Computers in quantitative gas chromatography : an assessment of processing technique accuracy

Computers in quantitative gas chromatography : an

assessment of processing technique accuracy

Citation for published version (APA):

Baan, A. (1975). Computers in quantitative gas chromatography : an assessment of processing technique accuracy. Technische Hogeschool Eindhoven. https://doi.org/10.6100/IR28555

DOI:

10.6100/IR28555

Document status and date: Published: 01/01/1975

Document Version:

Publisher’s PDF, also known as Version of Record (includes final page, issue and volume numbers)

Please check the document version of this publication:

• A submitted manuscript is the version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website.

• The final author version and the galley proof are versions of the publication after peer review.

• The final published version features the final layout of the paper including the volume, issue and page numbers.

Link to publication

General rights

Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain

• You may freely distribute the URL identifying the publication in the public portal.

If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license above, please follow below link for the End User Agreement:

www.tue.nl/taverne

Take down policy

If you believe that this document breaches copyright please contact us at:

openaccess@tue.nl

COMPUTERS IN

QUANTITATIVE

GAS CHROMATOGRAPHY

An assessment of processing

technique accuracy

Proef schrif t

Ter verkrijging van de graad van doctor in de

technische wetenschappen aan de

Techni-sche Hogeschool te Eindhoven, op gezag van

de rector magnificus, prof.dr.ir.G.Vossers,

voor een commissie aangewezen door het

college van dekanen in het openbaar te

ver-dedigen op vrijdag 24 januari 197 5 te 16.00

uur

door

ARIE BAAN ,

1\

.\M~h

\

cvi- 4

~,

L

\~

'-\

geboren te Dordrecht

Dit proefschrift is goedgekeurd door de promotoren

Prof. Dr. Ir. A.l.M. Keulemans en Prof. Drs. J .H. van den Hende

CONTENTS

1. INTRODUCTION

7

1 . 1 Necessity of automation

7

1. 2

Performance of gas chromatography 8

1.

3

Description of contents 10

References 11

2. USE OF DIFFERENT TYPES OF COMPUTERS IN

GAS CHROMATOGRAPHY

13

2. 1 Computer and gas chromatography

13

2.2

Historical developments and current trends 14

2.3

Review of various approaches

15

2 .4 Relevancy of the subjects of this thesis

18

2.S

Example of a distributed-function approach

18

References 19

3.

SHAPE OF GAS-CHROMATOGRAPHIC SIGNALS 21

3. 1

Necessity of a descriptive model

21

3.2

Gas-chromatographic peak shape

21

3.3

Applicability of convolution-function model

23

3.4

Origin of the distortion

27

References

32

4. ACQUISITION OF SIGNALS

35

4. 1 Components

35

4.2

Detector amplifier

35

4.3

Transmission lines

37

4.4

Multiplexer and amplifier

38

4.5

Sampling

39

4.6

Quantisation

40

4.7

Evaluation

43

References

44

5. DATA CONDITIONING: SMOOTHING

47

s .

1 Filtering

47

5.2 Digital-filter implementations

47

5. 3

Filters for smoothing

50

5.4

Performance of smoothing filters

SI

5.5

Noise suppression of smoothing filters

63

5.6

General remarks on smoothing 68

6. PRIMARY DATA REDUCTION: PEAK (-GROUP) DETECTION

71

6. 1

Peak-detection methods

71

6.2

Performance of differentiating filters

74

6.3

Noise suppression of differentiating filters

89

6.4

General remarks on differentiating filters

94

6.5

Limitations of peak detection

94

References

101

7. SECONDARY DATA REDUCTION : AREA DETERMINATION

103

7 .1

Area determination

103

7.2

Curve reconstruction

103

7.3

Baseline determination

105

7.4

Systematic errors in peak detection and area determination

106

7.5

Influence of noise on precision

113

7.6

Experimental verification of systematic errors

118

References

121

8. APPLICATION TO QUANTITATIVE-ANALYSIS PROCEDURES

123

8. 1

Quantitative analysis

123

8.2

Example of performance with and without computer

124

8.3

Area apportionment of overlapping peaks

127

References

128

9. CONCLUSIONS

131

Appendix I Convolution-function model

133

Appendix II Derivation of filter frequency-response expressions

139

Appendix III Estimation of model parameters from experimental

curves

143

Appendix IV Example of estimation ofquantitative-analysis

error for a given gas chromatogram

145

LIST OF SYMBOLS

152

Summary

154

Dankwoord

156

Noch ein Buch, noch ein gro{ks Buch? Tausend aufgeblasene Seiten?

In welche Reihe stellst du dich, und ist nicht alles besser, was schon da ist? Mach dir nichts draus,

alles mu(3 wieder gedacht werden. Elias Canetti Aufzeichnungen 1949-1960

1 . INTRODUCTION

1 . 1 . Necessity of automation

Progress in the instrumental-analysis branch of analytical chemistry can be characterised by two main aspects :

Expansion of the number of methods by which relevant physical properties of chemical compounds can be measured;

Continuous improvement of resolution and precision of existing methods.

The latter development has resulted in more and more information being produced in each analysis. At the same time, and of even higher importance, greater demands are made on the processing of this information, to retain the precision reached. This has led to a rapid growth of the application of digital-processing techniques and digital computers in instrumental analysis.

The analytical procedure of finding an answer to an analytical problem can be seen as a sequence of actions with and operations on chemical information, with the purpose of converting it into a more manageable form. When these actions and operations are placed in elementary groups, fig. 1 . 1 is obtained. The classical analytical procedures, such as gravimetric and titrimetric methods, have a simple analytical sequence : a limited number of steps which are easy to understand. The later developed methods, for instance those based on the interaction of electro-magnetic radiation with matter, are more complex: the radiation has to be generated, filtered, detected and transformed. More elementary steps are required and their connection is less comprehensible.

QUESTI6N

SAl1PL1NB AND ;

---'lll11EASURE11ENT PREPARAT18N

_ _ .::,iRECl'lRDING --~PR8CESSINB ..___..,.ANSWER

er

RESULTS

er

RESULTS Fig. L 1. Elements of the analytical procedure.

Addition of digital processing techniques has, on its turn, increased the number of elements. Examples are : electronic circuits for conditioning, transmission and digitisation of signals, transmission lines and algorithms for the automatic processing of the digitised data. Each of these new elements influences, and possibly distorts, the information passing through.

This thesis is concerned with the application of digital computer systems for the acquisition and processing of signals in gas chromatography. Results are, however ,

QUEST I SN GAS- 11EASUREtlENT: SR11PLING AND f'REPARATil'IN t----CHR811ATl'IGRAf'HtC 1---.,.DETECTl!R ANALYSIS SIGNAL

R11PL IFICRttBN REGISTRATI8N BY INTERPRETRTI 8N 8F

'

,,,,.. P8TENT18t!ETRIC ,,,,..

_'

8F CURVE BY RULER

SIGNAL REC8RDER 8R PLAN111ETER

~ PR8CESSING BY 11ANURL CALCULRTI8N QUANTITATIVE i----::t1RNALYSIS , E.G. 100 X 11ETH8D RNRLYSlS REP8RT ANSWER

Fig. 1.2. Analytical procedure of quantitative gas chromatography using registration with

recorder and manual calculations.

valid for other fields too, because signal characteristics of gas chromatography are very similar to those of a number of other instrumental-analysis techniques. In gas chromatography, as in most modern instrumental methods, there exists a large discrepancy between the efforts required for performing the analysis and the time for manually processing the resulting data. Fig. l . 2 shows the analytical procedure for this case. Manual integration and correlation of the data resulting from a gas-chromatographic analysis using a capillary column can take up to four hours, while the time required for generating the data is less than one hour 10

• Hence,

it was already in a very early stage that the aid of automatic analog and digital processing techniques was called upon to improve the performance of gas-chromato· graphic analysis. And this has resulted in today's situation, where almost any interaction with the gas chromatograph and its results can be performed by the digital computer. Fig. 1 . 3 gives an example of the analytical procedure in this case. This development also brought new disciplines into the realm of the gas chromato-grapher, such as digital electronics and algorithm design. Specialised knowledge is required to exploit these new items thoroughly. This fact may be an explanation why sometimes excellent gas-chromatographic data, generated by carefully

controlled instruments, are spoiled by incorrectly 'tuned' data-processing techniques.

1 . 2 . Performance of gas chromatography

Extensive investigations have been carried out to find the instrumental specifications for giving gas chromatography its inherent accuracy and precision. Accuracy is used here in the meaning of' closeness to the true value', while precision indicates the

scatter of the values. The work ofGuiochon et al. 3

•4•5•8•9 and Clarke and Grant2•7

are excellent examples. Clear results stating the degree of control of the various operating parameters, to reach given precision levels, have been obtained. However, although high precision and accuracy are possible, implementation will generally not be feasible in situations where economic factors prevail. Apart from this aspect, the utmost level of performance is not always required.

The introduction of digital computers has shifted the relevance of problems in this situation. It is easy, by using the computational and decision-taking power of computers, to improve the precision and accuracy level of some instrument specific-ations by one or more orders of magnitude. Other specificspecific-ations, however, still require delicate mechanical components for improvement, thereby forming an economic boundary. At the same time, the performance of the instrument does not have to exceed that of the data-processing technique used.

In contrast with the situation on the instrument side, the relation between the accuracy and precision of the various data-acquisition and processing elements has not been studied exhaustively. The parameters of the data-acquisition and digitisation process have been treated 6• 13 • The general conclusion of these studies

is that this step is not the limiting factor in performance in most situations. Investigations of the operation of the next step - the computer program for data

QUESTI8N SflMPLlNG RND PREPRRRTISN

GRS-i----

CHR811AT8GRAPH IC ANALYSIS t1EASUREMENT: 0£TECT8R SIGNAL RMPLifICRTI8N RND C8NDITI8NlNO 8f SIGNRL TRANSHI8Sl8N

er

SIGNAL AllPLifICATI8N AND t----:i!!C8Nl:JITI8NlNG 8F SIGNAL

ANRL8G- l:JIGITAL ORTA REIJUCTI8N:

T8-DIBITRL i---::ioC8NOlTI8NING 1----P£AKC-GR8UP l

C8NYERSI8N 8F SIGNAL 0£TECT18N

DATA REDUCTI8N: PEAK-RR£R D£TERt1INATieN QUANTITATIVE ANALYSIS, E. G. lot! % METHOD 0£RIVAT18N 81'

REQUIRED RESULTS 1 - - -. . . RNSMER

AND REPORTING

Fig. 1.3. Analytical procedure of quantitative gas chromatography using a digital computer ftrr data acquisition and processing.

processing - can generally be split up into the following categories : Sophisticated programs for extracting results with a high accuracy and precision level from various data sources are described. The work of Van Rijswick 14 _{and of Kelly and Harris lh} 12 _{are typical of this approach;}

Study of programs utilising more elementary algorithms, which are used to process chromatograms generated by high-quality instruments. Examples are given by Wijtvliet 15 and Chesler and Cram 1 _•

A third category - relatively simple algorithms used in routine applications - is remarkably absent. Commercial gas-chromatography programs usually are based on this class of algorithms. Results have been published on the precision of algorithms in specific situations but, owing to lack of depth, extrapolation is difficult. In this thesis, a study of the relation between the data-acquisition and processing elements is described, which is based on the demands of routine quantitative gas-chromato-graphic analysis. The applicability of the results can be extended, however, to the high-quality performance of the gas chromatograph/computer combination. In practical situations a precision level of 1

%

absolute for the retention time and peak area is usually stated for reasonably well-assembled equipment9'10_{• The 0.1 %}

level might be easily obtainable if the decision-taking capability of the computer is applied in the control of the instrument. The precision of the data-acquisition and processing elements should preferably be an order of magnitude better to have only a minimum influence on the performance of the total system. For this reason, error levels of 0.01 - 0.1 % are specially emphasised in this thesis.

Another point about the performance of data processing, often ignored in discussion on the subject, is the reliability of operation, i.e., the exclusion of the risk of gross errors. Especially for completely automatic routine operation, this is an essential characteristic. In this kind of application, the value of a program which gives a precision of results of 0.01

%

in 98

%

of the cases is less than that of a program which has a precision level of 0.1

%

in 99 .5

%

of the time. This aspect also suggests the use of simple algorithms because the introduction of additional complexity to extract more information can make the program less reliable.

1 . 3 . Description of contents·

Chapter 2 contains a review of the development and current situation of gas-chromatography automation by digital computers. One of the conclusions is that for routine analysis, with its strict requirements as to reliability and continuity, a considerable number of the various approaches feature simple equipment and algorithms, as emphasised in this study.

The shape of signals in gas chromatography is considered in chapter 3. As the data-processing procedure should be designed with the particularities of the signals in mind, a mathematical model which approaches the experimental shape and which is also easily manipulable in simulation studies has been selected. The convolution

of a Gaussian function and a truncated exponential function has been chosen, both for its theoretical relevance in describing distortion processes of the first order and for its applicability to experimental shapes. This is shown by an example.

In chapter 4 the performance of the electronic elements which condition, filter, transmit and digitise the gas-chromatographic signal, is discussed. The relevancy of the findings of chapter 3 is verified and requirements for operation parameters are stated.

The main part of this investigation can be found in chapters 5,6 and 7, in whieh algorithms for data conditioning, peak detection and area determination are examined. The commonly used algorithms are reviewed and their performance is compared using a new approach, which demonstrates their operation both from a time-domain and a frequency-domain point of view. The systematic errors of these techniques are compared with the random errors originating in the noise in the signal. An experimental verification of the results is described. Furthermore, directions are given for using combinations of algorithms and for assessing their accuracy.

In chapter 8 the data described in the previous chapters, obtained for single peaks, are related to the various techniques for quantitative analysis in gas chromatography by which results for separate peaks are combined to derive composition data. Chapter 9 contains a review of all obtained results.

The derivation of the majority of the expressions used are given in the appendices I

and II. Appendix III gives the description of a peak-parameter estimation procedure.

In appendix IV the various results are illustrated by an analysis of the systematic and random errors for a complete quantitative gas-chromatographic analysis.

References

1. S.N. Chesler, S.P. Cram, Anal. Chem., 43, 1922-1933(1971).

2. A. Clarke, D • .W. Grant,' A study of the effects of variables on accuracy and precision : katharometer systems', in 'Gas chromatography 1970', R. Stock, ed., London, 1971. 3. M. Goedert, G. Guiochon. J. Chromatog. Sci.,

z,

323-339(1969).

4. M. Goedert, G. Guiochon, Anal Chem., 45, 1180-1187(1973). 5. M. Goedert, G. Guiochon, Anal Chem., 45, 1188-1196(1973). 6. M. Goedert, G. Guiochon, Chromatographia, ~. 76-83(1973). 7. D.W.Grant,A.Clarke,~, 1951-1957(1971).

8. G. Guiochon, J. Chromatog., 14, 378-386(1964).

9. G. Guiochon, M. Goedert, L. Jacob, 'Precision in quantitative gaschromatography', in 'Gas chromatography 1970', R. Stock, ed., London, 1971.

10. R. Kaiser, 'Chromatographie in der Gasphase, IV/ l, Quantitative Auswertung', Mannhein, 1969.

11. P.C. Kelly, W.E. Harris, Anal. Chem., 43, 1170-1183(1971). 12. P.C. Kelly, W.E. Harris, Anal., Chem., 43, 1184-1195(1971). 13. P.C. Kelly, G. Horlick, Anal. Chem., 45, 518-527(1973).

14. M.H.J. van Rijswick, Ph.D. Thesis, Eindhoven University of Technology, 1974. 15. J.J.M. Wijtvliet, Ph.D. Thesis, Eindhoven University of Technology, 1972.

2 . USE OF DIFFERENT TYPES OF COMPUTERS IN GAS CHROMATOGRAPHY

2 . l . Computer and gas chromatography

The commercial availability of digital electronic computers almost coincided with that of gas-chromatographic equipment : 1952 - first generation of computers 10 _, 1955 - first commercial gas chromatograph 14• Combination of the two dates back to the same years, but only recently has the computer been seen to enter all stages of the gas-chromatographic technique.

Gas chromatography has now become one of the most frequently used instrumental-analysis methods, stimulated by a unique combination of features :

Large separating power; High speed of analysis; High sensitivity;

The possibility of using simple and inexpensive equipment.

This position, together with the inefficient manual data-processing methods mentioned in the first chapter, resulted in a large interest in computer application in this field. This is indicated by five recent symposia devoted (almost) entirely to the gas chromatograph/computer combination 1- 5 •

Several excellent reviews have been published on the development and structure of gas-chromatography computerisation 6' 11- 13' 16' 17 • In this chapter several

current solutions to the automation problem are discussed, with special emphasis on their data-processing facilities, in order to survey the scope of the present investigation.

When discussing gas-chromatography automation, it is useful to divide applications into two broad fields :

Research and development work, featuring constantly changing demands on instrument performance;

Routine analysis, with emphasis on continuity and reliability.

These two categories are usually served by different automation approaches. The research and development laboratory can be characterised by :

A large variety of gas-chromatographic conditions; A large number of instruments, irregularly used;

Instruments placed all over the laboratory, leading to considerable variation in distance to the (central) computer system;

The necessity of good precision and accuracy because no time can be spent on calibrations;

Less emphasis on economic items: cost per analysis, pay-off time, etc.; Professional personnel;

The routine laboratory generally has the reverse characteristics : Less variation in instrumental conditions;

A smaller number of instruments, which are, however, used intensively; Reproducibility is required; lack of accuracy may be compensated by using correction factors;

Gas chromatographs are more concentrated at one location (although they can also be located inside a chemical plant to avoid sample-handling problems);

Economic operation of the laboratory is more crucial and can be better controlled;

Reliability and continuity of operation and availability of back-up facilities are essential;

Personnel at technician level;

Chromatographic results generally have the same purpose : quality control.

2 . 2 . Historical developments and current trends

The overall picture of the gas chromatograph/computer combination has changed completely during its existence, not so much by alterations in the gas-chromato-graphic technique, as by the very rapid development of data-processing equipment, which has resulted in totally different cost/performance figures every three to five years.

The first major introduction of electronic processing techniques in gas chromato-graphy was through the digital integrator: a useful, but - at that time - rather inflexible instrument. It had the great advantage of eliminating the subjective process of manual peak-area determination. However, interpretation of the output of the digital integrator and further calculations still required considerable effort. An attempt was therefore made to shift this task to the computer. Two directions of development resulted :

The addition of computer-compatible output units to the digital integrator (e.g. paper-tape punches). A time-sharing computer is then used to process the results;

The direct coupling of computer and gas chromatograph.

The second development - on-line computer use - has, in its turn, resulted in two main directions :

Scaling up to large time-shared systems, serving large numbers of users and many types of instruments, apart from other tasks, for instance

administration 2 ., 22 ;

Scaling down to dedicated mini-computer systems, interacting very intensively with the gas chromatograph 9

•

electronic data-processing functions into smaller and smaller modules (large-scale integration or LSI) will certainly bring the computer closer to the gas chromato-graph 7 • It can therefore reasonably be expected, that the distinction between

dedicated computer system and digital integrator will decrease. The introduction of the digital computing integrator already gives an indication 18

• It is almost

certain that this level of digital processing and control capacity will be a standard feature of future gas chromatographs 20• In cases where more processing power is

required, connections can be provided to networks of computer systems of various types, in which each type is devoted to the tasks it can perform most efficiently8'15•

In this way information on the composition of process streams can be transferred directly to the information system of a plant. Rapid feedback then becomes possible.

2 . 3 . Review of various approaches

At present, most automation approaches form unique solutions to unique problems. Sophisticated commercial equipment has only recently become available and, because of poor design and widely diverging requirements, has to be adapted and modified in many cases. A division into groups of increasing complexity has been made, considering the main item of interest of this thesis accuracy of and facilities for data-processing techniques.

The following seven approaches can be distinguished :

1. A digital electronic integrator with off-line (paper-tape) or on-line connection to a large computer centre;

2. A digital computing integrator;

3. Data-acquisition equipment (data logger) with off-line connection to a large computer centre;

4. A dedicated (mini-)computer system serving one gas chromatograph; 5. A small- or medium-sized computer system, serving a number of gas

chromatographs, with either analog signal transmission or a local analog-to-digital converter (ADC) and digital transmission;

6. A dedicated (mini·)computer system serving one gas chromatograph, connected to a large computer system or network;

7. A small· or medium-sized computer system, serving more gas chromatographs, connected to a large computer system or network.

In fig. 2 . 1 the various approaches are shown, with emphasis on the location and distance of gas chromatograph and computer system. Elements of their performance from the point of view of the characteristics described in section 2. 1 , are listed in table 2. l .

z

3 4 5 6 7

~

!ADC

I

GAS-CHR0MAT0GRAPH

L0CATI0N

L0CAL

CLAB0RAT0RY)

C0MPUTER

REM0TE

C0MPUTER

CENTER

DIGITAL JNTEtlRAT8R BR LARGE C8tlPUTER 1---~~s_Y~ST~E~tl _ _ __, C8tlPUT!Ntl tMTEtlRAT8R ORTR-ACQUISITI8N EQUIPtlENT SYSTEl'I DEOlCATEO BltALL C811PUTER 5Y6TE11 ~---~ SYSTEM S11flLL C811PUTER

___

___.,. SY ST EH GAS CHR8HAT8BRAPH

LBCAL flNRLBG-T8-0lGITAL C8NVERTER 814-LINE C8NNECTI8N COIOITRLl 8N-LINE CBNNECT18N CANRL8Gl 8Ff-LINE C8NNECT18N LARGE C81'1PUTER BYSTEtl LARGE C81!PUTER SYSTEM LARGE C8Mf'UTER SYSTEM

TABLE 2 . 1

Characteristics of automation approaches

Approach Characteristic 1 2 3 4 5 6 7 Possible analog data-transmission problems* - - - + + Flexible data reduction**

₊₊

+ + ++ Availibility for continuous use**

₊₊

₊₊

++

++ + + + Turn-around time for results** + - - ++ ++ ++

++

Possibilities for expansion** - + + ++ Initial costs*** -

-

- _{+ + +} Costs of operation***

--

--

+ - +

Skill required for operation and

maintenance**** - -

++

+

++

++

Complex organisation inside or outside the

laboratory**** - - + ++ ++ Ease of modification in data processing**

--

- ++ - + + ++ Commercial availability** ++ ++ ++ ++ -* +=yes , =no

** =bad - =limited + = reasonable ++ good

'

'

*** =low =moderate

,

+ = expensive

2 . 4 . Relevancy of the subjects of this thesis

Summarising the contents of table 2 .1 , the following statements can be made : Limitations in the complexity of data processing (especially in peak detection and area determination) are pronounced in the first two approaches, which use digital integrators;

They are also present in approaches 4 and 6, which use a mini-computer, because program development for this system type has hitherto remained a tedious task. Machine-oriented programming languages of low level prohibit program exchange and the absence of peripheral equipment such as mass-storage units and line printers reduces development rate. When a

connection to a larger system is provided, as in approach 6, some improvement can be expected, both for program preparation and data processing. If, however, a back-up facility is necessary, as often happens in routine analysis, processing programs still have to be supplied for the smaller system, because the larger system plus the communication link may not have the required availability;

Using medium-sized computer systems (approaches 5 and 7) will reduce the above-mentioned limitations because these are more flexible;

Approach 3 has the advantage of direct use of a large computer system. The off-line communication, however, might lead to a long turn-around time for the results;

Limitations in data processing may therefore be expected in all but the most sophisticated automation approaches. This is especially true of the routine-analysis laboratory, where cost factors weigh heavily and where back-up facilities are required.

2 . S . Example of a distributed-function approach

A short description of the implementation of a distributedfunction approach -the system for laboratory automation in -the Koninklijke/Shell Exploratie en Produktie Laboratorium (KSEPL) at Rijswijk, the Netherlands - is given here. The gas-chromatographic data used in the current investigations were acquired with this system. Some of its parameters are discussed in the following chapters to illustrate the theoretical conclusions.

The nucleus of the system consists of two interconnected computer systems. One of these (IBM System/7) is completely devoted to the on-line acquisition of various signals and intermediate storage of data ; the other (IBM l · 130, in future UNIV AC

1106) is used for subsequent processing.

Eight gas chromatographs, distributed over various laboratory rooms, are currently connected. The analog signals are transmitted to the central computer by means of separate, twisted-pair, shielded cables. The distance is of the order of 100 metres.

The signals are sampled and digitised at a rate of two samples per second. All data are stored unprocessed on a magnetic-disk memory. At regular times the contents of the disk are transmitted to the other computer system, which performs final data reduction. As all information is stored for some time, processing can be repeated with different parameters, if required.

The type of work of the gas-chromatography laboratory comprises partly routine analysis of crude-oil samples, to characterise origin and quality, partly research into gas-chromatographic methods.

The characteristics of the automation of routine gas-chromatographic analysis, mentioned in the first chapter, can also be found at KSEPL:

Reliable operation of processing programs; Ultimate precision not required.

References

1. Symposium 'Quantitative gas chromatography - from fundamentals to automation', proceedings in the December 1967 issue of Journal of Chromatographic Science. 2. Symposium 'Computer automation of analytical gas chromatography', proceedings in the

December 1969 and January 1970 issues of Journal of Chromatographic Science. 3. Symposium 'Chromatography and computers an economical approach for every

laboratory', proceedings in the December 1971 and January 1972 issues of Journal of Chromatographic Science.

4. Symposium 'Computer chromatography and associated techniques', proceedings in the February/March 1972 issue ofChromatographia.

5. Symposium 'Computers in analytical chemistry - with emphasis on chromatography', proceedings in the September 1974 issue ofChromatographia.

6. R.E. Anderson, Chromatographia, ~. 105-107(1972).

7. F. Baumann, J. Hendrickson, D. Wallace, Chromatographia,

7,

530-538(1974). 8. H. Ch. Broecker, H.G.W. Millier, Chromatographia,

7,

432-437(1974). 9. M.F. Burke, R.G. Thurman, J. Chromatog. Sci.,

!!•

39-45(1970).

10. D.F. Calhoun, 'Hardware technology', in 'Computer science', A.F. Cardenas, L. Presser, M.A. Marin, eds, New York .. 197 2.

11. K. Derge, Chromatographia, ~· 284-290(1972). 12. K. Derge, Chromatographia, ~. 334-338(1972). 13. K. Derge, Chromatographia, ~. 415-421(1972). 14. L.S. Ettre, Anal Chem., 43, 14, 20A-31A(l971).

15. J.S. Fok, E.A. Abrahamson, Chromatographia, '}_, 423-431(1974). 16. J.M. Gill, J. Chromatog. Sci., ?_, 731- 739(1969).

17. J.M. Gill, J. Chromatog. Sci., 10, 1-7(1972).

18. J.D. Hettinger, J.R. Hubbard, J.M. Gitl, L.A. Miller, J. Chromatog. Sci., ~. 710-717(1971). 19. H.W. Jackson, J. Chromatog. Sci.,

2•

706-709(1971).

20. L. Mikkelsen, J. Poole, A. Stefanski, H.R. Biesel, Chromatographia, ?_, 44 7-451(1974). 21. G. Schomburg, F. Weeke, B. Weimann, E. Ziegler, J. Chroma tog. Sci., 2, 735-741(1971). 22. G. Schomburg, E. Ziegler, Chromatographia, ~. 96-104(1972).

3 . SHAPE OF GAS-CHROMATOGRAPHIC SIGNALS

3 . 1 • Necessity of

a

descriptive model

Gas-chromatography data·processing techniques and instruments should be

designed with the specific characteristics of the gas-chromatographic signals in mind. To study the influence and performance of these instruments and techniques, it is essential to have a mathematical description for the shape of the signals processed. Thus, it would be possible to compare performance objectively. Also, the basis would be laid for the relation to a more general discussion of data processing in instrumental analysis, because for various techniques the signal shapes are very similar, mainly differing in time scale and contamination with noise.

This chapter describes the choice of a versatile mathematical model for gas· chromatographic peak shapes. The results of a study on its applicability to practice are presented.

3 . 2 . Gas-chromatographic peak shape

The shape of gas-chromatographic peaks has been studied extensively in recent years for a variety of reasons. Some of the more important spheres of interest are:

Investigation of in-column and extra-column effects in the gas-chromato-graphic system, to quantify and improve its performance;

Characterisation of gas-chromatographic peaks to determine physico-chemical variables with which the basic processes in gas-chromatographic separation can be described;

Improvement of the resolution of badly separated peaks using curve-fitting methods after the chromatogram has been recorded;

Study of the performance of signal-processing techniques for gas-chromato-graphic data.

The basic gas-chromatographic separation process in an ideal system will lead to peaks with the shape of the Gaussian or normal density function of time

y ( t, µ, q) a 1 _{( 2tr ) -1h exp [ ( t - µ)} 2

_I

_2a 2 _{] 3. 1}

where

t time

µ = mean

a = standard deviation

Yc (t, t 0, w, A) A exp [ - ( t - t0 ) 2

_{I 2 w}

2 ] 3.2 where t time t₀ retention time

w peak width : half width at 0.606A A =amplitude at t = t₀

To avoid confusion with other types of standard deviation, the term peak width will be used in the following text for the standard-deviation parameter of a gas-chromatographic peak.

This description has its merits as a fïrst-order description and has been used extensively as such in the literature on the above-mentioned items. For instance, references 4, 10, 11, 15, 17, 21, 23,27-31,34,36, 37, 39, 40, 42, 46, 47. In practice, however, one seldom encounters a purely Gaussian shape. A large number of sourees of deviation from the ideal behaviour of the gas-chromatographic system exist, and at least a few of them will occur in almost any normal equipment. Some of these have only a broadening effect, in which case the Gaussian character of the shape is generally retained. Others, however, introduce asymmetry. As this aspect is important in the current investigation, a number of sourees of deviation are listed here :

The presence of finite mixing voPumes before and after the column; The fini te response rate of the detector's sensing element and the associated electronic circuitry;

The slow evaporation of the liquid sample;

Limitations in the equilibration rate of concentrations at the gas/liquid interface in the column;

Irregular flow patterns in the connections of the column (abrupt diameter changes) or bends;

Chemical processes in the column.

Several authors introduced alternative models or modifications of the basic Gaussian shape to account for asymmetry. The most relevant of these are : (see also table 3.1)

The bi·Gaussian function, which is essentially a combination of two Gaussian half-curves with different widths 6

' 19' 20' 33' 38' 47 •

The Poisson function 6' 11' 19' 2 0.

Sternherg's model, which is a combination of a Gaussian function, a linear rampand a truncated exponential function 7 '8' 16' 37'44.

Chesler and Cram's model, which is a Gaussian function with exponential and hyperbalie tangent contributions 9.

McNaughton and Rogers's skewed Gaussian function 34•

Hock's skewed Gaussian function 3' 12 '24• 25

The convolution of a Gaussian and a truncated exponential function 1•2>11•14>18•22•26>32•35•41•44•45•48

Most of these asymmetric peak-shaped models contain parameters which cannot easily be associated with those of the gas-chromatographic system. Thus, they are not particularly useful for the present approach, because they do not allow a fundamental investigation. Other models, using differential equations to describe the transport phenomena in the column , have also been investigated 13 • They

have the advantage of being theoretically interpretable, but are awkward in mathematical manipulation.

A good compromise between theoretical plausibility and simplicity of mathematical expression has been found to be the convolution of the Gaussian and truncated exponential functions (for the sake of simplicity hereafter referred to as 'the convolution function' ). This model describes the distortion of a Gaussian-shaped input signal by a process governed by a first-order differential equation. One of the parameters of the function is the time constant of the process. First-order

processes occur frequently in the gas-chromatographic system (for example, the first four sources of deviation mentioned before). This gives rise to the expectation that the convolution function will be a good approach to the experimental curve in the case where one of the asymmetry-introducing factors is substantially larger than the others. But even in the case where two or more of the first-order processes are of comparable influence, reasonable agreement is obtained, as shown by McWilliam and Bolton 48•

The derivation of the expression of the convolution function in table 3 . l is presented in appendix I, together with other relevant data on this model. Summarising, in this study the convolution function was chosen as the basic function for theoretical developments for the following reasons :

Theoretical applicability in that the effect of first-order distortions can be quantified;

Simplicity of expression;

Applicability to experimental gas-chromatographic peaks, as stated in the literature 1' 14'41 and as illustrated in the next section.

3 . 3 . Applicability of convolution-function model

The following sections of this thesis deal with a theoretical study of sources of systematic error in peak-detection and integration procedures. The results of this study are verified with chromatograms. In order to check the validity of this verification, a number of peak models were fitted to experimental data :

The Gaussian function; The bi-Gaussian function; The convolution function.

TABLE 3 .1.

Expressions of mathematical models of gas-chromatographic peaks

1 . Gaussian function 2 . Bi-Gaussian function 3 . Poisson function =

=

A exp [ - ( t - t 0 ) 2 / 2w 1 2 ] A exp [ (t t₀ )2 /2w/] Yp ( t, µ,A) = A exp [ - µ] µ t ( t!) - 1 4 . Stemberg's model y₈(t,t_{0 ,w,A,psl'Ps2'Ps3,p84 )} = Aexp [-(t-t_{0 )}2 /2w2 ] + 81 Psi ( t Ps2) + 82 Ps1 ( Ps3 - Psz) exp [ - (ps3 - t)

I

Ps4

l

with

s

₁ =

o, s

₂ =

o

s₁ = I , s₂ =

o

s₁ = 0 , s₂ = l if t

<

p₈₂ if P s2 ~ t ~ P s3 if t

>

p 83 5 . Chesler and Cram's model

A [ exp [ - ( t t 0 ) 2 / 2 w2 ] + ( 1 - Y ₁ ) Y _{2 ]} where y₁ = 0.5(1 tanh(pc₁(t Pc₂)))

TABLE 3. l . (continued)

6 . McNaughton and Rogers's skewed Gaussian function

7. Littlewood, Gibb and Anderson1_{s skewed Gaussian function}

8 . Hock's skewed Gaussian function

9 . Convolution function

Yc(t,t₀,w,A,r) = w(rr1 (2n )*exp[w2 /2r2 _(t-t

0)/r] X erf[ (t-t₀)

I

w\/'2 - w

I

r\/'2] where erf(x] = (n )-*

l

exp [ u2 ] du - 0 0

In the above expressions the variables have the following meaning

t time

t₀

=

retention time

A

=

amplitude of peak maximum or of maximum of Gaussian component w = peak width

µ = mean of Poisson function p = parameter specific for each model

Apart from the parameters describing the peak, also the baseline contribution was included in the curve-fitting procedure. The magnitude of the baseline signal was taken to be constant under each peak. This resulted in estimation of the following parameters for the three models :

Amplitude, width, retention time and baseline signal for the Gaussian model; Amplitude, width of left and of right half of the curve, retention time and baseline signal for the bi-Gaussian model;

Amplitude, width and retention time of the Gaussian parent curve, decay constant of the exponential component and baseline signal for the convolution-function model

The curve-fitting technique used was a univariate gradient method, in which only one parameter was optimised at a time 5'43• Between 20 and 60 data points were

included for each peak. Iteration was concluded when the improvement in the residual-squares sum for the fit was less than 0.1 % for each parameter improvement.

Fig. 3 .1 . Experimental gas-chromatographic curve and fitted theoretical models. A : fit with Gaussian function. B : difference of experimental data and fitted Gaussian function. C : fit with bi-Gaussian function. D : difference of experimental data and fitted bi-Gaussian function. E : fit with convolution function. F : difference of experimental data and fitted convolution function. The difference curves are drawn on the same amplitude scale as the original curves.

A

c

E

R

c

•

B

=v

v

f

[\~

= -

"V

Fig. 3. 2 . As fig. 3 .1, but here a peak from the same gas chromatogram with 12 times larger amplitude has been fitted.

Results are presented in figs 3 .1 - 3. 3, which show both original gas-chromato-graphic curves and fitted model curves. Although both experimental and theoretical curves are drawn with similar lines, it will be clear that the curve with most

fluctuation is the experimental one. The curves originated from one gas-chromato-graphic analysis and the relative peak heights were l, 12 and 263 for figs 3 .1, 3. 2 and 3.3 respectively.

The difference curves of figs 3 .1 - 3 .3, which Show the difference between the experimental curve and the approximating curve, indicate the best agreement for the convolution-function model. The slightly poorer fit for the largest peak, in fig. 3. 3, can be ascribed to non-linear operation of the detector amplifier of the gas chromatograph.

Fig 3 .4 shows the gas chromatogram from which the peak data points were taken. The gas chromatogram was produced by analysing a petroleum-ether sample with a boiling range of40 60 °C. The instrumental parameters are described in appendix IV. Fig. 3 .4 is the result of computer processing of the gas-chromatographic data and has been drawn using a digital plotter. Results of the peak-detection and area-determination procedures are included in the plot, but these were not used in the

R

c

E

B D

,.

A~

" A/'..__

A A r--._

Fig. 3.3. As fig. 3.1, but here a peak from the gas chromatogram with 263 times larger amplitude has been fitted.

experiments described in this chapter. Each division on the horizontal (time) scale corresponds to 100 sampling points, acquired in 50 seconds. For further details, see fig. 3.5, which shows the same chromatogram, but now with a 100 times extended amplitude scale.

3 . 4 . Origin of the distortion

The numerical results of the curve-fitting process for a large number of peaks from the same gas chromatograph showed a relatively constant value for the time constant associated with the exponential component of the model function. As the time constant, which was approx. 5 seconds, was too large to be ascribed to the electronic elements of the system, its origin was expected to be in the pneumatic elements.

A test mixture of n-pentane, n-hexane and n-heptane, with some minor contaminations, was chromatographed at equal temperatures but at different carrier-gas volume flow rates. For members of a homologous series of compounds

the following relation holds where

nc

t 0(c) t 0(a) cl, c2

= number of carbon atoms in the molecule

= retention time of compound c

=

retention time of inert compound (e.g. air)

=

constants

3.3

When the retention times of three members of the series are known the 'air peak' time can be calculated. Then the volume flow rate of the carrier gas follows from the expression

3

.4 where

v = carrier-gas flow rate de = column diameter le = column length

The time constants associated with the three peaks were estimated using a curve-fitting procedure. The apparent dead volume of the gas-chromatographic system was then calculated with the expression

3.5 where

v d

=

apparent dead volume

r

=

time constant

In each case a value of approx. 0.05 ml was obtained for the apparent dead volume of the gas-chromatographic system. This value is plausible considering that it represents the volume of approx. 1.5 cm of tubing with an internal diameter of 2 mm. Upon further investigation the injection system of the gas chromatograph was found to contain this dead volume. For the described equipment the source of asymmetry could have been eliminated by using a splitter in the injection system. Thus the volume flow rate would increase and the time constant would decrease, at constant dead volume.

Sternberg has discussed the frequent occurrence of similar situations in capillary gas chromatography44•

w 0

c

8

1

z

3 8

Fig. 3.4. Gas chromatogram of petroleum·ether sample. Instrumental conditions described in appendix IV. R

c

J

References

1. A.H. Anderson, T.C. Gibb, A.B. Littlewood, J. Chromatog. Sci., ~, 640-646(1970). 2. J.W. Ashley, C.N. Reilley, Anal Chem., 37, 626-630(1965).

3. J. Baudisch, H.D. Papendick, V. SchlOder, Chromatographia, ~. 469-477(1970). 4. F. Baumann, E. Herlicska, A.C. Brown, J. Chromatog. Sci., '!_, 680-684(1969). 5. P.R. Bevington, 'Data reduction and error analysis for the physical sciences', New York,

1969.

6. T.S. Buys, K. de Clerck, Anal. Chem., 44, 1273-1275(1972). 7. S.N. Chesler, S.P. Cram, Anal Chem., 43, 1922-1933(1971). 8. S.N. Chesler, S.P. Cram, Anal. Chem., 44, 2240-2243(1972). 9. S.N. Chesler, S.P. Cram, Anal. Chem., 45, 1354-1359(1973).

10. H. Clough, T .C. Gibb, A.B. Littlewood, Chromatographia, ~. 351-35 3(1972).

11. E. Cus6, X. Guardino, J.M. Riera, M. Gassiot, J. Chroma tog., 95, 14 7-157(1974). 12. R.W. Dwyer Jr, Anal. Chem., 45, 1380-1383(1973).

13. J.C. Giddings, 'Dynamics of chromatography. Part I', New York, 1965. 14. H.M. Gladney, B.F. Dowden, J.D. Swalen, Anal Chem., 41, 883-888(1969). 15. M. Goedert, G. Guiochon, Anal Chem., 42, 962-968(1970).

16. M. Goedert, G. Guiochon, Chromatographia, ~· 116-128(1973). 17. M. Goedert, G. Guiochon, J. Chromatog. Sci.,

!.!•

326-334(1973). 18. M. Goedert, G. Guiochon, Chromatographia, ~. 76-83(1973}.

19. E. Grushka, M.N. Meyers, J.C. Giddings, Anal. Chem.,~. 21-26(1970). 20. E. Grushka, ChemTech, .!_, 745-753(1971).

21. E. Grushka, G.C. Monacelli, Anal. Chem., 44, 484-489(1972). 22. E. Grushka, Anal. Chem., 44, 1733-1738(1972).

23. H.A. Hancock, L.A. Dahm, J.F. Muldoon, J. Chromatog. Sci., ~. 57-62(1970). 24. H.A. Hartung, R.W. Dwyer, Anal Chem., 44, 1743-1747(1972).

25. F. Hock, Chromatographia, ~. 334-339(1969).

26. H.W. Johnson Jr, F.H. Stross, Anal. Chem.,~. 357-364(1959}. 27. D.W. Kirmse, A.W. Westerberg, Anal. Chem., 43, 1035-1039(1971). 28. K. Kishimoto, S. Musha, J. Chromatog. Sci.,

2·

608-611(1971).

29. K. Kishimoto, H.Miyauchi, S. Musha, J. Chromatog. Sci., 10, 220-223(1972). 30. A.B. Littlewood, Z. Anal. Chem., 236, 39-51(1968).

31. A.B. Littlewood, T.C. Gibb, A.H. Anderson, in 'Gas chromatography 1968', C.L.A. Harbourn, ed., London, 1969.

32. R.J. Maggs, A.S. Mead, in 'Gas chromatography 1970', R. Stock, ed., London, 1971. 3 3. H.D. Metzger, Chromatographia, ~, 64- 7 0(1970).

34. D. McNaughton, L.B. Rogers, Anal Chem., 43, 822-826(1971). 35. D.C. Nelson, D.L. Paull, Anal. Chem., 35, 1571-1575(1963). 36. D. Obst, J. Chromatog., 8-16(1968).

37. T. Petitclerc, G. Guiochon, Chromatographia,

z,

10-13(1974). 38. H. Pralzel, Z. Anal. Chem., 261, 369-376(1972).

39. E. Proksch, H. Bruneder, V. Granzner, J. Chromatog. Sci.,

z,

473-483(1969). 40. C.N. Reilley, G.P. Hildebrand, J.W. Ashley Jr, Anal. Chem., 34, 1198-1213(1962). 41. S.M. Roberts, D.H. Wilkinson, L.R. Walker, Anal. Chem., 42, 886-893(1970). 42. S.M. Roberts, Anal. Chem., 44, 502-507(1972).

43. H.A. Spang III, SIAM Review,'.!· 343-365(1962).

44. J.C. Sternberg, Advances in Chromatography,~. 205-270(1969). 45. F.A. Vandenheuvel, Anal Chem., 35, 1193-1198(1963). 46. R.L. Wade, S.P. Cram, Anal. Chem., 41, 893-898(1969). 47. A.W. Westerberg, Anal. Chem., 41, 1770-1777(1969).

4 . ACQUISITION OF SIGNALS

4 . l . Components

Between the gas-chromatographic detector and the memory of the computer in which the digitised data are stored, a number of electronic components transmit the signal and prepare this for digitisation. In the most complex design, the following elements can be distinguished :

A detector amplifier;

An amplifier and filter for signal transmission; A transmission channel;

An amplifier and filter for analog-to-digital converter; A multiplexer;

An analog-to-digital converter.

A possible lay-out is shown in fig. 4. I . As already indicated in chapter 2, many variations are feasible. The transmission of the signal can be virtually absent, because the data-acquisition system is located next to the gas chromatograph. This also holds for the digital integrator, which combines nearly all above-mentioned functions in one instrument. As this thesis is mostly concerned with computer applications, digital-integrator design is not discussed further. Only in automation approaches with a central computer system are signal transmission problems encountered. Here a choice has to be made between analog and digital modes of operation, as is also shown in fig. 2 .1 . The multiplexer is not required when the data-acquisition equipment serves only one gas chromatograph.

The reason for including the operation of these electronic elements in the present discussion is that they may influence the signals passing through them. The most important areas of distortion are :

Non-linearity;

Limited response speed, leading to asymmetry; Noise level.

It will be clear that all of these may deteriorate the performance of the data-processing procedure. The characteristics of most of the above-mentioned electronic elements will be discussed in this chapter. The conclusions will be used to evaluate the performance of the data-acquisition elements used for the experiments described in this thesis.

4 . 2 . Detector amplifier

Each detector type produces signals with very specific characteristics. The detector amplifier serves to normalise the output signal. generally to a higher voltage and a

FLAHE-I6NlSRTl6N 0£TECT6R OETECT6R AHPLIFIER FILTER

~----~----~

~----~----~

LINE-DRIVER RHPLlflER

--;;.

FILTER TRANSH1SS10N LINE /

'

MULTIPLEXER CRNRL6GJ

'

.,..

LI NE-RECEPTl 6N RHPLIFIER ANRL0G-T8-DIGITRL CONVERTER

'

,,.

C6MPUTER SY STEii

Fig. 4.1 . Possible lay-out of data-acquisition elements in computerised gas chromatography.

lower impedance level. Although some work has been done on detectors with a direct digital output 8_{, most currently used designs produce analog signals in the}

form of currents or voltages. For the scope of this section the discussion will be confined to the flame-ionisation detector and the thermal-conductivity detector. The performance of the flame-ionisation detector amplifier was investigated by Gill and Hartmann 5 and Knapp and Keller 10' 11' 12 .Gill and Hartmann stated that

the electrometer amplifiers in general use in flame-ionisation detection do not form the limiting factor in system performance : noise originating before and in the detector exceeds the amplifier contribution. Although this is true for signal

registration using potentiometric recorders, the limits may have been shifted for two reasons by the introduction of digital computers :

The linear range of most amplifiers ( 4 decades) is less than that of the detector

(6 decades or more for a good design). Inaccuracies of the potentiometric recorders which were (and are) in frequent use for the registration of the signal, are much larger, so that this limitation is not felt. Computer-based data-acquisition can accomodate the large dynamic range. The useful range can even be extended by applying corrections for non-linearity.

The high-impedance character of the flame·ionisation detector can also cause low response speeds, and thus large time constants, if the amplifier is not designed properly. Typical values are 0.5 1 s. The response of the potentiometric recorder is of the same order of magnitude. The high data· acquisition rates of modern digital equipment could support high-speed analysis.

In

that case the time constant of the detector amplifier should be reduced considerably. Sternberg pointed out, however, that also other instrumental parameters have to be improved considerable to permit high· speed analysis, so progress in this area does not depend on the detector amplifier only 16•

For the thermaf.conductivity detector, the linear range is not more than 5 decades, so amplifier performance is not too critical. Also, the response characteristics are less important because the thermal-conductivity detection technique is somewhat slow.

According to data presented by McWilliam and Bolton 18 , peaks with basewidths

of 20 seconds or more (peak widths 3 4 seconds) can be measured without appreciable distortion using most 'normal' flame-ionisation detector amplifiers. This also follows from Knapp and Keller's advice to select a time constant of one tenth the minimum peak width to reduce distortion to an acceptable minimum 12_•

The time constant of the flame.ionisation detector amplifier used in this investigation was claimed by the manufacturer to be 0.5 s. Verification of this value by measuring the amplifier response to a step input signal with a fast potentiometric recorder gave no cause for doubt. This indicates that, compared with the accidentally large time constant of the pneumatic system of the the gas chromatograph, the detector·amplifier response has hardly any deteriorating influence . The noise level for the flame·ionisation detector plus electrometer amplifier was of the order of 0.2 mV peak-to-peak (five times the standard deviation), when measured on the digitised data.

4 . 3 . Transmission lines

When the distance between the gas chromatograph and the data-acquisition system becomes appreciable, data-transmission problems have to be solved. Two approaches can be considered :

Transmission of the analog signal and digitisation by the (multiplexed) analog-to-digital converter of the data-acquisition system;

Local digitisation (near the gas chromatograph) of the signal and transmission of the digitised data.

Busch has discussed these two approaches 2• He states that the only reason for

choosing analog transmission may be an economic one (high cost of the analog-to-digital converter). Analog transmission is difficult and unreliable owing to the low signal levels and different grounding points of instrument and computer. However, sound design makes analog transmission possible with excellent performance over considerable distances, as shown for example by Schlereth and Greiner 14.

In accordance with experience from other implementations, separately shielded, twisted-pair cables were used for analog transmission of gas-chromatographic signals to the laboratory-automation system at KSEPL. The typical length is 100 metres. The noise level introduced by the environment into these cables is of the order of 0.05 mV peak-to-peak. This value was measured by terminating the cable on the gas-chromatograph side with a 50-ohm resistance. On the computer side a simple RC-filter is present with a time constant of 0.05 s. Digitisation at a rate of two samples per second gave the above-mentioned values for a series of 1000 samples. As the cables run near a lift shaft, signal transients in the form of' spikes' aie sometimes encountered. These can be discarded by the usual program logic, as suggested, for example, by Wijtvliet 17 and Van Rijswick 13•

4 . 4. Multiplexer and amplifier

If more signal sources are connected to the computer's analog-input system, a multiplexer is generally installed in order to be able to use the (relatively expensive) analog-to-digital converter economically. This is especially true of gas chromatography, which requires only low sampling rates: up to 10 - 20 times per second. If the time required for analog-to-digital conversion plus storage of the resulting values in the computer's memory is estimated at 200 µs, dedicated use has an efficiency of only 0.2 - 0.4

%.

Here the low switching speeds from one channel to another can be easily realised with low-cost relay multiplexers. No special care is required for this element to meet the specifications for accurate gas-chromatography data-processing.

The high-speed, multiplexed analog-to-digital converters used in general-purpose, computer-based data-acquisition designs require high input-voltage levels to reach sufficient precision. An auto-ranging amplifier is usually provided to optimise the converter's output with respect to the input signal level. In this way a good resolution can be achieved, even for low signal levels. A short settling time of this device is required for high-speed switching between different channels. Accurately known amplification-factor ratios for the various ranges are important in gas-chromatographic applications, considering the large dynamic range. The amplifier can be of relatively simple design because the dynamic range of the analog-to-digital converter is limited : between 3 and 4 decades for a twelve-bit type,

47i

decades for a fourteen-bit type.

The analog-input system of the IBM System/7 computer, used at KSEPL, has an auto-ranging amplifier with seven ranges, giving a full-scale input voltage for the analog-to-digital converter at amplifier input voltages of 10 mV to 5 V. Fig. 4.2 shows the input/output

voltage relationship of this amplifier/converter combination. The way in which the device attempts to keep its output voltage on high level is clearly indicated.

6 0UTPUT V0L TAGE 5 4 3 2 0 1

v

10

v

INPUT V0LTAGE 1 MV 10 MV 100 MV

Fig. 4. 2. Relationship between input and output voltage for auto-ranging-amplifier/ analog-to-digital-converter combination of analog-input system of IBM System/7 computer. Output voltage expressed in volts.

4 . 5 . Sampling

Most methods of digitisation also imply a short sampling duration, i.e. the signal being sampled is only monitored for a very small fraction of the sampling interval. The voltage-to-frequency converter types, which are usually present in digital voltmeters, are an exception because they integrate the signal during most of the sampling interval. Here only the non-integrating devices are considered because of their common occurence in computer-based data-acquisition systems. In this case sampling interval is negligible with respect to the time interval between the samples. Then the sampling rate which is required for subsequently recovering the character-istics of the original analog signal with sufficient accuracy, is of interest.

Basic considerations on this subject come from Shannon's sampling theorem, which is based on a frequency-domain representation of signals. The theorem states that the sampling rate should be at least twice the highest frequency giving an appreciable contribution to the frequency spectrum of the signal. Only in this case does the digitised sample series approximate the input signal properly. If the sampling rate is lower, the aliasing effect will occur, giving an unwanted influence of high-frequency components. The sampling theorem is discussed extensively by

Bracewell 1 and was demonstrated by Goedert and Guiochon 6 _{and Kelly and}

Horlick 9 • The minimum sampling rate following from the frequency spectrum

only suffices in those cases where the shape of the signal is accurately known. If this knowledge is not available a rate which is 5 - 10 times larger has to be used for proper subsequent recovery.

Fig. I .4 of appendix I presents frequency spectra of the convolution function with a width parameter of I s, as a function of the asymmetry/width ratio. It can be seen that components with frequencies above 0.7 Hz do not contribute significantly to the frequency spectrum. Hence, the minimum sampling rate would be approx. 1.5 samples/second. In practice, rates of 7 15 samples/second should be used. This will result in approx.

4o -

75 sampling points per peak. This figure has been confirmed by Chesler and Cram 3 and by Goedert and Guiochon 6 _•

An additional source of errors may be the scatter in the moment of sampling. In a dedicated computer system, operation will be centred on data acquisition. This leads to high regularity of the sampling moments, determined mainly by the stability of the clock which controls sampling. In a multi-function computer system the situation is less ideal, because a variety of tasks have to be executed, each one with its own priority and length. Switching from one task to another of higher priority may cause considerable delays. It depends on the efficiency of this switching procedure and the load of the system whether this effect causes problems. The distributed-function approach of automation can be advantageous for this purpose because here the data-acquisition system can be optimised to its task. This problem of course only holds, if the data-processing algorithms assume equal time intervals between the data points. If the actual time of sampling is recorded along with the sampling value, larger delays can be tolerated, although at the cost of higher data-reduction complexity.

The sampling rate used for gas·chromatography data acquisition at KSEPL is two samples per second. Hence, peaks with a minimum width of 4 5 seconds can be assessed accurately.

It also follows that the time constant of the RC-filter used in the analog·input system (0.05 s) may be too small for suppressing influence of high-frequency noise, resulting in aliasing distortion. As, however, the amplitude of the high-frequency noise is relatively small, no problems have been encountered.

The IBM System/7 computer, used at KSEPL, has a hardware-determined time of switching between tasks of different priority of only 1.8 microseconds maximum. The data-acquisition programs are given a high priority, so that hardly any interruptions of these tasks occur. For the few cases which do have a higher priority, the delay time is set at a maximum of 0.1 milliseconds. It will be clear that for the gas-chromatography application this has a negligible influence.

4 . 6 . Quantisation

quantisation step. By this process the analog signal, which is in a continuous range of voltages, is approximated by a number from a sequence of finite length and finite resolution. The quantisation level is the difference between two successive values of this sequence. Three characteristics are of special importance for the present discussion :

Resolution and dynamic range; Aperture time;

Linearity.

To indicate the meaning of the first of these, it is useful to look at the analogy between the sampling and quantisation processes. For the last process, the signal has to be represented by its amplitude distribution : the relative occurrence of particular signal values. The quantising step is then equivalent to sampling the amplitude distribution. The amount of' detail' in this distribution determines the minimum quantisation level required for recovering the characteristics of the original signal from the quantised values. This point of view has been discussed by Kelly and Horlick 9 and Soucek 15 • It depends on the purpose of

the digitised data, what resolution level is required. For the gas chromatography case it will be clear that the quantisation needed when the baseline signal has to be followed accurately is finer than when one is only interested in signal va1ues on the whole peak with their larger range. Soucek stated that, if a signal has an approximately Gaussian amplitude distribution, the range of values of the signal, when quantised, should extend over at least eight quantisation levels for accurate recovery. Thus, a dynamic range of 8000 quaritisation levels is needed if both the baseline signal and a peak with signal-to-noise ratio of 1 OOO have to be determined accurately. The term signal-to-noise ratio is used here for the peak height divided by the standard deviation of the noise in a gas-chromatographic signal. This range is supported by a fourteen-bit analog-to-digital converter. A twelve-bit type will be able to handle peaks with signal-to-noise ratios of up to 250.

The variable-gain amplifiers introduced in section 4.4 can be useful for this problem. They allow both high resolution of the low-voltage levels of baseline noise and enough dynamic range for handling large peaks.

The second characteristic of analog-to-digital converters, which may result in limitations, is aperture time, i.e. the time during which the signal is used for generating the digital approximation. If the input voltage changes too much during this time, the output value will lose its accuracy. The magnitude of this error depends on the mode of operation of the converter. If the signal is integrated during the aperture time, as in the commonly used dual-slope integrating converter 7

, the influence of voltage changes is minimum. However,

for the other current type, the successive-approximation converter, severe errors can occur. This device compares the input voltage with reference voltages of increasingly finer resolution. The comparison process is disturbed by input-voltage changes in an early stage. A sample calculation will illustrate this effect. Suppose a Gaussian input signal, described by