any technology, but this is of littleinterest since the limit is rarely attained.

Finally, cultural differences and communicationbarriers that exist bewteen the R&D engineers andmarketing personnel can cause additional difficulties.This problem has been widely studied in managementliterature (Brockhoff and Chakrabarti, 1988; Gupta etal., 1986; Norton et al., 1994). In order to resolve it,numerous solutions have been proposed: developingin-service programs to facilitate communication andunderstanding among the personnel of both R&D andmarketing departments (Millar, 1989); the implan-tation of organizational structures to favor interdepart-mental cooperation (Carroad and Carroad, 1982); reg-ular, short-term transfers of personnel from bothdepartments (Schmitt, 1985; Souder, 1980), etc. Allthese measures contribute to making both groupsincrease their field of vision from what they considertheir own responsibilities (Szakonyi, 1988). In thisway, on the one hand, the technicians would concernthemselves more with the needs of the clients, and onthe other, those on the commercial end would under-stand the technical difficulties.

3.2.1 DSPs efficiency parameterAs with all complex mechanisms, DSPs have

numerous characteristics that can be used as tech-nology performance indicators: longitude of data withwhich it can work, internal memory, capacity to directmemory, etc. In Table 3 we can see the main technicalcharacteristics of a sample of 29 DSPs that were intro-duced into the marketplace between 1976 and 1995.In the last column the parameter efficiency values areindicated. This parameter has been defined on thebasis of two characteristics of the technology of DSPswhich are easily quantifiable by R&D engineers:cycle time and data time. The efficiency parameter canbe obtained by dividing the data type with which theDSP can work and its cycle time. The results are stan-dardized with respect to the information receivedfor ADSP21060.

After evaluating different alternative indicators, wehave opted to define efficiency based on cycle timeand data time for two fundamental reasons: (1) theyare the most representative characteristics of the totalsum of configuration variables, as they depend on theproperties of the semiconductor material that is used(silicon) and on the current architecture of themicroprocessors; and (2) they directly affect the pro-

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TABLE 3. Main characteristics of a sample of 29 DSPs

Year Model Family Manufacturer Data type Cycle time (ns) Efficiency

1978 S2811 Fixed AMI 12 300 1.0037E-361980 uPD7720 Fixed NEC 16 250 1.9275E-351982 TMS32010 Fixed Texas Instruments 16 390 1.2356E-351982 HD61810 Fixed Hitachi 12 250 1.2047E-361983 MB8764 Fixed Fujitsu 16 100 4.8188E-351983 6386 Fixed Toshiba 16 250 1.9275E-351985 TMS32020 Fixed Texas Instruments 16 195 2.4765E-351985 uPD77220 Fixed NEC 24 100 1.2353E-321985 WEDSP32 Floating ATT 24E8 160 0.15621986 ADSP2100 Fixed Analog Devices 16 125 3.8551E-351986 LM32900 Fixed National 16 100 4.8188E-351986 uPD77230 Floating NEC 24E8 150 0.1661987 TMS320C25 Fixed Texas Instruments 16 100 4.8188E-351987 DSP56000 Fixed Motorola 24 74 1.6671E-321987 MB86232 Floating Fujitsu 24E8 150 0.1661988 DSP16 Fixed ATT 16 55 8.7617E-351988 ADS2101A Fixed Analog Devices 16 80 6.0235E-351988 WEDSP32C Floating ATT 24E8 80 0.3121988 TMS320C30 Floating Texas Instruments 24E8 50 0.51990 TMS320C50 Fixed Texas Instruments 16 50 9.6375E-351990 ADSP21010 Floating Analog Devices 24E8 50 0.51992 ADSP21020 Floating Analog Devices 24E8 30 0.8331992 DSP32C Floating ATT 24E8 50 0.51993 TMS32C50 Fixed Texas Instruments 16 40 1.2047E-341993 TMS320C30 Floating Texas Instruments 24E8 40 0.6251994 DSP1610 Fixed ATT 16 25 1.9275E-341994 TMS320C31 Floating Texas Instruments 24E8 33 0.7581994 ADSP21060 Floating Analog Devices 24E8 25 11995 TMS320C5x Fixed Texas Instruments 16 25 1.9275E-34

duct offerings that incorporate DSP components andthey are easily identifiable by their users.

Nevertheless, these characteristics will have greaterimportance according to the application that the userwishes to carry out. It can be believed that the mostimportant of these qualities is the processing speed(cycle time). In Fig. 8, the evolution of cycle timecan be observed. The time consumed in processing aninstruction has gone from 300 split seconds in 1979 to25 in 1995. In the first approximation, this progressivereduction in the instruction cycle duration reflects anincrease in the DSPs technology performance.

Fig. 8. Cycle time evolution.


However, the parameter cycle time in itself cannotsufficiently explain the performance of the DSPs. Itis possible to find one device with less speed thananother which is, at the same time, capable of realiz-ing operating calculations with a higher performance.Therefore, it is necessary to consider another factor,equally as important as the speed of processing: theformat that is used to represent the data (data type). Ifthis parameter is considered, processors can be brokendown into two families: those that operate in fixedpoint and those that do so in floating point (see Table3). With the first format an inferior values ranking ofdata type is obtained. On the other hand, the floatingpoint is a more dynamic margin and a greater volumeof data can be treated. To evaluate the performanceobtained from the technologies of the DSPs, the twofamilies should be analyzed.

3.3 Third phase: construction of the S curve

Once a technology performance indicator isdefined, it is necessary to construct the S curve. Con-structing the S curve consists of representing the tech-nology performance evolution based on an explica-tory variable. To do this, Foster (1986a) recommendsrelating the performance improvements with the effortexpended in the development of the technology.Without any doubt, the technology effort variable hasgreat explicatory capacity. To measure this variable,


numerous indicators have been proposed: expensevolume in R** Unknown entity - D ** the number ofresearchers and engineers dedicated to R** Unknownentity - D ** years of research, etc. Nonetheless, theproblem that occurs when it comes to obtaining con-crete data about the effort expended by a specific firmin the development of a concrete technology is note-worthy. The strategic nature of this informationmakes the firms resist spreading this data, which, inturn, makes the creation of empirical studies quite dif-ficult.

Most of the published studies have resolved thisproblem by using the dimension of time to constructthe S curve. In this way, the research of Roussel(1984), Becker and Speltz (1983, 1986), Lee and Nak-icenovic (1988), Hilbrink (1990) and Ayres (1994)regarding the impossibility of obtaining informationabout the technology effort has represented the evol-ution of the performance parameter based on time.

Along the same lines, the analysis of DSP tech-nology was realized as a result of the temporal evol-ution of the efficiency parameter. We are aware thatthis option does not fulfill one of the basic recommen-dations made by Richard Foster. To a certain extent,by relating the evolution of technology performancewith time, instead of expressing it based on the tech-nological effort, one of the fundamental elements ofthe S curve model is being modified. We concur withFoster in pointing out that the mere passage of timedoes not provoke performance increments in a tech-nology and that the time variable, in itself, lacksexplicatory capacity.

Nevertheless, solid arguments can be found to jus-tify the representation of the S curve based on time.In the first place, the definition of the S curve couldbe justified based on time using the same argumentsthat support the use of time series models in otherfields. Time series models have been and are usedin varying fields of economy and management withimpressive success. These models allow for thebehavior analysis of variables and establish predic-tions about future values bases on historical data.

Representing technology performance based ontime is an attempt to explain its evolution by usingthe analysis of its behavior in the past. This claims:(1) to accept that the technology performance variablehas the capacity to explain itself; or (2) on the con-trary, to recognize the impossibility of relating itsbehavior with other variables. According to this lastalternative, the temporal dimension of the S curvemodel would hide a multitude of potentially explica-tory variables that the researcher cannot quantify.


Developing this argument, Butler (1988) pointedout that the accumulation of knowledge is the princi-pal explicatory variable behind performance increasesof a technology. Influencial scholars (Utterback,1994; Nelson and Winter, 1982) have attributed a sig-nificant role to the experiential effect and to theaccumulation of knowledge in the process of inno-vation technology. Recently, Nonaka and Takeuchi(1995) have studied the learning processes, ident-ifying the factors that determine the accumulation ofknowledge. According to this research, claiming toexplain the improvement in the performance of a spe-cific technology exclusively by using the increases inexpenses in R&D and/or in the number of researchersis an oversimplification of reality.

It has been pointed out that there are numerous fac-tors that are difficult to quantify which are related to(intangible) resources and (dynamic) capabilities thatdirectly affect the results of effort on R&D in a con-crete firm (Mahoney and Pandian, 1992; Peteraf,1993). Only if the technological effort makes learningand accumulation of knowledge easier will the resultsindicate an increase in technology performance. Thisimplies that the performance increment of techno-logies is not a lineal process. This is a long, uncertainand accumulative process in which the past conditionsthe future and where there is a lack of economies withrespect to time (Dierick and Cool, 1989). The techno-logical effort that contributes to the accumulation ofknowledge about a technology, as with other intan-gible claims of a firm, constitutes, at the same time,an input and an output (Imai, 1987). In addition, tech-nological understanding is quite tacit and thereforedifficult to quantify.

These observations add arguments that contributeto the justification of the construction of the S curvebased on a temporal dimension. Recognizing theinfluence of the learning process implies reducing theexplicatory capacity of the technological effort vari-able. The results of the effort expended in the devel-opment of a technology will depend, to a large extent,on the learning capacity of the firm that gives the verymagnitude of effort. Consideration of the learningeffect and the difficulty in estimating the value of thetechnological effort, have made the performance evol-ution of DSPs based on time advisable.

3.3.1 Evolution of the technological performance ofDSPs

In accordance with previous reflections of theanaylsis of the technology performance of DSPs, theevolution of efficiency parameter values over timeshould be represented. Fig. 9 shows us the perform-

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Fig. 9. Efficiency evolution.

ance evolution of DSPs in general, including thoseof fixed point as well as those of floating point. Theefficiency values have been represented only for thoseyears in which an improvement is produced. It ispossible to observe that the efficiency of the familyof DSPs that work in fixed point is practically non-existent, while the evolution of the efficiency of theDSPs that work in floating point increases exponen-tially starting in 1985. This is because, in the firstfamily the evolution of data type was negligible andthe instruction cycle time diminished slowly, whilein the second family the data type takes off, as theinstruction cycle time diminishes. In this way,efficiency increases considerably. In this figure twophases can be distinguished. One phase stands outduring the first few years (19781985) in which per-formance scarcely increases. After that period, whichcould be characterized as an apprenticeship, and as aresult of accumulated knowledge, the technologyimproves its performance in a way that becomesexponential from 1987 on.

The next issue that is discussed in this analysis isthat of estimating the efficiency limit of the family ofDSPs that work in floating point. Of all the appli-cations used to determine performance limits, the Scurve model is possibly the most well-known. Know-ing when a technology has reached its perfomancelimit is vitally important to a firm. This informationshould help to orient its technological strategy, as theproximity to limits increases the probability that tech-nological ruptures may be produced. In this situation,investing resources in the development of a tech-nology that is near its limits accentuates the risk of notobtaining the anticipated technological performances.The appropriate thing to do would be to invest in thedevelopment of technologies of an emerging nature.

The main difficulty that arises when it comes todetermining the performance limit of a technology is


estimating, beforehand, the precise data to representthe final phase of the S curve. From a mathematicalpoint of view, in order to represent a logistical func-tion, it is necessary to know (Foster, 1986a): a certainnumber of historical values, the inflection point andthe superior limit or an estimation of time that it takesto reach it. To resolve this problem, Foster suggestsapproximating these values with qualitative provisiontechniques. However, it should be emphasized thatthe principal usefulness of the S curve model is inanalyzing the evolution of performances in order tounderstand what has happened and to verify therationality of the technological strategies. Therefore,it seems unreasonable to insist on graphic represen-tations of the S curve of a high degree of precision.

Fig. 10 shows the forecasted evolution of theefficiency of floating point DSPs. The estimation wasformulated on data obtained to date. It is presumedthat in 1994 an inflection point in the logistical func-tion is produced and that the maximum efficiency thatcan be obtained with this technology is 2. We can seethat this family of DSPs is found in an exponentialgrowth phase. This leads us to believe that the ceilingin the efficiency of floating point DSPs will not bereached at least within the next 10 years.

4. CONCLUSIONSIn accordance with the proposed objectives, the

conclusions that are drawn in this paper can begrouped into two different categories. Some areobservations of a theoretical nature and others arepractical recommendations.

The theoretical reflections, that can be found inSection 2, have allowed us to relate the S curve modelto diffusion and life cycle models. Initially weattempted to use these relationships to increase the

Fig. 10. S curve model and the efficiency evolution of DSPs.


theoretical and analytical consistency of the S curve.For this reason, the origin and conceptual foundationsof these diffusion and life cycle models have beenanalyzed, pointing out the existent similaritiesbetween these and the S curve model. With the excep-tion of certain methodological differences, it hasbecome evident that the technological factor consti-tutes a solid nexus among these models. Accordingto this, the following observations can be made:

I the diffusion speed of a technology depends, tolarge extent, on the evolution of its technologicalperformance;

I the life cycles of products/industries are con-ditioned by the evolution of the technology per-formances that characterize them; and

I of all the life cycle models of technology, the Scurve model is the one that best reflects the evol-ution of technology performance.

With this theoretical analysis, we have intended tocontribute to the elimination of the barriers that havetraditionally separated research in the fields of econ-omy and management. Progress in both the under-standing of technological change and the developmentof technology management make it essential for us tomake an effort to coordinate these two fields ofresearch. The passage of knowledge and the termino-logical normalization are essential requirements inorder to produce significant advances in both theunderstanding and the nature of the process of inno-vation technology. With these theoretical conclusions,we have intended to enhance the hypothesis about theexistence of conceptual relationships between modelsof different origins: diffusion models (industrial econ-omy, marketing), life cycle models (strategic manage-ment, production management, marketing), S curveand technology life cycle models (technologymanagement). It would be profitable if, in futureresearch, the study of the relationship between thesethree family models were further investigated. Point-ing out empirical contrasts and the analysis of the cor-relation between the life cycles of products/sectors,diffusion speed and the evolution of the technologyperformance of different technologies can contributeto this advancement.

The second series of conclusions have a clear prac-tical orientation. The analysis of the technology ofDSPs has served to develop an operative method-ology that helps to implement the S curve model. Theproblems that the practical application of the S curvemodel presents are grouped into three phases thatdefine this methodology: (1) the selection of the tech-nology to be analyzed; (2) the definition of the tech-nology performance indicator; and (3) the construc-


tion of the S curve. The analysis of the technology ofDSPs using the proposed methodology has allowedus to verify that this technology is found in a stageof growing productivity which is characterized by:

I experiencing exponential increases in perform-ances measured by the efficiency parameter; and

I being even further from having reached the limitof its technological performance.

The relationships that have been defined in thetheoretical findings allow us to widen the scope ofthe conclusions. Based on these relationships, impli-cations of increases in technology performance ofDSPs can be derived. In fact, keeping in mind theexisting relationship between the diffusion processesof innovations, life cycle models and the S curvemodel, the following conclusions can be made:

I it is logical to expect the technology of DSPs tobe adopted by a growing number of enterprises,and to experience large diffusion in the comingyears;

I considering DSPs as intermediate products that areincorporated into other final products (since theyare support technologies in the system of ICTs)their sales will increase extraordinarily; and

I these technologies will modify the life cycle of theproducts that incorporate them, generally by pro-longing it. The same could be said of the evolutionof industrial sectors where these technologies areapplied.

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Mariano Nieto is a Professor of OperationsManagement and Technology Managementat Universidad Complutense de Madrid,Spain. Previously, he was teaching at theUniversidad Politecnica de Madrid. His pri-mary research field is strategic managementof technology and innovation, with manag-ing product development as a supplementaryfield of interest. He holds a Ph.D in Econom-ics and Business Management from Univer-sidad Complutense de Madrid (Spain). Apartfrom his current academic tasks, he has doneextensive consulting work and research projects, primarily related totechnology management.

Francisco Lopez has a Ph.D. in Telecom-munications from Universidad Politecnicade Madrid. He is Professor and Chairman ofSignal and Communication Theory Depart-ment at Universidad de Alcala de Henares,Madrid, Spain. Previously, he was Professorand the Head of the Circuits and SystemsEngineering Department at Universidad Pol-itecnica de Madrid. His main research inter-ests are in digital signal processing, filterdesign (fixed and floating point realizationsfor minimum roundoff noise digital filters)wavelets and multirate filter banks.

Fernando Cruz received the M.S. of Tele-communications degree from the Universi-dad Politecnica de Madrid. He worked in theDepartment of Development Engineering inTelettra, Spain. He has been Professor in theDepartment of Circuits and Systems Engin-eering at Universidad Politecnica de Madridsince 1990. His research interests are in digi-tal signal processing (filter design) andmultirate filter banks.

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