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An Integrated Circuit Analog Computer South Dakota State University Open PRAIRIE: Open Public Research Access Institutional Repository and Information Exchange Electronic Theses and Dissertations 1972 An Integrated Circuit Analog Computer Sthaporn Udomsin Follow this and additional works at: https://openprairie.sdstate.edu/etd Recommended Citation Udomsin, Sthaporn, "An Integrated Circuit Analog Computer" (1972). Electronic Theses and Dissertations. 4844. https://openprairie.sdstate.edu/etd/4844 This Thesis - Open Access is brought to you for free and open access by Open PRAIRIE: Open Public Research Access Institutional Repository and Information Exchange. It has been accepted for inclusion in Electronic Theses and Dissertations by an authorized administrator of Open PRAIRIE: Open Public Research Access Institutional Repository and Information Exchange. For more information, please contact [email protected]. AN INTEGRATED CIRCUIT ANALOG COMPUTER BY STHAPORN UDOMSIN A the sis submitted in partial fulfillment of the requirements-for the degree Master of Science, Department of Electrical Engineering, South Dakota State University 1972 ', , SOUTH DAKOT� STATE UNIVERSITY LIBRARY AN INTEGRATED CIRCUIT ANALOG COMPUTER This the sis is approved as a creditable and independent investigation by a candidate for the degree , Master of Science, and is acceptable as meeting the the sis requirements for this degree, but without implying that the conc lusions reached by the candidate are necessarily the conclusions of the major department. Thesis A�or Date Head, Electrical Engineering Date Department ACKNOWLEDGMENTS I would like to take this time to acknowle dge the ge nerous and valuable help give n me by two members of the Elect ric al Engineering Depart me nt here at S . D . S . Fir st , I wo uld like to express deep U. gr at it ude to R. A. Higgins , advisor, who aided me in both the Dr. my re search andwri t ing of this thesis. Se cond, I would like to thank R. Mostad for his kind assistance in solvi ng technical Mr. W. proble ms. s. u.- TABLE OF CONTENTS Chapter Page I. INTRODUCTION . • • . • . 1 A. An application of Computers . • • . 1 B. Analog Computer • . • . • . • • . • • . • . 2 Educational Analog Computer • • . • • • . 4 c. D. Purpose of the Study . • • . • . • • . • . 5 - II. OPERATIONAL AMPLIFIER • . • . • • . • . • • . • 6 A. Ideal Operational Amplifier . • . • . 6 B. A741 Operational Amplifier • • . 6 J-L • . • . Load Impedance , Input Impedance, Output c. Impedance and Open-Loop Voltage Gain • . /,; 8 D. Offset, Drift and Noise . • • . 14 ,..--- E. Stability, Bandwidth and Slew Rate . 23 F. Line rity • . • • . • . 25 III. DESIGN . • . • • • • . • • • . • 27 A. General Description . • . • . • 27 B. Operational Amplifier • . • . • . • • 29 Power Supply . • . • . • . • • . • 31 c. 10 V egulated Power Supply D. R • . • . • 33 E. Panel Meter . • 36 m F. A plifier Nulling • . • 36 G. Coefficient Potentiometer Setting . 39 H. MUltiplier . 42 I. Repetitive Operation . 42 Ch ap te r Page APPLICATIONS • • • . • . • . • • . • • • 47 IV. A. Accurac y in Analog Computation • • • • • . • • . • 47 B. • . Example 1, Si multaneous Algebraic Equations • • 50 Example 2, Second Or de r Differential Equation • • • c. 52 D. Example 3, Simulation of an Electric al Network • . • 53 E. Exampl e 4, Si mul ation of a Nonlinear Control -- System • . • • • . • • • . • • . • . • • . • 57 ._ . F. Example 5, Se cond Degree Differe ntial Equations • 66 . G. Exa mple 6, Narrowba nd Freque ncy Mo dulation • • . • . 69. CONCLUSION • . • • . • . • . 75 v. REFERENCES • • . • . • • . 79 . APPENDIX A • • . • . • • . • . • • • • • 81 . APPENDIX B . • . • • . • • • . • • • . 86 . LIST OF FIGURES AND TABLES Figure Page 1. Relative cost ve rsus acc urac y of analog anddi git al computer for di ffere nt sizes of installations. • • 2. Operational amplifier with inve rting fee dback configuration. • • • • • • • • • • • • • • • . 10 3. mum possible load of an operational amplifier. 1 2 Maxi 4. Eq uivalent circuit for st udyi ng effect of bi as curre nt, offset curre nt andof fset voltage . • • • • • • • •• 16 5. Schematic di agram for measuri ng amplifier dr i :rt. 18 6. Rec orded results for determining the dr ift. • . ••' 19 ?. No ise model of the operational ampli fi er. • • • • . 22 8. Schematic di agram for the analog computer. 28 9. Ci rcuit di agram for the operational amplifier. JLA ?41 . • • • • • • • • • • • • • • • • • • • 32 10. Ci rcuit diagr for power supply voltage regulator , µA ?23 . • • • • • • • • • • • • • • • • • , • • 34 11. Circuit di agram for 10 V power supply regulator. 35 12. Panel meter connectio n. • • • • • • • • • • . J? 13. Simplifie d diagram for amplifier nulling. • • . J 8 14. Coefficient-setting pote ntiometer wit h load. 40 15. fLA?25 connected as a voltage followe r. • • • • • . 41 16. Ci rcuit connection of the AD530K multiplier. 43 17. Ci rcuit di agram of the multivibrator for repetitive operation. • • • • • • • • • • • • • • • • • • 45 18. The front panel of the integrate d circuit analog computer. • • • • • • • • • • • • • • • • • • • • • • • • 46 Figure Page Component layout on the chassis of the integrated circuit analog computer. • • • • • • • • • • • • • • • • 46 20. Programming diagram for Example 1. 51 21 . 2. Programming diagram for Example . 54 22. Computer solution for second order differential equation, Example 2. • • • • • • • • • • • • • . 55 Computer solution for second order differential equation, Example 2. • • • • • • • • • • • • • '24 . Circuit diagram of the electrical network simulated in Example • • • • • • • • • • • • • • • • • • • • • • • 3 58 Programming diagram for simulation of an electrical • • • • • • • • • • • • • • . network of Example J. 59 26. Computer solution of Example J. • • • . 60 27. Block diagram. of general switching controlled plant. • • 62 28. Block diagram of the system to be simulated in Example 4. • • • • • • • • • • • • • • • • • • . 63 .. 29. Computer setup for simulation of the switching controlled system, Example 4. • • • • • • • • • • • • • • 64 JO. Phase-plane plot of the switching controlled system Example 4. • • • • • • • • • • • • • • • • • • . 31 . Programming diagram for Volterra's equation. 32. Computer solution for Volterra's competition equation, Example 5. • • • • • • • • • • • • • • · • • • • • • • . 68 JJ. Block diagram for narrowband system of Example 6. 70 FM 34. Computer setup for narrowband system of Example 6. 71 FM 35. results for narrowband 6. Recorded system, Example 72 FM J 6. Operational amplifiers connected as voltage limiter and frequency discriminator for narrowband frequency modulation detection. • • • • • • • • • • • • • • • • 74 Table Page 1. Characteristics of f.LA?41 in comparison to three other operational amplifiers. • • • • • • • • • • • • • • 30 1 CHAPTER I INT ROD UCTION A. An Applicat ion of Computers Tra diti onally, engineers apply both mat he matical analysis and experimentation to the solution of engineering problems . Physical syste ms are frequently expressed in terms of mathe matical models for whi ch the solution may be obtained. ge neral the problem ean be In describe d by a set of differential equations, the soluti on of which gi ve s the dynamic respon se of the system. Without the use of a · com­ put er , solvin g these equations may be tedious and exhaustive. A di gital computer acc omplishe s this task with great ac cur acy; theoreti­ call y the ac curac y of a di gital computer solution is unli mite d. But an analog computer, alth ou gh less accurate , can be used to handle the t.a sk far more rapidly an d easily. Man y engineering pr oblems do not require accurac y be yond three signi ficant fi gu res, and therefore do not require the employment of a di gital computer. Even in the cas es whe re hi gh acc uracy is re quired, it is o�en de sirable to obtain an analog solution before seeking the final solution on a digital computer. The chief advantage of an alog computation is that the operator can gain insight int o the pr oblem. Analog computer r esults are normally presented gra phi cally. The coefficients in the pr oblems c an be varied by corresponding parameter changes and. the block of computing elements can be visuali zed as a mat he matical operation. Considering the cost, an analog computer is less expen sive, but with 2 a specified component accurac y of better than 0.1 percent , its cost ri se s sh arply for even small acc uracy improvement. Figure 1 shows a quantitat ive comparison of the cost between an analog and a digital computer. Besi de s the acc uracy, ot he r di sa dvantages of the an alog computer are it s inabilit y to st ore the results and to make logical decisions. Hybrid computers have been de velopedto reali ze the advantage s of both types of computers and prove d to be the most convenient for engineering de sign applicat ions. B. Analog Computer Analog computers used toda y may be divide d into two broad categorie s, general purpose and special purpose . The ge neral purpose computers can be further su bdi vide d into two classes: the di rect or ph ysical anal og comp t..er and the indirec t or mat he matical ana log com­ puter.3 Since the mat he matical analog computer simulates the system behavior, it maybe refe rre d to as an an alog si mulat or. but more comm.only as an analog computer. He re an y re fe rence to analog computer will mean in particular the electronic mat he matical analog computer. The electronic analog computer consists of basic element s which perform specific mat he matical ope rat ions. 1. Summation and subtraction of two or more variable s. 2. Multiplicat ion and divisi on of a variab le by a constant. 3� Inte grati on and diffe re nt iat ion of a variable with re spect to time . .,., CIJ 0 {) .,.,: ...., � & I I I I I I I lli A I c:rea na.iog \ s:tng comp I Size ute� o:f' in stall ation 10.0 1.o 0.1 Co111po 0 nent .01 acc 0.0 uracy, 01 P82'ce nt o:f' 1'ull. scaie Fig"Ure Re lati V 1. e cos co11tp t Ver uter sus a :f'or di ccur :f':f'e:re acy o:f' nt Si anai zes o og a :f' ·ins nd dig talla i tai tions, 2 - w 4 4.
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