a I E> RAHY OF THE UNIVERSITY Of ILLINOIS 510. 84 no. 271-278 cop. 2 • ' * The person charging this material is re- sponsible for its return to the library from which it was withdrawn on or before the Latest Date stamped below. Theft, mutilation, and underlining of books are reasons for disciplinary action and may result in dismissal from the University. UNIVERSITY OF ILLINOIS LIBRARY AT URBANA-CHAMPAIGN HDV ?2 W* JAN 2 8 Wtt L161 — O-1096 Digitized by the Internet Archive in 2013 http://archive.org/details/analysisofregres273wood 5/0, * * Tru-Zt, Report No. 273 AN ANALYSIS OF THE REGRESSION MODEL FOR NONSATURATING LOGIC CIRCUIT ANALYSIS by George Donald Wood May 10, 1968 THE LIBRARY OF THE AUG I > I MERSIlY Ui- ilUnOIS Report No. 273 AN ANALYSIS OF THE REGRESSION MODEL FOR NONSATURATING LOGIC CIRCUIT ANALYSIS* by George Donald Wood May 10, 1968 Department of Computer Science University of Illinois Urbana, Illinois 6l801 This work was supported in part by the Advanced Research Projects Agency as administered by the Rome Air Development Center under Contract No. US AF 30(602)laUU and submitted in partial fulfillment of the requirements for the degree of Master of Science in Electrical Engineering, June, 1968. Ill ACKNOWLEDGEMENT The author acknowledges with pleasure the assistance and encouragement of Professor Richard M. Brown, whose many helpful com- ments and suggestions contributed greatly to this thesis project. Also, Professor Thomas A. Murrell, in whose researches the problem treated here originated, contributed much time and many useful sug- gestions during a number of thoughtful discussion periods. The author would also like to express his sincere gratitude to the Department of Computer Science of the University of Illinois and to the ILLIAC IV project for providing financial support for a portion of this project. Many thanks are also due to Mrs. Mildred Pape for her dili- gent and careful typing of the manuscript. IV TABLE OF CONTENTS Page 1. INTRODUCTION 1 2. THE DEVELOPMENT OF THE REGRESSION MODEL AND ITS RELATIONSHIP TO CONVENTIONAL CIRCUIT MODELING 7 2.1 Basic Modeling Elements 7 2.2 Small Signal Parameter Models 9 2-3 Piecewise Linear Model Construction 13 2.k Ideal Diode Model Construction l6 2.5 The Regression Model 21 3. COMPARISON OF TWO COMPUTER PROGRAM CIRCUIT ANALYSIS METHODS 30 3.1 Discussion of a Basic Circuit Analysis Problem . . . 30 3-2 Solution of the Current Convergence Problem ■ Partition Method 30 3*3 olution of the Current Convergence Problem - Regression Model Method 39 3*4 Cutoff Conditions and the Regression Model ^9 3«5 Extension of the Regression Model 53 3.6 Conclusion ^k h. APPLICATION OF NLAP TO LOGIC CIRCUIT ANALYSIS 63 4.1 Introduction 63 k.2 Preparation of NLAP Input Data Deck 63 U.3 Solution Control Codes 67 h.k olution Output and Identification 68 4.5 Conclusion 69 REFERENCES 72 V Page APPENDIX A. A NETWORK ANALYSIS PROCEDURE 75 1. Introduction 75 2. Matrix Equation Formulation 75 B. REGRESSION MODEL SUBROUTINE Qk 1. Subroutine Iterate Listing Qk 2. Comments on Program Changes 92 C. LINEAR REGRESSION PROGRAM 93 1. Linear Regression Program Listing 93 2. Typical Output 99 3« Instructions for Preparing Linear Regression Program Control Cards 103 k. Typical Input Data Deck 106 5» Linear Regression Input Data Transformation Program 108 D. REGRESSION MODEL EFFECTIVENESS PROGRAM 109 1. Regression Model Effectiveness Program Listing 109 2. Typical Output 110 3- Program Comments 112 k. Typical Input Data Deck -. . 114 E. NLAP OUTPUT SUBROUTINE LISTING 115 VI LIST OF FIGURES Figure Page 1. Two Forms of Emitter Coupled Logic (ECL) 2 2. Emitter Coupled Logic Transfer Characteristic .... 3 3« Dependent Sources and Their Voltage -Current Characteristics 8 k. Computer Program for Calculating I = f(l ) Ik 5- Piecewise Linear Approximation of a Function .... 15 6. CI Transistor Common Emitter Output Characteristic . 17 7« Stepwise Development of an NPN Common Emitter Transistor Model 19 8. Comparison of Hybrid and ECAP Transistor Models ... 22 9* Regression Model with Equations 2k 10. CI Transistor Base to Emitter Voltage Versus Collector Current 28 11. CI Transistor Current Gain Versus Collector Current . 29 12A. Oven Heater Driving Amplifier Schematic Diagram ... 31 12B. Oven Heater Driving Amplifier Equivalent Circuit . . 32 13* Dependent Current Generator Matrix 3^+ 1*4-. Independent Voltage Source Matrix 35 15* Coefficient Matrix Element Values 37 16. Impedance Matrix Element Values 38 17. NLAP Common Emitter Test Circuit 1+1 18. ECAP Standard Branch 1+2 19. Nodal Conductance Matrix with BETA Explicitly Shown . 1+7 Vll Figure Page 20. Nodal Equivalent Current Vector with BETA and V__ Explicitly Shown kQ BE 21. Flow Chart of Iterative Regression Model Solution Method 22. DC Solution Matrix Obtained Prior to Iteration . . 56 23. NL Solution Matrix Obtained After Completion of Iteration 57 2k. Nodal Conductance Matrix Calculations for BETA = 50 58 25. Nodal Current Vector Calculations for BETA = 50 and V = -1.25 Volts 59 BE 26. OR Emitter Follower Voltage Offset Characteristic . 6l 27. OR Emitter Follower Schematic Diagram 62 28. NLAP Calling Sequence 6k 29. Typical NLAP Input Data 66 30. Typical NLAP 133 Column Solution Printed Output . . 71 Al. An Equivalent Network 76 A2. Branch Level E, JG, V, and I Matrices 77 A3« Branch Level Z and A Matrices 78 Ak. Network Analysis Program 82 A5« Output of Network Analysis Test Program 83 Vlll LIST OF TABLES Table Page 1. Analysis of Regression Equation for BETA, C l V CE " 3 -° V DC 51 2. Analysis of Regression Equation for V C V CE " 3 -° V DC •'• 52 3« Summary of NLAP Output Variable Storage Arrays ... 70 1 . INTRODUCTION Many approaches to the computer aided design problem are being studied. To date these efforts have not resulted in the general 2 availability of automatic circuit design programs . If, however, one subdivides the electronic circuit design process somewhat, one of the principle facets which emerges is the need for a through analysis capability. With such a tool available to the designer, electronic system response may be simulated over the entire space of component variations and operating conditions. One of the fundamental steps in designing electronic cir- cuits is the choice of the "static d.c." or quiescent operating point. Its optimization is often an iterative process. An example, from logic circuit design, occurs when designing emitter coupled logic 3 circuits such as those of Figure 1. The typical design process requires that a number of interdependencies be met in order to obtain the nonsaturating output characteristics of Figure 2. The process begins with the selection of the voltage levels representing each binary state. The on and off state base-to-emitter voltages may be determined by superimposing the source line upon a set of the tran- sistor 's input characteristic curves. The output levels are next determined for various loadings, such as the next stage of Figure 1A, or the output level restoring emitter followers of Figure IB, using the transistor's output characteristic curve family. This procedure is then repeated for varying input and output conditions to insure 5 the convergence of the logic levels to the desired voltage levels. +V D :> LT> o CT1 <-^ CM 1 1 1 1 > II > e + + + + + + w 8 in CO O in CE CD --CNJ ! o Fh o • -P -P •H in CM CVJ £ OO'E 05 '1 00' OS'T- 00*G- i-oixJsnoA *30biiOA indino OS'Tr 00 '9- The amount of calculation required for effective design of an emitter coupled logic block can "be substantial due to the numerous iterations which may be needed to prove satisfactory operation under varying tolerance conditions. The point being made here is that the circuit designer could save a significant amount of computation time by employing a flexible computer program whose output could be, for example, the emitter coupled logic circuit's output voltage transfer characteristic . The above "static" design discussion employed graphical analysis which has been a standard circuit design tool for many years. Introductory electronic circuit texts introduce this approach as being the best way to handle nonlinear circuit elements and indeed it is for simple exploratory analysis. However, for computer-aided design, such as is possible with a parameter variation program, it is necessary to enter the transistor's characteristics in the form of equations. These equations are known as the transistor modeling equations and may take many forms. Some of the models currently used are: Ebers-Moll, Piecewise Linear, Admittance or Y Parameter, Hybrid or H Parameter, Z matrix, and the M Parameter Model. Each model evolved for the purpose of simulating some portion of a transistor's range of opera- tion. No analysis or simulation program can be effective unless the transistor model used accurately represents the transistor's voltage- current behavior throughout the region of operation in the simulated circuit. For this reason, the basis of each of the above models will be discussed in section 2 in order that they may be compared with a 7 new model related to the Z matrix model but including the additional constraints : BETA = A + A (In ^ ) + A (in ■=$■ f U V BE = B + A l (in T Q > + A 2 < ta | ) 2 These additional constraints are formed by the Linear Regression program of Appendix B whose input data points are taken from measurements or from manufacturer's data sheets. This Regression Model thereby enables the designer to employ linear equation solution methods to obtain a nonlinear solution to his circuit problem. Thus the quantities BETA and V^ are no longer restricted to constant values Bill as is the usual case. The usefulness of the Regression Model rests upon the ease of its application and upon the accuracy of its predictive capability. In an effort to satisfy the first goal, the Regression Model sub- o routine written by Guth was converted from IBM 1620 compatible language to FORTRAN IV for use on the IBM 360 Model 75 as a part of this thesis project. 9 In the process of conversion a new version of ECAP became available which provided true worst case solutions. This new version of ECAP was modified to work with an updated version of Guth's sub- routine, a listing of which is given in Appendix B of this thesis. The complete program is now called NLAP (Nonlinear Analysis Program) and is contained in the program library at the Department of Computer Science, University of Illinois. The KLAP calling sequence is given in Appendix E, together with the input and output of a test program. The final goal posed for this thesis was to evaluate the possibility of extending the useful range of the Regression Model from the normal active region to include operation in the cutoff region as is encountered in emitter coupled logic circuit operation. The evaluation of this extension, together with a discussion of the IBM 36O ECAP network solution method, will be presented in section 3« The application of NLAP to the solution of transistor logic circuits is discussed in section k. The required topological codes are given for the various types of branch level statements. Two illustrative examples are presented as a further guide. It is recommended that the user consult sections 3«^+ through 3*6 before undertaking use of the NL solution option discussed in section h.3- 2. THE DEVELOPMENT OF THE REGRESSION MODEL AND ITS RELATIONSHIP TO CONVENTIONAL CIRCUIT MODELING 2.1 Basic Modeling Elements The basic components for an electronic model are the ideal- ized pure resistance (R), pure inductance (L), and pure capacitance (C) elements of linear and reciprocal network theory. Their elemental voltage -current relationships are simply Ohm's law. To form a compact set of elements, it is necessary to add the controlled source for modeling of the amplification process and the ideal junction diode for simulating variable amplitude, unilateral transmission. Dependent current and voltage controlled sources are of four possible types; voltage controlled voltage, voltage controlled current, current controlled voltage, and current controlled current. The internal impedances of these sources are identical with their independent counterparts of linear network theory. The direction of output current flow, or of output voltage polarity, is dependent upon the driving source and may be of either polarity. The two port volt age -current relationships of each controlled source type, together with their schematics, are summarized by Figure 3« The ideal junction diode has the voltage -current relationship: . / qV/MKT . v i = i Q (e H ' -1). This equation derives from a solution of the one -dimensional diffusion 11 equation. The factor M in the denominator of the exponent facili- tates adjusting the theoretical V-I relationship to match that observed physically. Use of this ideal diode equation, together with the other 6 (a) INPUT CURRENT CONTROLS OUTPUT CURRENT ll • ► • + it ei (T)/3e, e, (b) INPUT VOLTAGE CONTROLS OUTPUT CURRENT (c) INPUT CURRENT CONTROLS OUTPUT VOLTAGE (d) INPUT VOLTAGE CONTROL OUTPUT VOLTAGE i 2a ij all •0 - --aij 2aij -*e« i 2 2/9« x £e x ♦e, -2)9e 1 ' I -2yii I I -r'i —I — I'- ll t I I I I I I I ♦ ei I i I I It t -28ej 1 i 1 -8e x + 8ex 1 1 + 28e x 1 1 1 1 1 1 1 1 1 1 1 l 1 1 1 1 1 1 1 Figure 3* Dependent Sources and Their Voltage -Current Characteristics four basic modeling elements, plus an independent current or voltage 12 source element , are sufficient for most modeling work whether the circuit model be derived from basic physics or from the circuit "black box" approach. 2.2 Small Signal Parameter Models A general network or "black box" may be described in terms of its two port parameters. At each port the voltage and input current are measured, providing four variables for network description. Any 13 two of these quantities form a basis " for the solution space of the network and, therefore, they completely characterize the network's behavior. The two port parameters may be established from a graphical plot by following the definitions established during their derivation. One pair of general relationships between the two port voltages and current is: e i = t{i i> V e 2 = g (!-(_, i 2 ) These general functional relationships will in general be nonlinear. This creates the need for their transformation into linear functions for use in linear network analysis. Expanding in a Taylor series, with two independent variables, obtains: 10 e l ( V i 2 ) = > (l_, I p ) + ° e l ^1 (in - i_ = I. I,) + 3e l 1 ^ (i 2 - I 2 ) I« = I- + higher order terms ( V 1 2 ) = . 2 (l r I 2 ) + H (in " = I : = i. d 2 - 1 2 ) i„ = I, + higher order terms provided e, (i. i p ) and e p (i , i ) are analytic functions. The crucial point is that there are two ways for these Taylor expansions to reduce to linear functions. First, if the basic functional rela- tionships are linear, then the value of all derivatives of higher order than one are zero. Second, if the operating point Q (i , i ) is selected such that the deviations (i - I ) and (i - I ) are small (thereby restricting the validity of related circuit calculations to "small signal") then the higher order Taylor series terms, (i. - I.) , J J become sufficiently small so as to become negligible. Several changes of variables, such as: ( v y ■ e .i (I i> V + Ae yields the equations : 11 Ae. 1 3e i t Ai -, + T^ I, = I, 1 oe 2 h** i„ = I, Ae^ = ^e 2 di 33 2 i_, = L Ai l + sr 1 1 2 *2 = I 2 1, = h «* i« = I, in which the quantities e.'s and i.'s are incremental by definition with one exception; the case where the basic function is sufficiently linear for all the higher partial derivatives to be at least close to zero. de. The partial derivatives -r-r^ each have the dimensions of impedance. With this in mind, the incremental equations may be written in matrix form where the definitions of Z. . are obvious by inspection. Ae, Ae, Z ll Z 12 Z 21 Z 22 " A1 l" * _ A1 2_ Now we arrive at the fortunate result where it is not neces- 1k sary to assume small signal conditions in order to obtain a valid linear model of a transistor using "small signal Z parameters". However, it is necessary to locate those portions of the operating 12 regions for each transistor where all four z. 's are sufficiently linear before this is a valid model. 15 There are four other sets of "small signal" parameters A) The Y, or admittance parameters y ll y i2 y 21 y 22 B) The H, or hybrid parameters h 21 ~\ — L 12 _ ■* X l L 22 S 2 C) The A, or transfer parameters: A B D) The M, or inverse hybrid parameters m 11 m m 12 m. 21 22 Each of the above coefficient matrices, in its linear region may be arranged to represent common emitter, common base, or 13 common collector orientations through a series of well-known trans- -1 c formations . In this respect this matrix representation is very useful for model construction. In summary, the so-called small signal parameter models may form useful quiescent models in the regions where all four coefficients of each coefficient matrix are linear. However, lacking sufficient data on which to justify their use, the systems analyst should use a distinctly nonlinear model such as a Piecewise Linear Model, Ideal Diode Model, or Regression Model which is valid over the range of interest. 2.3 Piecewise Linear Model Construction Another class of models may be generated using piecewise 17 linear techniques . The Piecewise Linear Models are also valid for a wide range of operating points provided a sufficient number of segments are employed. An example of a Piecewise Linear Model of a forward base-emitter diode coded in the Jovial subset of ALGOL is shown in Figure k. In a computer program, such a model consists of logical statements defining the values at which the individual segments should be switched in and out of the model's network. Construction of a Piecewise Linear Model begins with a graph of the objective function (Figure 5). A series of straight line seg- ments are then constructed which, when appropriately summed, form the required objective function within the desired accuracy. An example Piecewise Linear Model for the I_, versus V^^ input characteristic of B BE an KPN switching transistor is presented in Figure 5B. Several other 14 * 1.00 FLOAT; * 2.00 READ E17; * 3-00 Q5RS = 0.60; * 4.00 ZO = 40; * 5.00 FORMAT HD5,S20,C*CHARACTERISTICS OF TRANSISTOR Q5*//> * 6.00 FORMAT HD5U,C* IB IC HFE RC VSAT * 7 . 00 VCE VOUT ES */ ; * 8.00 PRINT HD5; * 9-00 PRINT HD5U; * 10.00 FOR IB 5 = 0.005, 0.005, 0.060; * 11.00 BEGIN * 12.00 IC5MAX = ((E17/ZO)-0.45)/l3-0952U; * 13-00 IF IB 5 GQ AND IB 5 LS 0.007; * 14.00 IC5 = 52.5*IB5; * 15.00 IF IB 5 GQ 0.007 AND IB 5 LS 0.0l4; * 16.00 IC5 = 0.18 + 26.66667* 135; * 17.00 IF IB 5 GQ 0.014 AND IB 5 LS 0.0325; * 18.00 IC5 = 0.3 + 17 -71429*185; * 19.00 IF IB 5 GQ 0.0325 and IB 5 LQ IB5MAX; * 20.00 IC5 = 0.45 + 13. 09524* IB5; * 21.00 Zl = (E17/IC5)-Z0; * 22.00 HFE = IC5/IB5; * 23.00 VSAT = IC5*Q5RS; * 24.00 VCE = IC5*Z1; * 25.00 VOUT = E17 - IC5*(Z1+Q5RS); * 26.00 ES = VSAT + VCE + VOUT; * 27.00 FORMAT Q,F7.4,F10-3, F9.1,2F9- s,Sf8.2,F9.2; * 28.00 PRINT Q,IB5,IC5,HFE,Z1,VSAT,VCE,V0UT,ES; * 29.00 END * 30.00 FORMAT QS,C* */>H8,F12.4,C* *// ; * 31-00 PRINT Q£,8H(IB5MAX =),IB5MAX; * PRINT COMPLETE Figure 4. Computer Program for Calculating I = f(l D ) 6* ea 70 72 74 76 78 .80 BASE TO EMITTER VOLTAGE IV,,)- VOLTS A) C3 Emitter Diode Input Characteristic 15 5 40 SEGMENT A — . _ >' ^1-— ^ ** -^ i * .66 61 70 72 74 76 78 .80 BASE TO EMITTER VOLTAGE ( V„)- VOLTS B) Piecewise Linear Approximation Segment A Equation v = 0.680 + 192.85 * r. BE A B B v BE = 0.727 + 591-39 * i B v = 0.755 + 1569.23 * I ■Dtp b D ^BE = °' 7lk + 3153 * 81+ * Z B C) Piecewise Linear Equations Figure 5« Piecewise Linear Approximation of a Function 16 1 o approaches for generating piecewise linear models are given in Anner , which is the most comprehensive reference on the subject. One con- straint on the use of Piecewise Linear Models is that they must be entered into a computer program in segments whose equations must be switched in or out of the model as a function of V^^ by conditional program logic statements, such as the "IF statement" of FORTRAN Iv , in order for the total functional value 3L = f(V ) to be correct. 2.h Ideal Diode Model Construction Suppose a problem is given whose solution requires rather exact simulation of a transistor's output characteristic such as is depicted in Figure 6. This set of curves shows a set of measured, static characteristics of an Emitter-Coupled-Logic nanosecond switch- ing transistor. Contrasting these with the voltage-current relation- ships of the controlled sources of Figure 3 suggests that with the 20 application of appropriate mathematical nonnegativity restrictions one could form a suitable model. An effective way of realizing the nonnegativity restrictions is by adding ideal junction diode elements to the model. Thus, by employing the diode model in appropriate series and parallel config- urations, the controlled sources for quadrant V-I characteristic may be transformed into the desired form. One possible algorithm using the current and voltage conventions of Figure 7A is : A) Shunt the controlled current source with an ideal resistive element, R_, to provide a modified set of 17 --my) S3H3dwvn"iiw-( D i) iN3a«no HOioinnoD <\j -H i i n C 'CE c) D) X 'CE 'CE •NOTE : V CE = V C ,-V„ Figure 7. Step-wise Development of an NPN Common Emitter Transistor Model 20 as to inhibit V nT . from becoming negative. The output current is by KCL : i C ■ Vol (« -^^-1) ♦ V^R, - I 02 (e-^/^-D while the input current is E "" 01 K J By KCL and KVL these equations may be couched in normal common emitter variables; !_, instead of I and V d E CE instead of V_. with the result : OB 1„ - °F L + X C0 (e -1 V ° S - Win*.!) t f-i^s, \ t ~q V BE/Mkt n N _ / -q( CE- BE)Mkt . v h = ~hs (1 " a F ) (e - 1} + ^s (e "^ - v cb/r c which are the equations of the curves in Figure 7D. 21 These relations, according to Gibbons , provide a represen- tation of transistor output characteristics which ds sufficiently accur- ate that it falls within the typical manufacturing spread for a given transistor type over most of the normal active region. Also, one finds 21 22 upon comparing the Ebers Moll Model equations with those of paragraph C above, that there is good agreement in the forward active region. The above intuitively derived nonlinear model is easily extended to include inverse operation by adding an QLi^p generator, as suggested by the Ebers Moll Model, plus a shunting ideal resistor R to facilitate modeling of the reverse characteristic slope, of physical transistors, as shown in the third quadrant of Figure 6. The quantities, I . , I._, OL and R , in the above equations are variables and, therefore, need to be evaluated experimentally. 23 Malmberg states that evaluation of these variables requires one to make a substantial number of measurements. 2.5 The Regression Model The Regression Model combines the simplicity of the Hybrid parameter model with the nonlinear modeling flexibility of the non- linear model utilizing the ideal junction diode as discussed in the previous section. No longer is one restricted to an incremental variation about the "static" or quiescent operating point as is true with the unmodified Hybrid parameter model of Figure 8. The operating range is extended by equations for BETA (I ) and V (I ) . C BE C The first step in the modification process is to convert the Hybrid parameter model of Figure 6A to the ECAP direct current model of Figure 8. This is accomplished by 'substituting a battery V^ B for the h «i voltage generator and substituting the direct current re c to gain, BETA, for the small signal forward current gain, h„ • 22 B o- + t Vbe 'b E o ,h re j c OE A. Hybrid Parameter Model B. ECAP Direct Current Model Figure 8. Comparison of Hybrid and ECAP Transistor Models 23 The final step involves the use of modeling equations devel- 2k oped by Guth "but in normalized form so that the natural logarithm is taken of a dimensionless quantity. These modeling equations con- trol the base to emitter voltage drop V-^ and th? current gain BETA of the ECAP model. The advantage of this approach is that the cir- cuit analyst need not use the ideal junction diode as a modeling element. Instead of the exponential function and its attendant numerical evaluation problems when used in matrix equations, the user 25 may attain the equivalent circuit simulation range from curves derived from either measured or manufacturer's data points. The data points are fed into the Linear Regression curve fitting program of Appendix C for the purpose of generating in closed form, a mathe- matical equation which describes the actual variations in vL^ and BE BETA as a function of operating point (collector current, I ) for each transistor used. In this manner the nonlinear volt age -current rela- tions of any transistor may, in general, be established for any desired operating range below saturation. Note that the nonlinear Regression Model of Figure 9 is an extension of Guth's model for the purpose of permitting simulation of transistor circuit operation in both the active and cutoff regions as is required, for example, for modeling nonsaturating Emitter Coupled Logic circuitry. The modification consisted of adding the program logic required to switch to a zero valued function of collector current, I , whenever the base current, I , decreased below a preselected refer- ence level, I , or reversed sign from the normal forward direction of positive amplification. Also, the base circuit is modified by setting 2k COLLECTOR J Ib h ie BASEO-t-* — WV — | |— T+ + ' ' - I V Vbe h oel (*)BETA*I B EMITTER O L B 'CE A) ECAP Direct Current Model BETA = B + B. (in S) + B Q (in r^f Cx2 v be = v i + V 2 ( ^ n r } + v 3 < in r> B) Regression Equations Figure 9- Regression Model With Equations 25 this circuit equal to a branch with V™ = V , where V is the cutin ^ BE y' 7 voltage, in series with a resistance of five megohms, whenever igSo. Thus the solution set of the Regression Model is now restricted to positive values of BETA, I , and I , by the addition of a conceptual transistor base-emitter diode which behaves in the cutoff mode in a similar manner to the ideal junction diode of the Ideal Diode Model constructed in Section 2.k above. The application of this Regression Model requires the user to calculate BETA using the equation: BETA = T^ =£L B2 " Bl where BETA is defined as the spacing between the common emitter out- put characteristic curves of the Ebers Moll Model operating in the normal active region. There is an implied extension of this defini- tion of BETA required in the use of this model. For example, to extend the Regression Model's validity into the cutoff region, it was necessary to obtain BETA and v_,„ data at low currents where the output BE characteristic curves are highly nonlinear. However, the Regression Model specifically allows BETA to be a variable whereas in the Ebers Moll Model BETA is defined as a constant. The use of the above equa- tion is justified for currents which are near zero, since the collector current, I , approaches zero at a much greater rate than does the base 26/27 current, I . In the limit the above equation does not converge to zero 13 as desired, but it is a simple matter to define BETA as being zero at 1=0 and 1— = 0, since this is consistent with all physical observa- tions of BETA'S behavior. The base to emitter forward diode drop, V^, voltage data BB is obtained from the common emitter input characteristic curves. Thus, the user supplies as input to the Linear Regression program a table of I_, BETA, and V which contains sufficient data to completely define C BE each transistor in the region to be modeled. The accuracy with which the Regression Model, in conjunc- tion with the ECAP program, will simulate circuit operation is directly affected by the "goodness of fit" of the regression equations to the experimental data. A plot of typical measured physical variations of V and BETA as a function of the collector current, I , for BE the comparison with the Linear Regression prediction equations, is shown in Figures 10 and 11, respectively. The Linear Regression pro- gram of Appendix C was used to derive these equations. A convenient program to test the Regression Model's effectiveness is given in Appendix D. In conclusion, this discussion of models has shown the relationship of the Regression Model to other types of transistor models currently in wide use. It is believed that this model will form the basis of a useful parameter variation simulation program. 28 o az a D CM \— CO I 1 1 — 1 CO LJ :z CJ cr > cc 0V8 OO'B 09'^ OZ'L 08*9 0TT9 (i-OIX)SIIOA 4 39A '3QU11QA U311IW3 3SB9 00 '9 29 CJ CO LU _l Q_ D >- > 1— O HI o o CM h- en 1 1 i — i CO LU 2 CJ CE > CC h + 8 • 8 c& -p G 8 tu o'CO (4 LU o CC LU u Q_ o 85 4-> o CD H cn-j t— 1 H o o 11 co 3 at w 8^ 0) > m. . g h- •H ■z r^ LU az -P 4.00 CUR •H « 0) -p w > o H •H 32 u o UJ c! o 10 ,^JU¥l a: oo AAA- 4 VyA> * -e- ■nCj -WAr- * K», 3* N AAA 1 O IM AAA 1| 4 QC O ro AAA- (0 •H W *n (D •H *H •H H fclD •H > •H P £h (L) -P cd a; W fl a; eq OJ fe 3* or q CVJ 33 The matrix equations are: 3L = I.. - JG = I M- = A T *L„ - JG M aT *V*m - JG = [A T *Y M *A] * E - JG ■ t A ^V A] * [E B * V " JG = [A T *Y M *A] * E B + [A T *Y M M] * E^ - JG - [A T *Y M *A] * Eg + [A T *Y *A] * Z*JG - JG The dependent collector current generator matrix, JG, and the indepen- dent voltage source matrix, E_, are shown in Figures 13 and lk, respec- tively. Note that the elements of the JG matrix are factored to show the dependent relationship between the elements of this matrix and the i . elements of the I matrix for which the solution is being obtained. Bj ±5 Therein is the current convergence problem, referred to above, in that certain of the unknown currents appear on both sides of the matrix equations. However, through the use of matrix partitioning, the depen- dent current values, I , may be obtained and the remaining independent current values, ]_., calculated. The procedure is: Let J = Q * I n where Q = [^ k x 1 and q^ = current gain of the n transistor, (BETA) . 3U D ^5 (_i B5 } ^ES ( ' i B3 ) Amperes Figure 13* Dependent Current Generator Matrix 35 -V. BE5 -V. beU -V. D5 -V, DU -V. BE 3 E Volts Figure Ik. Independent Voltage Source Matrix 36 Thus given the A and Z matrices in Figures 15 and 16 one may solve for the branch current matrix, I , where: I B = [A T *Y M *A] *E B + [A T -Y M -A] *Z*Q*I M - Q*!^ By partitioning the I_ matrix into dependent and independent parts one obtains: h h d = Y* $ + Y* Z*Q*I Bd Q*I Bd where is an appropriately dimensioned null vector in each case. Next the network admittance of Y matrix, where Y = A T *Y *A M may be partitioned into four parts Y 1 , Y 2 , Y 3 , and Y^ having the respective dimensions of: 3x3, 3 x 15, 15 x 3, and 15 x 15 for the 18 branch equivalent circuit of Figure 12-B. The branch cur- rent matrix, upon partitioning the Y matrix, becomes: h" ** Bi Y Y Y 3 Y h $_ h Y Y i 1 x 2 Y 3 \ Z-Q-I Bc Q*I Bd 37 HOOOOOOO OOrHOOOHO I OHOOOOHO OOOOOrHOO I o o o o o o o OOOOHHOO OOOOOHHO O O O O O O O O r-i H H I I o o o OOOrHOOOO O O r-\ I o o o o o o o O O r-i O OOOOOOOH CD H W •H s -p a 0) •H O •H «H • o B Figure 18. ECAP Standard Branch h3 where I is the current through the branch admittance element, Y. . , R ij of the circuit admittance matrix, Y, and J is the sum of the quantities J and J , which are the branch dependent and independent current gen- erator matrices, respectively. The network driving voltages, E, may be replaced, using Norton's Theorem, by the corresponding driving currents. Thus if E is the voltage source column matrix, the transformed source current is : J' = Y * E and the total driving current in the network becomes: J T = J I + J D + Y * E * Kirchoff's Current Law in matrix form is I = A*I = N B where now I £ = I R + J y , and thus, by expansion: I N = A * I B = [A * I R ] + [A * J T ] Consequently: A * Y * V = [-A] * J_ . K 1 From Kirchoff's Voltage Law in matrix form: V E " ^ * V hk Combining the two previous equations [A * Y * A ] * V N = [-A] * J j and solving for the node voltage matrix, V, N V N = [A * Y * A T ] _1 * [-A] * [J T ] = [A * Y * A J" 1 * [-A] * [J + J + Y * E] Following through now with the illustrative example, we begin by writing the KCL equations for the circuit of Figure 17. -i 2 -i 3 -i u \ ° +1. m -i, +± c -is = 456 These equations become in matrix notation I = A * I , or h _I nl" z m = > -1 -1 +1 1 +1 -1 +1 -1 *B1 X B3 he E and: h5 The voltage and current source matrices are, respectively: - e l e 2 e 3 % e 5 e 6 _ - 18.0 18.0 o V. J T = J Z + J D + ^E 18.0 18.0 -1.25 $ + J m = $ + J D1 ^D2 J D3 ^D5 J D6 BETA * i Bk [y*e] r + [Yj 18.0 18.0 o -1.25 1*6 Note that the voltage source matrix, E, clearly shows the role of V--, and that the dependent current generator matrix, J, BE D clearly shows the role of the transistor's current gain, BETA. These are the two quantities which are iteratively changed by the Regression Model- However, it is very difficult to solve the matrix equation, V N = [A*Y*A T ] _1 * [-A] * [J z + J D + Y*E], when the dependent current BETA*:L> is not known. For this reason, it is necessary to modify the above equation slightly. The requisite modification is obtained by writing the node equations for the circuit of Figure 17 • Upon substituting the equiva- lent expression for i , in terms of V , V , V , and R, and collecting terms one obtains the matrix relation: Y * V = J N N T 3^ where Y„ is the nodel conductance matrix of Figure 19 and satisfies the equation: Y = [A*Y*A T ] which was discussed above. The corresponding nodal equivalent current vector is given in Figure 20. This current ' vector satisfies the relation: J T " J I + J D + Y * E which was derived above. G O hi G O O ir\ H G ~o H + G O O I H + G O C— OJ + G O O H + G O O m o CQ >> H -P •H O •H H ft X o o G O O O G H H + G O o o G ^-^ o + G o LT\ G O ^-^ O H O Lf\ O ■* — ^ + LTN < H G ~H~ H pq O + O G <~ o EH O W r- pq j- i ~H~ 1 i pq ^S -P •H ■P o -p o I o o ■d o ON H •H >H kQ ! a ' o o IT\ <~ G G 1 O O pq O o ir\ LTN * W ^ H w pq pq pq > > > G O O o CM H 00" H G O m en GO o o pq > i h> k 9 3-U Cutoff Conditions and the Regression Model The conditions which must be satisfied for each transistor in a network, which is in a nonconducting or cutoff state, are BETA equal to zero and a base to emitter voltage, V , less than or equal BE 35 to the cutin voltage , V • The condition of BETA = implies that the collector current, I , is zero, provided the collector leakage amount I , is negligible, since at low values of I : Total I BETA = Total I B This further means that, when there is no significant base current flowing, V is determined by the circuits external to each transistor. BE From Figure 9, the Regression Model equations are: BETA = B n + B (in ^ ) + B (in -£ ) 2 1 X 3 ^ V BE = V x + V 2 (in j£ ) + V 3 (in ^ f Since the ECAP model is a strictly linear network, the currents in the base, emitter and collector circuit branches may flow in either the conventional positive direction for an NPN transistor or in the opposite direction. A transistor's current gain, BETA, may become zero in one of three ways. First, BETA may be made zero by using a logical operator statement, such as the FORTRAN IV code: 50 IF (I .LE. CUTOFF) BETA = 0.0 placed in Subroutine PIRATE after the BETA Regression Model equation has been evaluated. Second, it may become zero by carefully selecting the BETA regression equation which predicts a zero value for BETA at a suitably low value for the collector current, I . Third, a combina- tion of the previous two methods may be used. The first method tends to generate discontinuities which make convergence difficult whenever CUTOFF is an arbitrarily selected current level. The second method gives a smooth curve down to very large negative values of BETA, as I becomes increasingly smaller. An example of this event is shown in Table 1. Note that in the BETA equation of Table 1, CUTOFF corresponds to a value of I somewhere between 1.0 and 12.0 microamperes and I_ corresponds to 1.0 microampere. The third method involves a combination of the simplicity of the previous two, with CUTOFF chosen from the BETA equation and with the "IF statement" inhibiting negative values of BETA. A transistor's base to emitter voltage, V RT? , is a function of I throughout the active region. The quality of fit for a typical Regression Model V-^ equation is shown in Table 2. Note that with the same value of CUTOFF used for calculating V , one obtains a number BE close to V . However, as the drive to any transistor falls below V__ = V , the voltage across its emitter to base terminals becomes a BE 7 function of the external circuitry surrounding it. Thus at CUTOFF and below, a logical switch needs to be incorporated into Subroutine ITRATE; so that the V__ may be a function of some external circuit Bill current, I . A better external circuit dependent variable would be 51 CM * o H o • UN I o 52! i-h en cn ON t- VD + m o o cn 4- IAVD t^JJ- 0\OONHC\IO\HV0004-COlAiAOJCVI COCO O H onj- rnajHC\irowoM^iAODajcoooHi>-wo uamdco oj roo\ o cuoo_3- r- m un i>- h vo no cn ir\ en oj omai^h J- cn\£> ltn oo-ci- OOJMDJ-OJvQHUAOJr— tr-OOJ-HJ-OOvDOJOJOOVOJ-vXJOOt^- oo On O NO O-vD tfN-=t" CO UN O ONroroj- H CO LfN f-- H CO [^-H POO -^OOrHOOOOr-loO-H/-^- -3" I I cn CM H I I I I I H UN H UN CO O H O O I I I l I I H40Cf\H O H J- IAIACM IA\D OrOONrlHOOHMCOJ- t-lAJ-COCO f-CO O O fOj- tnt-CO t--OOt^OM--iACO(\IH( , nHl^(\104TOHOJh-0\ O OJOO OJ OJ NO UN OJ H NO NO PO UNNO OJ PO IT\ |>- rH UN NO 00 UN N0 _H/ O ojvo oj i^-ooh-4- oj r— >- co -H/ co _d- f-v£> oj oj no no unno h t— PO OnnO 0-4" t-NCO OOLTNH OO OO [v- o\ j- vO ON POCO UN OJ VO HOJ J- O OJ ON-cl- 0\r|vOO\OHHHOOMX)lAaj0^lArl>-iH 4H4-IA>-OOOOOHHHHHOOOOOO\0\0\COCOOO rH r-|Hr-lHr-|r-|pHHHf-H.r-IHH I OONONOONOONOO o on on o a\o ono o o onvq omoo\oo O OnnO O ON O ON O O O IA\X) C\l OO Cvl W IA o 0\ONOO\OOONO\CAOO\00 mmo(^ooo\OM^ooNOOoo ONCAOO\0 4-Cr\ONONOONOOOO CAONOCf\OcOCf\0\0\OCf\00 oo OoooouNootr— pounooooununoj OOWOiAOHM^-h f-NO NO H-cTOnOnOOOOOOOO HHHHHrHHH (\l4-04HO\COt^VDt-or)0 HOOOOCnChO\0\00O\00 H H H H H OOOONONONOOOOOOOOCOO O O O ON On ON O CO CO CO ON CO CO o r- o O O O ONONONO ON ON ON ON ON ON O CO o O O O ONONONO ON ON ON ON ON ON O ONO OOr-OJOOJUNt>-OJOJPOI>-t-OONO OOCOOCOONONONON OOf-OI>-HHi-li-| OOCOOCOOJOJOJOJ OOONOONONONONON OO ONO ONONONONON H OJ -3/ CO OJ OJ PO O CO UN OJ CO -J" ON >- ON PO O t-COJ" 4 ON -4- NO HCvl nvO H H Cv) (\J rOJ- J" UNt--COCO HWHOONiAOi^vO HCVIPOJ-iAvOt-COOCMUNHvOHNOOO ONCOvfl H H H CM Cvl romj" UNIA^O h- !> o cn II o O § •H ■s O •H CO w fH W) « O W •H w 5 H •3 < Eh W o > CO EH > ooooooooooooooooooooooooo ooooooooooooooooooooooooo cncncncncncncncncncncncncncncncncncncncncncncncncn 52 OJ * H "a H-3 00 LTN o o o • o I o OJ OO ro o V0 ON vO o\ -4- 4- lA O Ch O CO 1AJ- CM ir\ H J- O ON4 4- O H OJ VO PO LTNVO VO LTN LTN H CO ON ON PO VO H-4" ITN >- CO -j" vD4-HC\J\OvD4TOHOHHHC\llfMM OiHHOOOOOOOOOOOOO HOOOOOOOOOOOOOOO OPOH-ci-o\oopnoa\ O ON t— WHHOOOOOWIA ooooooooo ooooooooo ooooooooooooooooooooooooo I I I I I I I I I I I I I H v£> LTvO HOW lAVOCO 1A onco oj mr-j- roooj-4- VOCOJ- ON LTN LTN VO ONCO LPv ONCOH WJ-VDCOONO H H J" O ON -4" 4 01rlJO\onh-OH H CO ON ON OOVO H-4- LTNO-OOJ- ONHOJ H LTN ONVO 0J00 h- COCO OJ VO OJ VO H -=f OJOJOJCO-d--=|-ir\VOVQf-t— COCOONON -4" LTN vO vO vO vO vO vO C — t — C — C — C — t- — D — C — C~ — C — C — D — t — t— [— ["- C— 6666666666660006006006606 ooooooooooooooooooooooooo ooooooooooooooooooooooooo CO CO PO OJ OJ OJ HOOOV004-C04 I^VO LTN OJ O-OJVOOJ oj-o OOO(niAt-0\OHrlC\lC\l(\]nr04-UN\D^)ht-C0aM3\O vO vO vO vO vO vO vO C — C — C — C — t>- C — C — t^ t— E— t^- C — t~- 0- t^- E— E— 00 6666666666666666666666666 OOOONONONOOOOOOOOOOOOO OOOONONONOCOcOcOONCOcOOr-OOO O O O ONONONO ONONONONONONOOOO O O OOOOnONOnOONOnONOnOnONOONOOO ooNWoaiiAhciiajrot-NOONOOO CO O OO ON ON ON ON t— O C— H H H H CO O OO OJ OJ OJ CM ON O ON ON ON ON ON ON O ON ON ON ON ON HOJJ-COOJOJPOOCOLTNOJCO-ct-ONt^-ONPOO H(\irOvOHHCMOlm4-4-lA|^COCOriaj H OJ PO-3" LTNVO f-CO O CV] LTNHVO H H H OJ OJ t— CO -4- J- ON-* VO H O ON LTN OJ VO VO H VO O O On CO VO OO OO J- LTN LTNVO t— > o 00 II o o O o •H a o •H w w 0) ^ 0) K » OJ 0) H EH w o > CO EH > 00000000 00000000 ooooooooo ooooooooo 000000 000000 o o o o cnno^^cnooroon^foncnrnrooorornpooorrioorooororo 53 a voltage, but this leads to the matrix solution problem similar to that discussed in Section 3-2, where now node voltage is the indepen- dent variable. Note that both Table 1 and Table 2 were calculated using the Regression Model Evaluation Program listed in Appendix D. 3*5 Extension of the Regression Model Two approaches requiring only minor Regression Model modi- fication were explored. First, V^^ was set equal to the cutin voltage with the result that satisfactory predictions of network behavior can be made for operating conditions close to cutoff. Obvious inaccur- acies are introduced as each transistor's operating point passed well into the cutoff state. The second approach consisted of adding a large impedance, ZOFF, in series with the base circuit of the transis- tor for the purpose of simulating ideal diode behavior. The ZOFF impedance of 5> 555* 555*0 was switched into the circuit by a logical operation statement in Subroutine ITRATE whenever the I current became less than I • This latter approach was tested using the cir- cuit of Figure 1-B with the result that current convergence was not obtainable. A check was made of the effects of setting BETA equal to zero and V-,^ equal to V , by examining the matrices used in the matrix equation: Y * V = J . N N T 5h The solution to this set of simultaneous equations will exist provided the Y matrix has an inverse. By inspection of Figure 19, it is apparent that this will always be the case provided the admittances are real and positive; since BETA appears only in nonmajor diagonal terms. The possible range of variations in V--, also will not affect -Dili the existance of Y m inverse since V only appears in the J matrix i\ BE T of Figure 20. This means a solution for V will exist even if J is a zero vector. 3«6 Conclusion Summarizing briefly, the computer program MAP solves for the linear current in each of the branches. The resulting collector current is then used as the dependent variable in the Regression Model equations of Figure 9 hy Subroutine ITPATE. The iterative process is started in accordance with Guth's flow chart of Figure 21 until convergence. Then the proper values of BETA and V™ are obtained as a function of the collector current in the active -D-tLi region. The calculations made by the program may be checked both before iteration starts and after convergence is obtained by using the PRINT MI input code described in 4.3 • A set of matrices obtained in this are shown in Figures 22 and 23, respectively. One interesting example of the accuracy of NLAP is a DC option analysis of the linear test circuit of Figure 17 . The NLAP computed results are compared with manually calculated results, for the nodal conductance matrix, in Figure 2k, and for the equivalent current vector matrix in Figure 25 • The results compare closely out to the sixth decimal place. 55 Obtain a nominal solution Calculate new values for BETA and VBE using values of collector currents just calculated Yes Yes I Insert new values of BETA and VBE into the proper matrices Calculate a new set of collector current values Calculate the change in value of preselected reference current Calculate the changes between previous solution and the present solution END Figure 21. Flow Chart of Iterative Regression Model Solution Method. 56 NODAL CONDUCTANCE MATRIX ROW COLS 11-4 o. 238679200-01-0. U9999990D-02 0.0 0.0 15-5 0.0 2 1-1+ -O.50U99988D 00 0.10050732D 03-0.13333332D-03-0.21758056D-02 2 5-5 -0.10000002D 03 3 1 _ 4 O.I+9999988D 00-0.50013321D 00 0. 1000001 5D 03 0.0 3 5-5 0.0 ' k 1 - k 0.0 -0.21758056D-02 0.0 0.10000219D 03 h 5 - 5 0.0 5 1 - k 0.0 -0.10000002D 03 0.0 0.0 5 5-5 0.10000003D 03 EQUIVALENT CURRENT VECTOR NODE NO. CURRENT 1 0.22717916D-01 2 -0.38884987D 00 3 0.11538497D 03 h -0.29000000D 03 5 0.0 NODAL IMPEDANCE MATRIX ROW COLS 1 1 - k 1 5 - 5 2 1 - k 2 5 - 5 3 1 - 1+ 3 5 - 5 k 1 - h h 5 - 5 5 1 - h 5 5 - 5 0.5293588UD 02 0.521722U8D 00 0.69562887D-06 0.11351 i +l8D-04 0.521722U3D 00 0.52693899D 02 0.21+901+866D 01 0.332061+35D-05 0.5^1869600-04 0.21+904861+D 01 -0.11396619D-02 0.984712U3D-02 0.99999983D-02 0.21^2l+959D-06 0.98471233D-02 0.11464917D-02 0.5U186960D-04 0.72249166D-10 0.99997821D-02 0.5U186955D-04 0.52693894D 02 0.24904864D 01 0.33206432D-05 0.5^1869550-04 0.25004861D 01 Figure 22. DC Solution Matrix Obtained Prior to Iteration 57 NODAL CONDUCTANCE MATRIX ROW COLS li-U 0.23867920D-01-0.U9999990D-02 0.0 0.0 15-5 0.0 2 1-1+ -0.49911976D 00 0.10050l¥+D 03-0.13333332D-03-0.21758056D-02 2 5-5 -0.10000002D 03 3 1 - h O.49I+II976D 00-0.49425310D 00 0. 1000001 5D 03 0.0 3 5-5 0.0 h 1 - k 0.0 -0.21758056D-02 0.0 0.10000219D 03 4 5-5 0.0 5 1 - k 0.0 -0.10000002D 03 0.0 0.0 5 5-5 0.10000003D 03 EQUIVALENT CURRENT VECTOR NODE NO- CURRENT 1 0.22654877D-01 2 -0.37802932D 00 3 0. 11537^210 03 k -0.29000000D 03 5 0.0 NODAL IMPEDANCE MATRIX ROW COLS 1 1 - h 1 5 - 5 2 1 - h 2 5 - 5 3 1 - k 3 5 - 5 k 1 - k h 5 - 5 5 1 - k 5 5 - 5 0.52935133D 02 0.52783296D 00 0.70377616D-06 0.11U84368D-04 0.52783291D 00 0.52690314D 02 0.25196555D 01 0.33595354D-05 0.5^82l605D-OU 0.25196553D 01 -0.1139M+18D-02 0.98453338D-02 0.99999983D-02 0.21U21063D-06 0-98453328D-02 0.11U64137D-02 0.5 i +82l605D-Ol+ 0.73095358D-10 0-99997821D-02 0.5^82l600D-0U 0.52690309D 02 0.25196553D 01 0.33595350D-05 0. 5 i +82l600D-04 0.25296550D 01 Figure 23 • NL Solution Matrix Obtained After Completion of Iteration 58 N +0.00229606 +0.00000000 -0.00200000 +0.10000000 +0.003030^0 -0.10000000 ■0.10200000 +0.00000000 +0.10570380 a) Manual Calculations "N +0.22960991D-02 0.00000000D+00 -0.19999999D-02 +0.9999996+D-01 0.30304029D-02 -0.10000000D+00 -O.IOI99996D+OO -0.99999966D-07 +0.10570377D+00 b) MAP Calculations Figure 2k. Nodal Conductance Matrix Calculations for BETA = 50 59 +0.00400000 +0.1795 i +5 1 +5 -0.12750000 a) Manual Calculations +O.39999976D-O2 +0.1795 i +527D+00 -0.127i+9982D+00 b) NLAP Calculations Figure 25. Nodal Current Vector Calculations for BETA = 50 and V^ = -1.25 Volts is ill 60 A second example of the accuracy of NLAP is a E option analysis, the output of which is compared with laboratory measured performance in the graph of Figure 26 for the emitter follower of Figure 27. 61 CJ •H -P CO •H Fh CD -P O CC? *H CtJ O -P cd w «H O 4 CM ^* d d i i siioa - 39VH0A indino aaMO-nod aainwa ao o <0 o -=- e 1 = 2.9v I- 7.5K 0.770v (t) BETA*i B2 HH ! H^ i i^€) C3 TRANSISTOR Rl 200ft 53X1 IN + 0.01ft N. 62 N, [OR = 459 XI 1 [NOR = 1068X1 J 0.01ft r 8 y 100 K E OUT =- e 2 =l.l5v •I Figure 27. OR Emitter Follower Schematic Diagram 63 k. APPLICATION OF NLAP TO LOGIC CIRCUIT ANALYSIS 4.1 Introduction NLAP is intended to be used for analyzing nonsaturating logic circuitry such as emitter coupled logic blocks. The capability now exists within the program for linear region parameter variation analysis. Should the user desire to perform special calculations, a subroutine may be coded and called just prior to the return of control to the main program by Subroutine ITPATE. The NLAP calling procedure and its associated system procedure is given in Figure 28. k.2 Preparation of NLAP Input Data Deck The input language to NLAP is similar to ECAP's^ and is aligned closely with the language of the electronic engineer. Each of the circuit elements use a simple descriptive letter coding and the topology of the circuit interconnections is identified by a sequence of branch and node numbers. The polarity of positive current flow is inserted by ordering the nodal connection using identifying numbers in a from node m to node n arrangement. The general branch, or B., statement consists of a branch J number, j; the from and to node numbers, m and n, respectively; the braich resistance, R, in ohms; the independent voltage source E, in volts; and the independent current source I, in amperes. In other words, the general branch statement is: B. = N(m,n), R=7, E = e, I = i J 6k /*FORMAT PR,DDNAME=FT10F001,COPIES=l EXEC //JOBLIB // EXEC //MAP II II 'I, //FT05F001 DD //FT06F001 DD //FT07F001 DD //FT08F001 DD //FT09F001 DD //FTlOFOOl DD //FTllFOOl DD //FT12F001 DD //MAP.SYSIN /* DD DSNAME=SYS1.CKTLIB,DISP=( OLD, PASS) MAP PGM=MAP * EXECUTE MAP -- JOBLIB CARD REQUIRED //JOBLIB DD DSNAME=SYS1.CKTLIB,DISP=( OLD, PASS) DD DDNAME=SYSIN SYSOUT=A,DCB=(RECFM=FBA,LRECL=133,BLKSIZE=798) UMET=(CTC, , DEFER) ,DCB=(RECFM=F,LRECL=80,BLKSIZE=80) UNIT=(CTC, , defer) ,dcb=(recfm=f,lrecl,8o=blksize=8o) UNIT=(CTC,, DEFER) =DCB=(RECFM=F,LRECL=80,BLKSIZE=80) UM!T=(CTC, , DEFER) ,dcb=(recfm=f,lrecl=8o,blksize=8o) UNIT=(CTC, , DEFER) ,DCB=(RECFM=F,LRECL=80,BLKSIZE=80) UMET=(CTC, , DEFER) ,dcb=(recfm=f,lrecl=8o,blksize=8o) * MAP DATA DECK GOES fflIRE Figure 28. MAP Calling Sequence 65 where j, m, n, y , e and i are place holders for specific numeric values which vary from "branch to branch. An example of the specific coding for the circuit of Figure 27 is listed in Figure 29. The dependent current sources are denoted by a T statement containing the controlling and the controlled branch identification numbers, wotether with the associated current gain value, BETA. The regression equation coefficients for the BETA and V^- •BE equations are entered in T and B. statements, respectively, which k are of the form: T R BETA (i) = B 1 , B 2 , B 3 B. E(i) = V 1 , V 2 , V 3 where T v and B . start in card column one with the BETA (p) and the k J E(p) dependent variable statements starting column seven. The cyclical iteration process is controlled by two succes- sive statements CURRENT - 7 and TOLERANCE which imply that the iteration process is to terminate whenever the newest solution for the current in branch 7 changes by less than the prespecified amount, 5, from the previous iterations calculated value. 66 ID21 OR EMITTER FOLLOWER, RE = 1+59-6 OHMS -DCAP DC Bl N(0,l),R=53 ,E=1.0 B2 N(l,2),R=200.0,E=-0.770 B3 N(0,3),R=0.01,E=+1.15 B*+ N(U,0),R=0.01,E=+2.90 B5 N(3,2),R=7500 B6 N(5,^),R=^59-6 B7 N(2,5),R=0.01 B8 N(5.0,R=100000 Tl B(2,5),BETA=100 PRINT NV,BV,BA,BP,MI EX END A. DC Circuit Analysis Data Deck ID21 OR EMITTER FOLLOWER, RE = 459-6 OHMS -NLAP DATA NL Bl N(0,l),R=53 ,E=+1.0 B2 N(l,2),R=200.0,E=-0.770 B3 N(0,3),R=0.01,E=+1.15 Bk N(U,0) ,R=0.01,E=+2.90 B5 N(3,2),R=7500 B6 N(2,l+),R=l+59.6 B7 N(2,5),R=0.01 B8 N(5,0),R=100000 Tl B(2,5),BETA=100 PRINT NV,MI EX Tl BETA(5) = -55 1 +- 67056, +172.1+2553, -11. 1718 B2 E(5)=-0. 5^023, -0.021+29, -0.00021 CURRENT = 6 TOLERANCE =0.01 EX RETURN END B. NL Circuit Analysis Data Deck Figure 29. Typical NLAP Input Data 67 The amount of tolerable deviation from current convergence is stated in a decimal, not percent, format. One example is: TOLERANCE =0.01 which means current convergence to within one percent. ^•3 Solution Control Codes Two types of analyses are possible using NLAP, linear direct current and iterative nonlinear direct current. The solution control cards are DC and NL, respectively. A DC problem deck must contain only those cards up to the first EX or EXECUTE card as shown in Figure 29-A. The full set of ECAP/36O DC solution options ' SE, WO, ST, and MI are available to ' the DC user. These options obtain for the user: element sensitiv- ities, worst case tolerance analysis, standard deviations of the node voltages assuming component values which are statistically independent, random, and normally distributed about their mean values, and a set of solution matrices, respectively. An NL problem deck must contain the same network description cards as the equivalent DC problem deck, plus the regression equation cards for BETA and V_„ and the CURRENT, TOLERANCE, EXECUTE, RETURN and BE END cards as shown in Figure 29 -B. These last three cards are self descriptive and the user should observe that the 'END card is used to s ignal the end of the input data so that control may be passed to the system monitor. It should be noted that the only case where the PR or print card is essential is when the user desires to print out the nodal 68 conductance matrix, the equivalent current vector, and the nodal impedance matrix. To obtain these matrices the required code is: PRINT NV, MI This coding was used to obtain the matrices shown in Figures 22 and 23- h.k Solution Output and Identification When the user desires to perform a parameter variation analysis, careful attention should be given to the preparation of the title card which is placed at the beginning of each problem deck for solution identification purposes. The letters ID are placed in card columns one and two for the purpose of signal by the subroutine ITRATE to search for subse- quent code. Card column three is reserved for a problem identification number from one to nine which is read and written by the program in Al 39 format . Card column 5 is reserved for a flag which resets the solution number to one after a series of related solutions have been run for a given problem and the user desires to switch to a new solution series of the same or different problem. Any integral value between one and nine will reset the solution counter to one. There are a variety of output options which may be selected through the use of IBM 36O Job Control Language . The two principal modes of output communication are 80 column card images and 133 column printed text. In planning the FTXXF001 data sets listed in the system procedure of Figure 2k, the user was given a very flexible 69 list of data sets, numbers FT07 through FT12, upon which to call and use for parameter variation studies. As a result, these later data sets are all 80 bytes long and are blocked at 80 bytes so that the user may employ either cards or directed access devices for data transmission to an appropriate plotter. The MAP output routine ECB25 is listed in Appendix E. Thus, the user may select the required data set by consulting this subroutine and the definitions of the array names given in Table 3* A typical MAP solution obtained without use of the PRINT statement of ECAP is contained in Figure 30 and is the output of the FT06F001 data set. 4.5 Conclusion The range of validity of the Regression Model has been found to be limited to the active region. The modification of these equations and the subsequent testing were outside the scope of this investigation and are, therefore, a subject for further study. 70 OUTPUT VARIABLE NLAP STORAGE ARRAY Branch Voltage Branch Current Element Voltage Element Current Branch Power Dissipation Node Voltage Transconductance BETA Element Admittance Element Impedance CCSAV (1, J) CCSAV (2, J) CCSAV (3, J) CCSAV (k, J) CCSAV (5, J) CCSAV (6, J) CDSAV (1, J) CDSAV {2, J) Y(J) X(J) Table 3* Summary of NLAP Output Variable Storage Arrays 71 CM PO LfN O VO W OJ m OO OJ H CO ir\ r- PO po t— -=f VO ON ON vo v.O UN ON ON LfN ON OJ -4" ON OJ ON OJ H CO OJ O o rH OJ 1 o O o o o OJ PO o o O o o o vO H o o O o o o o OJ o o O o o o o o o o r- -=r LfN ro o o o I o o PO LT\ o PO CO PO PO o o • o o OJ o vO vO o o o o vO CO vO o o o o vO vO LfN OJ OJ ON ON o vO LT\ OJ H H I o OJ o o o • o o LTN PO o vO ON LTN -4 o o o o o o o o CO LT\ ON H -3- ON t- r- H H !>- OJ J- H LfN LfN ON ON ON CO o fc- OJ CM VO VO LTN vO VO O OJ CM VO VO -=t" O PO O o O o o t— CO t- CO o o CO r- vo LfN OJ OJ o O O O o PO O o CO LTN ON H J- ON I s - r~ H H t- OJ J- H LfN LfN (7N ON ON 00 o c- OJ CM VO vO LTN vO vO O OJ CM vO vO -=*■ o PO o o o O o t- CO t- CO o o o o vO vO vO vO o o PO LTN CM ■H J- ON o CO LTN [*- PO PO LfN o o r- -3- £- ON ON CM vO o VO Vi) o ON ON J- LfN o LfN ON r- J" ON OJ OJ o CM ON f- H CO ON H o CM o o • o o o o o H O o CO ON H H J" ON _3" o 6 pq Eh rx; vO -=J- ON PO CM CO CO ON LfN -P ft -P a 0) -P £ •H U ft £ O •H -P H O CO H O O PO ro o •H O PO •H ft o o o o o o o o • • • • • • • • o o o o o o o o t3 O CM o o o o H I s - o o LfN LfN O I s - rH ON O I OJ o o d o d OJ PO VO CO ft 72 REFERENCES 1. Brannin, F. H., et al. Computer Aided Design Issue, Proceedings IEEE , Vol. 55, No. 11, Nov. 1967. 2. Kuo, F. F., "Network Analysis and Synthesis", John Wiley and Sons, Inc., New York, 1966, Chapters 6 and 9« 3. Cardenas, Hector, "Design Considerations for High Speed Unsaturated Logic", Unpublished Paper, Texas Instruments, Inc., Dallas. h. Nanarati, R. P., "An Introduction to Semiconductor Electronics", McGraw-Hill Book Company, Inc., New York, 1963, p.l62. 5. Lo, A. W., "Some Thoughts on Digital Components and Circuit Techniques", IRE Transactions on Electronic Components , September, I96I, p.l+17. 6. Alley, C. L., and Atwood, K. W., "Electronic Engineers", John Wiley and Sons, Inc., New York, 1962, pp. 11 4 and 152. 7« Guth, G., "Unpublished MS Thesis", Department of Computer Science, University of Illinois. 8. Ibid. 9. Hogsett, G. R., "Electronic Circuit Analysis Program ECAP/36O-B", TBM Corp., Los Angeles, California, 1966. 10. Littauer, R., "Pulse Electronics", McGraw-Hill Book Company, Inc., New York, 1965, p.316. 11. Greiner, R. A., "Semiconductor Devices and Applications", McGraw-Hill Book Company, Inc., New York, 196l, Chapter "J. 12. Littauer, R., op. cit., pp. 17-19- 13. Ryder, R. M. , and Kircher, R. M. , "Same Circuit Aspects of the Transistor", Bell System Technical Journal , V.28, July, 19^9, P-370. Ik. Nanavate, R. P., "An Introduction to Semiconductor Electronics", Prentice -Hall, Inc., Englewood Cliffs, N.J. , 1963, P-151- 15. DePain, L., "Linear Active Network Theory", Prentice -Hall, Inc., Englewood Cliffs, N.J., I962, p. 65. 16. Brown, J. S., and Bennett, F. C, "The application of Matrices to Vacuum-Tube Circuits", Proceedings IRE , Vol. 36, July, I9U8, pp. 851-852. 73 17* Anner, G. E., "Elementary Nonlinear Electronic Circuits", Prentice -Hall, Inc., Englewood Cliffs, N.J. , 1967, pp. 28-42. 18. Ibid. 19. Golden, J. T-, "FORTRAN IV: Programming and Computing", Prentice -Hall, Inc., Englewood Cliffs, N.J. , 1965, P-31. 20. Smythe, ¥. R., Jr., and Johnson, L. A., "Introduction to Linear Programming with Applications", Prentice -Hall, Inc., Englewood Cliffs, N.J. , 1966, p. 68. 21. Gibbons, J. F., "Semiconductor Electronics", McGraw-Hill Book Company, Inc., New York, 1966, p.405. 22. Gray, P. E., et al, "Physical Electronics and Circuit Models of Transistors", John Wiley and Sons, Inc., New York, 1964, Chapter 9* 23. Malmberg, A. F., et al, "NET-1 Network Analysis Program", Report LA- 311 ? Los Alamos Scientific Laboratory, New Mexico, 1964. 24. Guth, G., op. cit. 25. Ibid. 26. Searle, C. L., "Elementary Circuit Properties of Transistors", John Wiley and Sons, Inc., New York, 1964, p. 48. 27. Seshu, S., and Balkonian, N. , "Linear Network Analysis", John Wiley and Sons, Inc., New York, 1959* p. 68. 28. Crothers, M. H., "Equations for Electrical Network", E.E. 429 Class Notes , University of Illinois, Urbana, Illinois, 1964. 29. Varga, R. S., "Matrix Iterative Analysis", Prentice-Hall, Inc., Englewood Cliffs, N.J. , 1962, Chapter 3. 30. Tyson, M. , et al, "1620 Electronic Circuit Analysis Program, (ECAP)". User Manual, IBM Report 1620-EE-02X , White Plains, New York, 1965. 31. Guth, G., loc. cit. 32. Hogsett, J. R., "ECAP/36O-E, Electronic Circuit Analysis Program", S/36O General Program Library , No. 360D-l6.4-4.001, IBM Corporation, Poughkeepsie, New York. 33* Tyson, M. , et al, op. cit., p.l6l. 7^ 3*+. Brannin, F. H., "Computer Methods of Network Analysis", Proceedings of the IEEE , Vol. 55, No. 11, Nov. 1967, p.1787. 35« Millman, J., and Taub, H., "Pulse, Digital and Switching Waveforms", McGraw-Hill Book Company, Inc., New York, 1965, P- 217. 36. Guth, G., loc. cit. 37. Tyson, M. , et al, "Electronic Circuit Analysis Program (ECAP)", User Manual, IBM Report, 1620-33-02X, IBM Corp., Poughkeepsie, New York, p. 2. 38. Hogsett, G. R., op. cit., p. 22. 39* Tyson, M., et al, loc. cit., pp.56-65^ UO. Editorial Staff, "IBM Operating System/360, FORTRAN IV", IBM Systems Reference Library, File No. S360-25, Form No. C28-6515-3 , Programming Systems Staff, IBM Corp., Poughkeepsie, New York, pp. 59-61. Ul. Editorial Staff, "IBM Operating Systems/360 Job Control Language", IBM Systems Reference Library, File No. S36O-U8, Form No. C28-6539-3, Programming Systems Staff, IBM Corp., Poughkeepsie, New York. 75 APPENDIX A A NETWORK ANALYSIS PROCEDURE 1. Introduction The formulation of an electronic circuit's mesh solution begins by writing the branch level matrices of Figure A2 for the net- work shown in Figure Al. Each of these matrices is a column matrix containing one row element for each network branch. 2. Matrix Equation Formulation The impedance matrix, Z, of Figure A3 is generated using the relation: Matrix element Z.. = Z , , . n branch. l The Kirchoff's Voltage Law coefficient matrix, A, of Figure A3 is formed by summing the voltages, V., around each mesh with the algebraic sign determined by the agreement (+), or disagreement (-), with the arbitrarily preselected positive current direction. This A matrix has as many rows as the network has meshes and as many columns as the network has branches. The quantities, Z, JG, E, and A, are processed by a series of matrix equations to arrive at the solution for the network's branch current matrix, I . These equations are: a) All Norton equivalent current sources are converted Thevenin equivalent voltage sources: 76 ure Al. An Equivalent Network 77 +10 Volts JG +2 +5 +2 Amps V V, v 3 v 5 V, Volts - — H *2 s h s *6 Amps Figure A2. Branch Level E, JG, V, and I Matrices 78 5 2 2 5 5 4 Amps ■1-1 0-1 0+1-1 0+1 0+1-1+1 Figure A3. Branch Level Z and A Matrices 79 N = Z * JG b) The converted current sources are summed with the native Thevenin equivalent voltage sources : EE = E + N. c) The voltage sources around each mesh are summed by a matrix equation: EM = A * EE. d) The mesh impedance matrix is formed by transposing the A matrix, premultiplying the Z matrix by A, and then post- T multiplying A * Z, the A * Z product by A : AM = A * Z * A T . e) The network's mesh current is calculated by premulti- plying the EM matrix by the inverse of the ZM matrix: IM = YM * EM. f ) The final step is to obtain the individual currents in each branch by summing up the mesh currents passing through each branch and then subtracting the current generator matrix, JG: IB = A T * m - JG. 80 3« Evaluation of Matrix Equations The above matrix equations are herein evaluated for the network of Figure Al. a) N = Z * JG = 5 2 2 000500 5 4 — - - - 2 10 5 10 * 2 = 10 . _ Volts b) EE = E + N = 10 — 10 10 10 10 10 + 10 = 10 L. • Volts c) EM -1-1 0-1 0+1-1 0+1 +1 -1 +1 10 -20 10 -* 10 10 = 10 - _1 Volts 81 d) AM = [A*Z*A ] -1-1 0-1 0+1-1 0+1 0+1-1+1 5 2 2 5 * 000050 4 _ _J -10 -1 +1 0-10 0+1 — +1 -1 -1 +1 -1 11 -2 -if -2 +9 -5 -k -5 1+ ohms e) IM = IM 3 = YM * EM = 10 +101 -1+8 -1+6 -1+8 +138 -63 +1+6 -63 +95 1- - — -2 1 -156 " B31 -33 +1 +3 —j ■1.88 ■0.397 ■O.0367 amps f) IB = A * IM - JG = -10 -1 +1 -1.88' 0-10 0+1 -0.397 +1 -1 -1 +1 +0.036 - [J] = +1.88 +1.1+8 +O.1+0 +O.036 -0.1+1+ +1.1+2 -0.12 +1.1+8 +1+.60 -1.96 -0.1+1+ +1.92 A network analysis computer program utilizing the above matrix equations is listed in Figure Al+, with a sample output shown in Figure A5« amps 82 * 1.00 FLOAT; * 2.00 ARRAY A 3 6 F; ARRAY E 6 1 F; * 3.00 ARRAY JG 6 1 F; ARRAY Z 6 6 F; * 4.00 ARRAY N 6 1 F; ARRAY EE 6 1 F; * 5-00 ARRAY EM 3 1 F; ARRAY AT 6 3 F; * 6.00 ARRAY ZAT 6 3 F; ARRAY AM 3 3 F; * 7-00 ARRAY YM 3 3 F; ARRAY IM 3 1 F; * 8.00 ARRAY IBM 6 1 F; ARRAY IB 6 1 F; * 9.00 ARRAY IBX 6 6 F; ARRAY IBS 6 1 F; * 10.00 ARRAY PD 6 1 F; ARRAY P 6 6 F; * 11.00 ARRAY RP 6 6 F; ARRAY S 6 1 F; * 12.00 ARRAY SP 6 1 F; * 13-00 A[0,0]=-1; A[o,iJ=-i; A[o,5l=-i; * 14.00 A[l,l]= 1; A[l,2]=-1; A[l,4]= 1; * 15-00 A[2,3]= 1; A[2,4]=-l; A[2,5]= 1; * 16.00 E[l,0]=10; * 17.00 JG[0,0]= 2; JG[2,0]= 5; JG[3,0]= 2; * 18.00 RP[0,0]= 1; RP[1,1]= 1; RP[2,2]= 1; * 19.00 Z[0,0]= 5; Z[l,l]= 2; Z[2,2]= 2; Z[3,3]= 5; * 20.00 A[3,3]= 5; Z[4,4]= 5; Z[5,5]= h; * 21.00 N = Z * JG; EE = E + N; EM = A * EE; * 22.00 FOR I = 0, 1, 2; BEGIN FOR K = 0, 1, 5; BEGIN * 23.00 AT[K, I] = A[I, K]; END END * 24.00 ZAT = Z * AT; AM = A * ZAT; YM = ZM** -1.0; * 25.00 IM = YM * EM; IBM = AT * IM; IB = IBM - JG; * 26.00 IBX[0,0] = IB[0,0]; * 27.00 IBX[3,3] = IB[3,0]; * 28.00 IBS = IBX * IB; * 29.OO PD = Z * IBS; P = RP** -1.0; * 30.00 S = P * PD; S = 100 *S; * 31-00 FORMAT LINE, S27, C*MATCK DATA OUTPUT*// * 32.00 PRINT LINE; * 33-00 FORMAT HDR, C* I Z IB PD RP * 34.00 S SP*/; * 35-00 PRINT HDR; * 36.00 FORMAT UNITS, C* BRANCH OHMS AMPS WATTS * 37-00 WATTS NONE PERCENT*/; * 38.00 PRINT UNITS; * 39-00 FORMAT MATCK, 16 ,6(Flo.2); * 40.00 FOR I = 0,1*5; BEGIN * 41.00 PRINT MATCK, I,Z[l,l] ,IB[l,0] ,PD[l,0] ,RP[l,l] ,5[l,0] ,SP[l,0] ; * 42. 00 END; Figure A4. Network Analysis Program 83 MATCK DATA OUTPUT I Z IB PD RP S SP BRANCH OHMS AMPS WATTS WATTS NONE PERCENT 5.00 -0.12 0.08 1.00 0.08 7.53 1 2.00 1.U8 U.38 1.00 4.38 1+38.17 2 2.00 -it. 60 1+2.37 1.00 1+2.37 1+237.32 3 5.00 -1.96 19.28 1.00 19.28 1928.1+5 k 5.00 -0.43 0.9I+ 1.00 0.91+ 93.81+ 5 1+.00 1.91 14.61+ 1.00 Ik. 6k 11+61+.37 Figure A5» Output of Network Analysis Test Program 6k APPENDIX B REGRESSION MODEL SUBROUTINE I SUBROUTINE ITERATE LISTING COMMON CCSAVIfc,20G) ,IDW0R0(74) DOUBLE PRECISIUN ZPRL150.50) GNL0O030 COMMON NMAX,NNODE , NTE RMS , NUMBL , NUMBR , NUMBC , IR TN , NTR AC E , NSWTCH , KTG, GNLG005 1 NPRINT(IO) GNLG0060 COMMON E(2CC),EMIN(200),EMAX(2CC) , AMP ( 200 ) , AMPM I N ( 200 ) t AMP MAX ( 200 ) GNL 000 7 n COMMON YI 200),YMIN<2 00) , YM AX< 200 ) , N I N I T ( 200 ) , NF IN ( 200 ) , MODE 1 ( 200 ) GNL 000 tK) COMMON Y TERM (200) , YTERMH<2 00) iYTERML(200I , I ROWT ( 200 ) , I COL T < 200 ) GNL00090 COMMON ERR0R1,ISEQ,MSEQ,M0,NUMM0, VFIRSTI50) , VSECNDI 50 I , VL AST ( 50 ) GNL 00 100 COMMON MOBRN(50),MOPARM(50) ,MOSTEP( 50),INX0UT(4) GNL00110 C GNL00120 C THE FOLLOWING VARIABLES ARE USED ONLY IN THE ECAP D.C. ANALYSIS GNL00130 COMMON AX1.SMLEPI 50) ,CURR ( 200 ), SMLE ( 200 ), EQUCUR ( 50 ) ,EX(200) GNL00 150 COMMON EBI2CO),AMPX(200),AMPB<200),VNOM«50) , STDSQ ( 5 ) ,L , M , IITOL GNL 00 160 COMMON JX1, JX4,JX5, DELTA, DUNK28) GNL00170 COMMON NW0RCS<72) ,NMCO( 2 , 201 , KLABEL ( 41 , KPUNC(5) , INDCI2,20) GNL001S0 COMMON INPUTEM9) ,NBC0(20) , KTYPE(5) , NBL ANK , NOEXEC , I TOL , NEQU I M , IPC GNL 00 191 COMMON INVAL,LL,IC0L,LTYPE,KCCL,NCUIT,ITRANS,K0,KS,KELAST,NUM,M1 GNL 00 192 COMMON M2tM3,KCARD,KG,NP,NTR,MAC,HNODE,TNUM,NOEL,N0E,N0I,NOIC GNL 00 193 COMMON EQUIVN(20J ,K0UT(2,10) GNL00194 COMMON MATA(200,4,3),YX(200I,V8(200) , YTERMXI 200 ) , YT ERMB ( 200 ) GNL00210 COMMON WCMAX(50),WCMIN(50) GNL00220 COMMON CCSAV(2,200) OOUBLE PRECISION SMLEP ,CURR, SMLE , EQUCUR GNL00240 C GNL00270 C THE FOLLOWING VARIABLES ARE USED ONLY IN SUBROUTINE ITRATE DIMENSION NITER(6,2),C0EFS150,5), ICRESI50) , IPTYPE ( 50) , I PLCC (50) GNL 00280 DIMENSION ICURR<2 5),T0L(25>,AMP0LD(25),BETA(200),GM(200) GNL 00290 DOUBLE PRECISION MACURI200) WNL00295 REAL*8 IREF WNL00297 C C INITIALIZE AND DEFINE DICTIONARY AND INDICATORS GNL00310 IF (NTRACE) 1,3,1 GNL00330 1 WRITE (6,2) GNL00340 2 FORMAT (• SUBROUTINE ITRATE, REGRESSION MODEL VERSION ENTERED') 3 NITERU.ll* -482328512 GNL00360 NITER(l,2)= -985644992 GNL00370 NITERI2,l)= -1019199424 GNL00380 NITER(2,2)= -465551296 GNL00390 NITER! 3, I )= -482328512 GNL00400 NITER13.2)* -700432320 GNL00410 NITER(4,1)= -985644992 GNL00420 NITERI4,2I» -415219648 GNL00430 NITER(5,1)« -733986752 85 NITER<5,2)= -700432320 NITER(6,l»= -650100672 NITER<6,2)= -985644992 GNL00440 DO 300 1= 1. 5C GNL00450 ICR€SII)=0 GNL00460 IPT^PEl 1 1=0 GNL00470 IPLOC(l)=0 GNL00480 DO 300 J=l»5 GNL00490 300 COEf S(IiJ)=0.0 GNL00500 DO 301 1= It 25 GNL00510 ICURRU> = GNL00520 TOL(l)=0.C GNL00530 301 AMPOLD(I)=0.0 WNL0053? DO 102 1=1,200 WNL00534 BETA(I)=0.0 WNL00536 MACURII ) = 0.0 WNL00538 302 GM(I)=0.0 GNL00540 INDCUR=0 GNLOO550 INDTQL=0 GNL00560 IN0TEM=0 GNL00570 TEMP=0.0 GNL00580 TEMPI=0.0 GNL00590 TEMPF=0.0 GNL00600 TEMPC=0.0 GNL00610 IINMM=0 GNL00620 ITEHP2=i GNL00630 C GNL00640 C READ AND LIST DATA CARD GNL00660 1000 READ 15,4) NWCRDS GNL00670 4 FORMAT (72A1) GNLOO6R0 URITE (6,5) NWORDS GNL00690 5 FORMAT (IX.72AI) GNLOOfOO KCARD=KCARD*l GNL00710 NOEXEC=N0EXEC*NQUIT C C CHECK FOR ■ IC CARD t#ww IF (NW0RDS(l)-INDC(l,15)) 1004,1001,1004 1001 IF CNtaORDSm-NMCDCltin 1 004, 1C02, 1004 1002 DO 1003 ICOL=l,72 1003 IDWORDI ICOL) = NWORCS< ICOL) GO TO 100C C 1004 CONTINUE _ , An „ GNL00720 IF INWOROS(1)-INPUTBI8)) 2 000 , 1 OOC, 2000 GNL00730 C , GNL00 740 C SUPPRESS BLANKS FROM COLUMNS 7-72 GNL00750 C GNL00760 2000 KCCL=6 GNL00770 DO 7 IC0L=7,72 GNL00780 IF (NWORDSUCOL)-NBLANK) 6,7,6 GNL00790 6 KCOt=KCCL»l GNLOO^OO NWORDS(KCOL)=NWORDS( ICOL) GNL00810 7 CONTINUE GNL00H20 C GNL00H10 C CHECK CONTENTS OF COLUMNS 1-6 GNL00840 C GNL00850 CO II 1C0L=1,5 GNLG0860 IF (NWOROSI ICOD-NBLANK) 8,11,8 GNL00870 8 DO 9 LTYPE=1,2 86 IF INWORDS( ICOL)-KLABEL(LTYPE)) 9,200,9 GNL00380 9 CONTINUE GNL00890 M3«5 GNL00900 15 ITRANS-6 GNL00910 10 WRITE (6,3006) Mi GNL00920 WRITE (6,3007) KCARD.ICOL GNL00921 WRITE (6,3008) GNL00922 NQliIT=l GNL00923 3006 FORHAT I'C ****♦ ERRCR NO.', 13,' **** MS6 FROM SUBROUTINE ITRATE') 3007 FORMAT (• CARO NG.=',I3,3K, 'APPROXIMATE COLUMN NO. IS', 13, l'HSG FROM SUBROLTINE ITRATE*) 3008 FORMAT (//) GNL00926 GO TO 1000 GNL00930 16 FORMAT ( '0' , 'SUBROUTINE ITRATE ERRO« MSG - CHECK YCUR INPUT DATA 1VER CAREFULLY, PGM SAYS YOU HAVE MADE A GOOF') 11 CONTINUE GNL00950 IF (KCOL-6) 500,12,13 GNL00960 12 M3=4 GNL00970 GO TO 15 GNL0098D 500 ITRANS=5 GNL00990 GO TO 10 GNL01JOO C GNL01010 C CHECK FOR TEMPERATURE, CURRENT, TOLERANCE, EXECUTE, MCOIFY OR C RETURN STATEMENT, INDEX NUMBERS 1, 2, 3, 4 , 5, 6 RESPECTIVELY. C GNL01030 13 ICGL=7 GNL01040 DO 20 IDhNT=l,6 IF C GNL01160 26 IC0L=ICCL*1 GNL01170 IF IICOL-KCCL) 27,21,21 GNL011R0 27 IF INWORDSI ICCL )-KPUNC( 1) ) 26,28,26 GNL01190 28 ICOk.= lCOL*l GNL01200 GO TO (50,29,39), IDENT GNL01210 C GNL01220 C PROCESS TOLERANCES AND/OR CURRENTS GNL01230 C GNL01240 29 IF IINDCUR) 21,30,21 GNLOl25n 30 IN0CUR=1 GNLC1260 41 1=0 GNLG1270 31 CALL ECB09 GNL01280 I=U1 GNL01290 NUM^TNUM GNL0 1300 IF (1-25) 42,42,21 GNL01310 32 ICURR(I)=NUM GNLG1320 I T=I GNL01330 33 IC0L=IC0L»1 GNL01340 IF IICOL-KCCL) 34,34,1000 GNL01350 34 IF INWORDSt ICGL )-KPUNC(3) ) 36,35,36 GNL01360 35 IC0L=IC0L*1 GNL01370 87 GO TO 31 GNL01380 36 M3=34 GNL01390 GO TO 15 GNL01400 39 IF (INDTOL) 21, 40, 21 GNL01410 40 INDT0L=1 GNL01420 GO TO 41 GNL01430 42 GO TO (500,32,43),IDENT GNL01440 43 TOLU) = TNUM GNL01450 JT=I GNL01460 GO TO 33 GNL01470 C GNL01490 C PROCESS TEMPERATURE GNL01490 C GNL01500 50 IF 4IC0L-KCCL) 51,51,36 GNL01510 51 IF UNDTEM) 36,52,36 GNL01520 52 INDTEM=l GNL01530 CALL ECB09 GNL01540 TEHPI=TNUM GNL01550 IC0L=IC0L*1 GNL01560 IF (IC0L-KC0L1 54,54,53 GNL01570 53 TEMP=TEMPI*273.0 GNL01580 ITEMP2=1 GNL01590 GO TO 1000 GNL01600 54 IF (NWOROSUCOD-KPUNCm ) 36,55,36 GNL01610 55 IC0L=IC0L»1 GNL01620 CALL ECB09 GNL01630 TEMPC=TNUM GNL01640 ITEMP2=2 GNL01650 ICOL-ICOLU GNL01660 IF .1 ICOL-KCCL) 56,56,36 GNL01670 56 IF INWORDSC ICOL )-KPUNC (4 I) 36,57,36 GNL01680 57 IC0L=IC0L»1 GNL01690 CALL ECB09 GNL01700 TEMPF=TNUM GNL01710 GO TO 1000 GNL01720 C GNL01730 C GET COEFFICIENTS AND OATA TYPE GNL0W40 C GNL01750 200 IC0L=ICCL*1 GNL01760 IF IICOL-KCOL) 201,201,21 GNL01770 201 I IN4JM= I INUMM GNL01780 IF IIINUM-50) 203,203,202 GNL01790 202 M3=36 GNL01800 GO TO 15 GNL01810 203 CALL ECB09 GNL01820 NUM*TNUM GNL01830 IPLOCd INUM*=NUM GNL01840 IF INWORDS<7)-INPUTB(5) I 204,207,204 GNL01850 204 IF CNWOKDS(7)-INPUTB(2) J 205,208,205 GNL01860 205 IF INWORDSI 7 )- INPUTBI 4) ) 206,209,206 GNL01870 206 IF INWORDSm-INPUTBOJ) 225,224,225 GNL01880 207 MTYPE=1 GNL01890 GO TO 210 GNL01900 208 MTYPE=2 GNL01910 GO TO 210 GNL01920 209 MTYPE=3 GNLC1930 210 IPTYPEI IINUM)=MTYPE GNL01940 211 IC0L=IC0L*1 GNL01950 IF IICOL-KCCL) 212,212,21 GNL01960 88 212 IF (NWORDSl ICCL J-KPUNCI2) » 211,213,211 GNL01970 213 ICOL-ICOLU GNL01980 IF UCOL-KCOL) 214,214,21 GNL01990 214 CALL ECB09 GNL02000 NUM-TNUM GNL02010 ICRESl IINUM)=NUM GNLO2020 ICOL=ICGL»l GNL02030 IF 4ICOL-KCCL) 215,215,21 GNL02040 215 IF (NWORDS< ICOL I-KPUNCI4II 206,216,206 GM02050 216 ICCfc=ICOL*l GNL02060 IF (ICOL-KCCL) 217,217,21 GNL02070 217 IF (NWORDSl ICOL )-KPUNC ( l)) 206,218,206 GNL02J80 218 IICOL=0 GNL02090 222 IC0L«IC0L*1 GNL02100 IF 4 ICOL-KCCL I 220,220,219 GNL02110 219 IF IIICOL) 5C0, 206, 1000 GNL02120 220 IICCL=I1CCL*1 GNL02130 IF 0 C GNL02260 8000 IF 4NTRACE) 890 1 , 89C0, 890 1 GNL02270 8901 WRITE (6,89081 GNL02280 WRITE (6,8902) ( TCL ( I ) , I = 1 , I T ) GNL02290 WRITE (6,89031 ( ICURR ( I ) , I = 1 , I T ) GNL02300 WRITE (6,89C6) GNL02310 WRITE (6,8904) ( ( COEF S ( I , J ) , J= I , 5 ) , I = 1 , I I NUM ) GNL02320 WRITE (6,8907) GNL02330 WRITE (6,8905) I I , I CRES< I ) , I P T YPE ( I J , IPLOC ( I ) , I =1 , 20 ) GNL023<»0 WRITE (6,8911) GNL02350 WRITE (6,8910) (CLRR (J ) , J = 1 ,NMAX ) GNL02360 8902 FORMAT I IHO , 1 CF 1 .4 ) GNL02370 8903 FORMAT ( 1HC , 1C ( 5X , I 5 ) ) GNL02380 8904 FORMAT (1X,5E17.7) GNL02190 8905 FORMAT ( IX , I 3 , 5X , I 5 , 5X , I 5 , 5X , I 5 ) GNL02400 8906 FORMAT ( IHO , 1 2HC0EFF IC IE NT S/ ) GNL02410 8907 FORMAT I 1 l-C , 2 X , 1H I , 7X , 5H IC RES ,4 X , 6HI PT YPE , 5 X, 5H I PL OC/ ) GNL02420 8908 FORMAT ( 1 HO , 2 3HT0LERANCES AND CURRENTS! GNL02430 8910 FORMAT (1X,8E16.7) GNL02450 8911 FORMAT ( 1 HO , 81-CURR ENT S / ) GNL02460 8900 IF 4 INDCUR+INDT0L-2) 80C1 , 8C02 , 8001 GNL024H0 8001 M3=35 GNL02490 GO JO 15 GNL02500 8002 IF 41T-JT) 8CC3, 8004, 8003 GNL02510 8003 M3=36 GNL02520 GO TO 15 GNL02S30 8004 CONTINUE GNL02540 NUM=0 GNL025bO GO TO (8098.8C5C) ,ITEMP2 GNL02560 C GNL0257O SINGLE TEMPERATURE 8008 CONTINUE 60 TO 1000 RANGE OF TEMPERATURES 8050 TEMPC=(TEMPF-TEMPI )/TEMPC TEMPF=TEMPF*273.0 TEMPI=TEMPI»273.0 TEMP=TEMPI GO TO 8098 8053 TEMP=TEMP»TEMPC NUM=0 IF ITEMP-TEMPF) 8098, 8098, 8054 8054 CONTINUE GO TO 100C ; STORE PRESENT CURRENT VALUES 8098 DO 8099 1 = 1, IT J=ICURR X'VAR N0.'4X'NAME'19X6HREG WT,4X,'BTA WT',4X,'WT SIG' ) X , 14, 3X, 21A1, F12.5.3F11.5 ) //) , 'RESULTS ARE IN RAW SCCRES'I 9 U 3086 FORMAT l'C',2)!, 'END Of PROBLEM'// *2't 430 FORMAT!'-', 2X,'END OF REGRESSION PG« , ,/'1 , 1 TOL-0. 00005 10 00 44 1=1,20 Aid I )*0.C 00 14 J«l,20 14 C( It J)=O.C C REAO TITLE REAO ( 5, 1C56) (TITLfcl I ) ,1=1, 16) C REAO NUMBER OF VARIABLES CARD , NVAR ■ 10 MAX 16 REAO (5,10CC ) N I NO , N VAR , 1 COR , I PR T , ICHG, T ST NIN0*NIN0*1 ICOCT«0 NVARM=NVAR*1 M=NVARM 1FINVARM .LT. 1) GOTO 650 20 DO 24 1=2, NVARM C REAO IN NAMES OF DATA VARIABLES CARO CCLS 7 - 27. 24 REAO ( 5,51C»( ANAMI J,I» ,J=1,24) C READ IN DATA FORMAT READ (5, 10C1HFMTI I 1,1 = 1,16 ) C WRITE TITLE OF OUTPUT DATA WRITE lb, 1CC2M TITLE U) ,K=1, 18) C WRITE FORMAT USED TO READ IN AND WRITE OUT THE PGM'S INPUT DATA WRITEI6.1C57) IFMT(K) ,K=1,16 ) IF! ICHG .LE. C) GOTO 3e KCH6=0 NTRANS = 4C DO 35 L = l, MRANS C READ IN DESIRED VAR. TRANSFORMATIONS, MAX = 10. REAO (5,80C1 ) (ACHGIL.J), J=l,4) IFlACHG(L.l) .LE. 0) GOTO 3e C WRITE OUT TRANSFORMATIONS WRITE (6,8002) L , ( ACHGI L , J ) , J=l ,4 ) KCHG=KCHG*1 35 CONTINUE C 38 WRITE(6,8C03) C WRITE NAMES CF INPUT DATA VARIABLES. 38 WRITEI6.615) (( ANAMI JK , IJ ) , JK= 1 , 9) , IJ=2 , NI NO ) C. READ IN NIND COLS OF DATA PER DATA FORMAT CARO, REF. STMT 1001 40 REAO I5,FMTM A( I) , 1 = 2, NIND) IFIAI2) .GE. TST) GOTO 60 C WRITE LIST OF INDEPENDENT VARIABLE INPUT DATA. WRITE 16.FMT ) ( A( I I , I=2,NINDI A( 1)=1.0 ICDCT=ICDCT*1 IFUCHG .GT. C) CALL CHANGG DO 55 1=1, NVARM 00 55 J=I .NVARM 55 CI I,J)=C( I,JJ*A( I )*AI J) GOTO 40 60 SIZE=CI1,1) C C WRITE ROW OF ♦* IF A(2) .GE. TST, PROVIDED LAST DATA CARD HAS ALL 9'S C OTHERWISE THE LAST DATA VARIABLE IS LISTED IN THE OUTPUT TWICE. WRITE (6,FMT)(A( I ),I=2,NINDI Vt ll=OSQRT(C< 1,1)) DO 74 1=2, NVARM IF IC(I.I) .LE. C) GOTO 72 95 V(II«(SIZE*C< I, I >-C( 1, l)*CU,I> )/*V<1) GOTO 74 72 ViIJ-l.0*vm 74 CONTINUE SSS=0SQRT(SIZE) SSS=1.0/SSS WRITE DATA STATISTICS HEADING WRITE<6, 1066) DO 76 I=2,NVASM STDV*VI I )*SSS SPST = V( I)»SSS SPST=SPST*SPST C0»ISIZE*SIZE)/((SIZE-1.0)*( SIZE- 1.0) ) SPST=SPST*CE SPST=DSQRT(6PST) AMEAN=CI 1* II/SIZE K=I-1 WRITE CATA STATISTICS WRITE (6,1C67)K,(ANAH( J, I ) , J = 1 , Z ) , AME AN , S TD V , SPST 76 CONTINUE REAC MODEL DEFINATION CARDS (INVERT CARDS) 80 READ I5,1CC6)(AH I ) , l = 2,NVARM ) All 11=1.0 IF (AH2I-3.C) 82,eCC,e50 82 AKNT=0.0 DO 84 I=1,NVARM IFU(I) .NE. 1.0) GOTO 84 AKNT = AKM»1.C 84 CONTINUE IF (SIZE .GT. AKNT) GOTO e6 WRITE <6,48fi)SIZE,AKNT GOTO 80 86 DO 92 I=1,NVARM IF (AID( I ) .GT. 0) GOTC 90 csm=i.o/vm GOTO 92 90 CS(I)=V( I) 92 CONTINUE DO 94 I=1,NVARM DO 94 J=I,NVARM 94 C( I,J) = C( I,J1*CS( I )*CS(J) DO 180 N=1,M IF (AKN) .EQ. 1) GOTC 96 SOUT=0.0 GOTO 98 96 S0UT=1.0 98 IF (SOUT .EC. AID(N)) GOTO 180 IF(C(N,N) .LE. 0) GOTO 170 IF (CIN.M .LE. TCL) GOTO 170 101 C(N,N)=1.C/C(N,N) IF ISOUT .GT. 0) GOTO 106 102 DO 105 1 = 1, K IF (I-NI103,1C5,1C4 103 C( I.NI=( 1.0-2.0*AID(I ))*C( I ,N) GO TO 105 104 C(N,I)=<1.C-2.0*AID( I))*C(N,I ) 96 105 CONTINUE y 106 00 111 I«1 V M 00 111 J=l,« SIGN*1.C-2.0»CABS< S0UT-AID(1)*AID( J) 1 IF -1 l-N 1107,111,110 107 IF IJ-NI108, 111,109 108 C( I, J)=C( I, J)*SIGN*C( I ,N)*C< J,NI*C(N,N) GO 10 111 109 C( I, J)=C< I, J J ♦SIGN*CI I,N)*C(N,JI»CIN,N) GO TO 111 110 C(I,J)=C(I,J)*SIGN*C(N,I)»C(N,J)*C) STER-CI I, I 1/SIZE AST=SIZE/(SIZE-AM) AOSSR=STER*AST STER=DSQRT(STER) ADSSR=SQRT(ACSSR) OF=SIZE-AM RR=l.O-PCT R = DSQPT(fiH) ADJRR=1.0-( l.C-RR)*( ( S I ZE-1.0 )/( SIZE-AM) ) IF (AOJRR .GT. 0.0) GOTO 340 ADJRR=0.0 ADJR=0.0 GOTO 344 340 ADJR=DSQRT(ACJRR) 344 K=I-1 C WRITE REGRESSION EQUATION STATISTICS WRITE <6,4002)IPRT WRITE (6, 66C) (TITLF(K), K = 1 ,16) WRITE (6,3009)K,(ANAM(MK,l ) ,MK=1,20) WRITE (6,490)SIZE,0F WRITE (6,301G)KR,R,STER WRITE (6.472JADJRR, AOJR.ADSSR WRITE(6,475) C WRITE TITLES FOR REGRESSION EQUATION COEFFICIENT TABLE. WRITE (6,3012) KJ=0 00 320 J=1,NVARM IF IAI0IJ4 .NE. 1.0) GOTO 320 IF A I-J1324,320,325 324 BETA>Ct I.J) GOTO 326 325 BETA=C« J, I) 326 BVAR=C( I, I )*C (J , J ) / < SI ZE-AMI BSTO = DSQRT(BVAR) TRAT=BETA/BSTD K=J-1 KJ"KJ*1 KZ(KJ)=K 6B(KJ)=BETA BVAR=BETA*V( J)/V(I) C WRITE REGRESSION EQUATION COEFFICIENTS WRITE (6,3053)K,( ANAH(NJ.J) ,N J=l , 21 ) , BETA ,BVAR , BSTO , TR AT 320 CONTINUE 300 CONTINUE C WRITE (6,3091) GOTO 80 98 800 WRUE (6,3066) IF(NVARM .IE. 0) GOTO 850 820 GOTO 10 850 WRITE(6,430) STOP END BLOCK DATA COMMON A, ACHG.CLD, ICDCT COMMON AI440),ANAM(2 5,40),FNT(18)»KZ<20),KCHG,TITLE(18) DOUBLE PRECISION A( 40 I , ACHG44C ,*) ,0L0, ICOCT DATA ANAM/'C', , , ,'N , , , S , , , I» ,»A» f »M»,«T , ,» • , • T • , ' E« , »R' , • M' 1 987*' •/ END SUBROUTINE CHANGG COMMON A,ACHC,DLD, ICOCT COMMON A I 140), ANAfM 25,40) ,FMT< 18) ,K2(20) , KCHCT I TLE ( 18 I DOUBLE PRECISION AI 401 , ACHGC4C,4> »DLD, ICDCT 00 100 l=l,KCHG KBAB=ACHG( 1,1) N0=4DINT( ACHC(I,2) ) MD=IDINT( AOCU.3) ) LD=IDINT( ACt-GII.A) ) MD*MD*1 N0=ND*1 LD=LD*1 DLC=AChG( I ,<.) GO TO < 1,2, 3, 4,5, 6, 7, 8, 9, 10, 11,12), KBAB 1 A(MC)=A(N£)**CLO GO TO 100 2 A(MO)=1.0/(MND)**0LC) GO TO 100 3 A(MC)=A(N£)*A(LD) GO TO 100 4 A(MC)=AINC l/MLC) GO TO 100 5 A(MO)=A(N0)-AILD) GO TO 100 6 A(MD)=DSQRTIA(ND) ) GO TO 100 7 A(MC)=DLOG(A(ND)) GO TO 100 8 AIMO) = 0EXP(A(NC) ) GO TO 100 9 A(MO)=A(ND)*A(LD) GO TO 100 10 A(MC)=ICDCT GO TO 100 11 A(MD)=A(NC)*OLD GOTO 100 12 A(M0)=A(NC)***2 -11.17180 -0.68292 1.42151 -7.85908 CEPENCENT VARIABLE IS NUM8ER - 18 - VBE SAMPLE SIZE = 14.0 OEGREES FREEDOM = 11. R**2 = 0.999 R = l.OCO STD ERR OF EST = 0.001 ADJ R**2 = 0.9S9 ADJ R = l.OCO ADJ STD ERR OF EST = 0.001 LINEAR «EGRESSICN ECUATION COEFFICIENTS VAR NO. NAME REG MT BTA WT WT SIG T-PATIO CONSTANT TERM 0.71791 23.37929 0.00038 1879.57800 4 LNUC, MILLIAMPS) 0.02716 C. 99830 0.00021 130.24236 5 LNUC, MILLIAMPS)**2 0.00021 0.01114 0.00014 1.45294 RESULTS ARE IN RAM SCORES END OF PROBLEM 101 C3 MICROAMPERE LINEAR REGRESSION PGM, C3 IC-NGMINAL DATA, VCE * 2.0 VOLT INPUT DATA FORMAT = <16X,3F10»3) ACHG( II = 7. 1. 4. C.O ACHGI 2) = 3. 4. 5. 4. NPUT CATA CCLLECTCR BETA VBE 106.500 0.0 0.658 540. COO 108.375 C.702 1080.000 108. DOC 0.720 1292. 999 106.500 0.725 1615.999 107.667 C.730 2139.999 IC4.800 0.738 2656.000 1C3.60C 0.745 3183.000 105. OOC 0.749 3688.000 101. OOC 0.754 4191.996 100.800 0.758 5212.996 102.100 0.763 6175.996 96.30C 0.770 7206.996 103. IOC 0.772 8229.996 102. 30C 0.775 ****************************** INPUT CATA STATISTICS VAR NO. NAME 1 2 3 4 COLLECTOR CURRENT BETA VBE LN( IC, MICROAMPS) MEAN POP STO OEV SAMP STD DEV 338C. 17693 2445.64334 2633.76975 96.39586 26.92444 28.99555 C. 73993 0.03071 0.03307 7.70398 1.12882 1.21565 LNIIC, MICR0AMPS)**2 60.62560 15.87491 17.09606 INTERCORRELATICN MATRIX COLLECTOR CURRENT 1 1.00 BETA 2 0.29 1.00 VBE 3 0.86 0.67 1.00 LNUC, MICROAMPS) 4 0.86 0.68 1.00 1.00 LNIIC, MICR0AMPS)**2 5 0.90 0.60 1.00 0.99 1.00 102 C3 MICROAMPERE LINEAR REGRESSION PGM, C3 IC-NOMINAL DATA, VCE = 2.0 VOLT CEPENOENT VARIABLE IS NUMBER - 18 - BETA SAMPLE SIZE = 14. C DEGREES FREEDOM = 11.0 R**2 = 0.918 R = 0.958 STD ERR OF EST = 7.705 ADJ R**2 = C.9C3 AOJ R = C.950 ADJ STD ERR OF EST = 8.692 LINEAR REGRESSION EQUATION COEFFICIENTS VAR NC. NAME REG WT BTA WT WT SIG T-RATIO CONSTANT TERM -554. 67056 -20.60101 68.90291 -8.05003 4 LNIIC, MICROAMPS) 172.42553 7.22899 19.99124 8.62505 5 LNIIC, MICR0AMPS)**2 -11.17180 -6.58700 1.42151 -7.85908 UEPENDENT VARIABLE IS NUMBER - 18 - VBE SAMPLE SIZE = 14.0 DEGREES FREEDOM = 11. R**2 = 0.999 R = l.OCO STD ERR OF EST = 0.001 ACJ R**2 = 0.999 ADJ R = l.OOC ADJ STD ERR OF EST = 0.001 LINEAR REGRESSION EQUATION COEFFICIENTS VAR NO. NAME REG WT BTA hT WT SIG T-RATIO CONSTANT TERM C. 54023 17.59311 0.00693 77.93624 4 LNIIC, MICROAMPS) C.C2429 0.89277 0.00201 12.07571 5 LNIIC, MICR0AMPS)**2 0.00021 0.10742 0.00014 1.45295 RESULTS ARE IN RAfc SCORES 103 3 INSTRUCTIONS FOR PREPARING LINEAR REGRESSION PROGRAM CONTROL CARDS C 1. TITLE CARD WITH FORMAT = 18A4, MAY START IN COL 1, ALL OTHER C CCNTROL CARDS MUST START IN CD COL 7. C C 2. MAIN PARAMETER CD - PROVIDES I/C PARAMETERS TC PGM. C C A. COL 7-8 NINO = 12, NUMBER OF INDEPENDENT INPUT VARIABLES C C B. COL 10-11 NVAR =NINO ♦ NO. VAR CREATED BY TRANSFORMATIONS C C C. COL 13 ICOR = II, IF IC0R=1, THEN I NTERCORREL AT ION MATRIX C APPEARS IN THE OUTPUTt OTHERWISE NO MATRIX IS PRINTED. C IF NVAR .GE. 15 SET ICOR = 0. THIS RESTRICTION DUE TO FMT. C BESL"RE TO INCLUDE A BLANK CARD AS THE FIRST INVERT CARD C WHENEVER ASKING FOR THE I NTERCORRELATI ON MATRIX. C C D.COL 15 IPRT=CARRIAGE CONTROL, SETS PAGE SPACING BETWEEN EONS C C MEANS FOR PRINTER TO SKIP TWO LINES C - MEANS FOR PRINTER TO SKIP THREE LINES C 1 MEANS FOR PRINTER TC SKIP TO NEW PAGE C 2 MEANS FOR PRINTER TO SKIP TO NEW HALF PAGE C C fc. CCL 17 ICHG=1 TO TRANSFORM VARIABLES, FOR NC TRANS, ICHG=0 C C F. CCL 19-27 TST = F FORMAT NC. .GE. MAX. DATA VAR ♦ 0.5 C TST USED BY PGM TO SIGNAL END OF DATA. C C 3. DATA VAR NAME CDS, ONE NAME PER CD. FCRMAT IS bA4. C C 4. INPLT CATA FORMAT CD, EX . ( 16X ,6F 10 . 3 » = ENTRY NEEDEO TO REAC C 6 SETS OF INPUT DATA. PARENTHESES ARE REQUIRED IN ENTRY. C IF A DIFFERENT FORMAT DESIRED CHECK INTO DATA TITLES OF C FORMAT STMT NO. 615. C C 5. CHANGE CARDS DEFINE THE VARIABLE TRANSFORMATIONS FOR FORMING C LINEAR REGRESSIONS EQUATIONS AS DEFINED BY THE INVERT CDS C C A. TRANSFORMATION CARD INPUT CODES APE... C C I COLS 7-8 IN FIXED PCINT FORMAT ONLY C J COLS 10-11 IN FIXED POINT FORMAT ONLY C K COLS 13-14 IN FIXED PCINT FORMAT ONLY C L OR DL COLS 19-27 IN FLOATING POINT FCRMAT ONLY 10U c C 8. TRANSFORMATIONS OPERATIONS COOE IS.. C 01 A(K)=A C 10 A(K)=ICDT C 11 A(K)=A(J)*DL C 12 A(K>=A(Jl*(DL> C C C. AN EXAMPLE TRANSFORMATION SPECIFICATION CODE IS... C C INDEX II JJ KK LLLLLL C CARO COL 7890123*56789 C TRAMS COOE C4 03 07 06. C C THIS CODE INSTRUCTS THE PGM THAT DESIRED TRANSFORMATION C IS 04 A(K)=A( JI/AILI. PGM IS TO DIVIDE VAR 3 BY VAR 6 AND C STCWE THE RESULT IN VAR AC7I. C C D. NOTE DL IS USED OCCASIONALLY AS A FIXED POINT CONSTANT C MULTIPLIER OR EXPONENT. DL IS ENTERED IN COLS 8-12 IN C PLACE OF L.. NOTE THAT L AND DL ARE NEVER REQUIRED IN THE C SAME TRANSFORMATION! C C E. ENTRY 00 IN COLS 7-6 MEANS MC MCRE CHANGE CARDS PRESENT* C C 7. AN ENC OF DATA CARD IS PUT AT THE CONCLUSION OF EACH SET. C THIS END CARD MUST HAVE A VALUE (IN THE FIELD OF THE FIRST C VARIABLE) THAT IS GREATER THAN TST BY 0.1 OR MORE, NOTE C VALUE FOR TST WAS ENTERED ON THE MAIN PARAMETER CARD 2. C SEVERAL SETS OF DATA CAN BE CONCATENATED IN ONE CMPTR RUN. C C 8. INVERT CARDS DEFINE MODELS USING COLS 7 - 37, WITH COL 7 FOR C VAR(l). C C A. AN EXAMPLE INVERT CARC CODE IS.... C CARO COL 7 8 9 12 3 C ENTRY 2 C 1 1 C C C B. REGRESSICN MODEL CODES.... C C COL 7=C = VARIABLE NOT USED C 1 = INDEPENDENT VARIABLE C 2 = DEPENDENT VARIABLE C 3 = RESTART P6M WITH ALL NEW VARIABLES, CAUSES C PGM START THRU THE SET OF MODELS ONCE AGAIN AS DEFINED BY C THE INVERT CD USING NEW DATA. C COL 7=4 = END OF PGM CARD, TERMINATES ALL PROGRAM CALC. C 3 = RESTART PGM WITH ALL NEW VARIABLES C c 105 9. SAMPLE CATA DECK C] . MICROAMPERE LINEAR REGRESSION PGM, CI TRANSISTCR OATA, VCE = 2.0 VOLTS c 03 05 1 2 1 12000.0 NIND.NVAR, ICOP.IPRTt ICHG.TST c COLLECTOR CURRENT VARIABLE NAME CARD c BETA c VBE c LMIC, MICROAMPS) c 4.N1IC, MICR0AMPS)**2 c ( 16X.3F 10.3 J INPUT DATA FORMAT CC c 07 01 04 0. VARIABLE TRANSFORMATION CD c 03 04 05 4. C c 00 c 3.00 C.00025C 38.300 90.667 0.632 2.368 0.000 C1DAT 99 c 3.00 Oi.000500 62. IOC 95.200 0.652 2.348 0.000 C1DAT100 c 3.00 O.C01000 112. 3CC 100. 40C 0.672 2.328 0.000 C1DAT101 c 3.00 0.002000 213. 5CC 101.200 0.691 2.307 0.002 C1DAT102 c 3. CO 0.C03000 320.800 107. 30C 0.703 2.297 0.000 C10AT103 c 3.00 O.C04000 428.300 107.500 0.710 2.290 0.000 C1DAT104 c 3.00 0.CO500C 535.300 107.000 0.716 2.281 0.003 CIDAT105 c 3.00 C.C0600C 642. 4CC 107.100 0.720 2.279 0.001 C1DAT106 c 3.00 0.007000 748. 80C 106.400 0.724 2.274 0.002 C1DAT107 c 3.00 C. 008000 854. ecc 106. COO 0.728 2.272 C.000 C1DAT108 c 3. CO 0.C1OOOO 1C79.000 112. IOC 0.734 2.266 0.000 CIDAT109 c 3.00 C.01200C 1287.999 104. 50C 0.737 2.263 0.000 C1DATU0 c 3.00 C.01500C 1589. OCO 100.334 0.746 2.254 0.000 C1DAT111 c 3.00 C.C20000 2113. OCO 104. BOO 0.755 2.245 0.000 C1DAT112 c 3.00 0.025000 2620.000 101.400 0.762 2.238 C.000 C1DAT113 c 3.00 C. 030000 3117. 999 99.60C 0.767 2.232 0.001 C1DATU4 c 3.00 O.C3500C 3608.000 98.000 0.772 2.226 0.002 C1DAT115 c 3. CO 0.040000 4094.999 97.40C 0.776 2.224 0.000 C1DAT116 c 3.00 C.05000C 5054.996 96.C0C 0.782 2.217 0.001 C1DAT117 c 3.00 C.C60000 5929.996 87.500 0.790 2.210 0.000 CIDAT118 c 3.00 O.C70000 6e64.996 93.500 0.794 2.206 0.000 C1DATU9 c 3.00 0.080000 7666.996 80.20C C.800 2.200 C.000 CIDAT120 c 3.00 000100 24.700 0.0 0.603 2.397 000 CIDAT 98 C999999999999999999999999999999999999999TST CARD TU SIGNAL END CF DATA C COMPLETELY BLANK CD SINCE IC0R= 1 C C 2 11 REGRESSION MCCEL OEFN -INVERT CD c 2 11 c 4 END CF PROGRAM CARD c c ****************END CF SAMPLE DATA DECK********************* TJTPICAL INPIT OAT* DECK 106 C3 MILLIAMPERE LI 03 05 1 2 1 COLLECTOR C BETA VBE LNilC, HILL LNdCt HILL I 16*, 3F 10.3 07 01 04 0. 03 C4 05 4. 00 2.00 0.C010C0 2.00 0.005000 2.00 0.010000 2.00 0.C12000 2.00 0.015000 2.00 0.020000 2.00 0.025000 2.00 0.030000 2.00 0.035000 2.00 0.C40000 2.00 0.050000 2.00 0. 060000 2.00 0.C7000C 2.00 0.C80000 NEAR REGRESSION PGM, C3 TRANSISTCR DATA, VCE * 2.0 VOLTS 12000.0 URRENT IAHPS1 IA^PS)**2 ) C 99999999999999999 C. 106500 C.5400C0 1.080000 1.292999 1.615999 2.139999 2.656000 3.183000 3.688000 A. 191999 5.212999 6.176000 7.207000 8.230000 9999999999 0.0 108.375 108.000 106.500 107.667 104.600 103.600 105.000 101.000 100.800 102.100 96.300 103.100 102.300 0.658 0.702 0.720 0.725 0.730 0.738 0.745 0.749 0.754 0.758 0.763 0.770 0.772 0.775 999999999999 9999999999999 .342 .298 .280 .275 .270 .262 .255 .251 .246 .242 .237 .230 .228 .225 999999 0.0 0.000 C.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 C30AT 27 C3DAT 28 C30AT 29 C3DAT 30 C30AT 31 C3DAT 32 C3DAT 33 C3DAT 34 C3DAT 35 C30AT 36 C3DAT 37 C30AT 38 C3DAT 39 C30AT 40 999999 9999999999999999 2 2 3 1 1 1 1 107 C3 X 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 9999 ICROAMPERE L 03 05 1 2 COLLECTOR BET* VBE LNUC, MIC LNIiCt NIC I 16K.3F10. 07 CI 04 03 C4 C5 4 00 00 C.C01C0C 0.005000 O.C10000 O.C12000 0.C1500C 0.020000 O.C25000 O.C30000 0.035000 0.04000G 0.050000 C. 060000 0.070000 C.08000C INEAR REGRESSION PGM. C3 TRANSISTOR DATA* VCE * 2.0 VOLTS 1 12000.0 CURRENT ROAMPS) R0AMPS)**2 31 .0 .0 999999999999 1C 54 108 129 161 213 265 318 368 419 521 617 720 822 99999 6.500 C.000 C.OCC 2.999 5.999 9.999 8.0CC 3.0C0 8.000 1.996 2.996 5.996 6.996 9.996 99999 0.0 108.375 108. OOC 106.500 107.667 104. 800 103. 60C 105. OOC 101.000 ioo. eoc 102.100 96.300 103. IOC 102.300 99999999999 0.658 0.702 0.720 0.725 0.730 0.738 0.745 0.749 0.754 0.758 0.763 C.770 0.772 0.775 1.342 0.0 1.298 0.000 1.280 0.000 1.275 0.000 1.270 0.000 1.262 0.000 1.255 0.000 1.251 0.000 1.246 0.000 1.242 0.000 1.237 0.000 1.230 C.000 1.228 0.000 1.225 C.000 C3DAT 27 C3DAT 28 C3DAT 29 C30AT 30 C3DAT 31 C30AT 32 C3DAT 33 C3DAT 34 C3DAT 35 C3DAT 36 C30AT 37 C3DAT 3B C3DAT 39 C3DAT 40 9999999999999999999999999999999999999999999 C 2 C 2 5 1 1 1 1 108 5 LINEAR REGRESSION INPUT DATA TRANSFORMATION PROGRAM THIS PROGRAM CALCULATES, USING MEASURED CARD INPUT DATA, BETA, MEAN COLLECTOR CURRENT, ICM, DATA FORMAT CONVERSION, AND PUNCHES CARDS WHICH ARE THEN USED AS INPUT OATA TO LINEAR REGRESSION MODEL COEFICIENT CALCULATING PROGRAM. COMMON VCEI26C),I8(260>,IC<260),VCB!2601,VBE!26C) COMMON BETA!260),TVCE(260) ,-VCEDE V < 260 ) COMMON OIC!260),DIB(26C»,ICAI26C),ICM!260I 200 FORMAT!* • ,4X ,F9. 3, 1X,F10.6, IX, F 10. 5, 1X,F6.3,5X ,F6 . 3 ) 300 FORMAT! • 1»» 301 FORMAT! ' 2' ,2X , • VCE • ,6X, • IB ' , 5X, • IC-MEAN* ,5X , 'BETA • , 7X, • V8E« , 7X , 1 •VCB',6X,«VCEDE W/l 400F0RNATI" •,F5.2,2F10.6,F10.3,3F10.3,6X,»C10AT«, 131 MA.REGSN 400F0RMAT!' ',F5.2, F 10. 6, F 10. 3, F 10. 3, 3F10. 3,6X, 'C1DAT • , 13 ) MICR.REG 401F0RMATM «,F5.2 , 2F 10. 6, F 10.3 ,3F 10. 3,6X, 'C10AT • , I 3 ,5X , 3F12.3I MA.REGSN 401 FORMAT! • • ,F5 .2 , 1 F 10 .6,F 10 . 3 ,F 10. 3, 3F 10. 3 ,6X, 'C ID AT • , I 3, 5X.3F 12 .3 IMICR. REG 402 FORMAT! •-•, 22 X • ********** ENO OF DATA *•*********•) REAL IB.ICICA, ICM N=000 BETAI1) = C.CCC DIB! 11=0. Old I) = 0. VBE! I) = O.C icm = ccoocooi IB(1) = CCCCCOCl VCE«1) = C.5 WRITE(6,3CC) DO a3 J=2,261 12 N=N*1 BETA(J) = C.000 10 READ!5,20C,ENC=14)VCE! Jl , IB« J ) , ICIJ I , VBE IJ> ,VCB!J) 13 CONTINUE 14 00 16 J=2, N IF(VCE!J«1) .NE. VCEIJI) GOTO 15 8 DIB!J*1) = IBIJ+1) - IB! J } DIC4J + 1) = IC( J + l) - ICIJ) IF!IB!J*ll .EG. IB! J ) ) GOTO 15 ICM!J*ll = !IC!J*1) ♦ IC!J))/2.C ICM!J*1) = ICM! J»l)*1000.0 BETAIJ+1) = DIC( J + 11/DIBIJ-U) 15 TVC£( J)=VBEi J) ♦ VCB1J) VCEOEVIJI = VCEIJI - TVCEiJI ICA4J) ■ ( ICM) 1/1.0 16 CONTINUE VCE«N*1I = 1CC.C 30 DO 40 J=2, N K=J-1 IFIVCEiJ+1) .GT. VCEU)) WRITE!6,301I WRITE16,401)VCE( Jl, IB!J),ICN! J), BETA! J) , VBEIJ) , VCB! J ) , VCEDEVi J I , K l.BETAIJ J.CICIJ J.DIBIJ I WRITE I 7,400 )VCE< J), IB! J), I CM I J) .BETA! J) , VBE I J) , VCB( J I ,VCEDEV! JI,K 40 CONTINUE V.RITEI6.4C2) STOP END 109 APPENDIX REGRESSION MODEL EFFECTIVENESS PROGRAM 1 REGRESSION MODEL EFFECTIVENESS PROGRAM LISTING COMMON VCEI200I, BET AMC20CI , VBEM1200 I , BETAC 1200 ) ,VBECI 200 I COMMON VDIFF(200I,BDIFF!200>,B<5),V!5),K,M,TITLEI8I .UNITS! 5) COMMON INT REAL ICMI2CC1 102 F0RMAT(6X,8A4) 104 F0RMAT(6X,4F12.5,21X,5A1) 106 FORMAT!6X,4F12.5,21X,5Al) 108 FORMAT! I 1 ,F5 .2 . 10X , 3F 10. 3» 200 FORMAT! M'i 5X, 'ANALYSIS OF REGRESSION EQUATION FOR BETA - «8A4/ l«-« ,5X,«BETA = ',F10.5,« ♦ '.F10.5,' * LN , 'VBE '.10X,' VBE • ,8X , «ME AS-CALC , / , 2 7X, 'VOLTS' ,6X, • !«,5Al, 'AMP SI ' ,7X,« ! — > • , 1 IX , • I -- ) • , 1 1 X , • I — ) • ) 208 F0RMAT(6X,F6.2,4F15.5) 10 K=0 M=l REA0I5, 102,END=40) ITIILEIII), 11 = 1,8) REAC<5,104) Bi 1 ),B(2),B(3) ,B<4) ,IUNITSIKK), KK=1,5) REA0(5,106) VI 1), VI2).V! 3) ,V!4) .1UNITS1KK), KK=1,5) BI4) = C.C VIA) = O.C DO 15 1=1, 2CC REAO15,108,Ef\D=2C) IN T , VCE ( I) , I CM ( I I , BETAM! I ) , VBEM! I ) IFIINT .GE. M GCTC 20 K = K ♦ 1 15 CONTINUE 20 DO 30 J=1,K BETACIJ) = B!l) ♦ B(2)*(ALUGi 1CM1J)) ) ♦ B I 3 ) * ( < ALOG < I CM ( J ))) **2 ) VBECIJ) = V!l) ♦ V!2)*!AL0G!ICM(JI) I ♦ V! 3) *( ( ALOG < ICM! J ) ) ) **2) BDIFF(J) = BETAMIJ) - EETACIJ) VOIFF(J) = VBEM(J) - VBECIJ) 3C CONTINUE HRITE!6,200) ! T I TLE I J J ) , J J= 1 , 8 ) , BI 1 ) ,8 1 2 ) , B I 3 ) WRITEI6.2C2) ILNITSiKK), KK=1,5) WRITE(6,204) ( VCE ( i ) , ICM ( I ) , BET AM I I ) , BE TAC ( I I , BO I FF i I) , 1 = 1, K) MRITE(6,205) I T 1 TLE i J J ) , J J= 1 , 8 I , V ( 1 ) , V( 2 ) , V( 3 ) WRITEI6,2C6) iUNITS(KK), KK=1,5) WRITE!6,2C8) ( VCE! I ) , ICM! I ) , VBE f ! I » . VBEC I I ) , VOIFF ! I ) , 1 = 1, K) INT = GOTO IC 40 STOP END TOPICAL OUTPUT 110 ANALYSIS OF REGRESSION EQUATION FOR BETA - C3 IC-NOHINAL VCE-2.0 VOC BETA 103.31700 ♦ 18.08138 * LN (Id ♦ -11.17180 * (LN(ICI)**2 VCE VOLTS 0.0 0.0 0.0 0.0 0.0 0.0 0.0 CO 0.0 0.0 0.0 0.0 0.0 0.0 IC MEASURED CALCULATED BETA BETA (MILL1AMPS) ( — ) <--) C.1C6C0 0.0 6.46486 0.540CO 108.37500 87.93373 1.08000 1C8. 00000 104.64238 1.29300 106.50000 107.22557 1.61600 107.66699 109.42172 2.14000 104.79999 110.60689 2.66800 103.59999 110.31653 3.18300 1C5.00000 109.27560 3.68800 101.00000 107.88643 4.19200 IOC. 79999 106.28398 5.21300 102.C9999 102.71432 6. 17600 96.29999 99.20450 7.20700 103.09999 95.44937 8.23000 102.29999 91.79503 BETA MEAS-CALC I — J -6.46486 20.44127 3.35762 -0.72557 -1.75473 -5.80690 -6.71654 -4.27560 -6.88643 -5.48399 -0.61433 -2.90451 7.65062 10.50496 ANALYSIS OF REGRESSION EQl;AT ICN FOR VBE C3 IC-NCMINAL VCE=2.0 VOC VBE = VCE VCLTS 0.0 0.0 0.0 0.0 0.0 0-0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.71791 ♦ 0.02716 * LN I IC) ♦ 0.00021 * IC MEASURED CALCULATED VBE VBE (HILLIANPS) I—) ( — 1 0.10600 C. 65800 0.65801 C. 54000 C. 70200 0.70125 1.C8000 0.72000 0.72000 1.293CC 0.72500 0.72490 1.616C0 C. 73000 0.73099 2.140C0 C. 73800 0.73869 2.65800 0.74500 0.74466 3. 183C0 0.74 900 0.74964 3.688C0 0.75400 0.75371 4.19200 C.7580C 0.75727 5.21300 C. 76300 0.76333 6. 176C0 C. 77000 0. 76806 7.207C0 C. 77200 0.77237 8.23000 C. 77500 0.77609 VBE MEAS-CALC -0.00001 0.00075 -0.00000 0.00010 -0.00099 -0.00069 0.00034 -0.00064 0.00029 0.00073 -0.00033 0.00194 -0.00037 -0.00109 Ill ANALYSIS OF REGRESSION EQUATION FOR BETA - C3 IC-NOMINAL VCE«2.0 VOC BETA = -554.67C41 ♦ 172.42562 * LN (JO ♦ -11.17180 * SMLE< I) ELEMENT CURRENTS 103 00 20 IM.NHAX 20 £UR*( I)=YX(l )*SfLE( I ) IF(NTERMS)21. 22, 21 21 24 23 22 21 DO 23 I-1,NTERMS NR*IROWT(II NC=ICOLT*SNLE(NC) CONTINUE DO 27 I=1,\HAX CCSAVU.I ) = CURR< I ) BETA SAVE 28 DO 28 N = l.NMAX NFBR = ICOLT(N) NTBR ■ IROWT(N) CDSAVI 1 .N ) = 0.0 CDSAV(2,N) ■ CDSAVI 1,N) = IFHCOLT(N) CDSAV(2,N) = CONTINUE 33 35 34 37 0.0 YTERM(N) EQ. 0) GOTO 26 (CDSAVI 1,N) )/( Y(NFBR)) BRANCH POWER LOSSES DO 29 I=1,NMAX 29 CCSAV(5,I >=CLRR(I>*SMLE1*NW30E SUM - SUN ♦ OABSI X( t II IF ISUM-ERR0R1 1 106 , 106,40 WRITEI6,141) WRITE 16,142) FORMAT! // 43H SOLUTION NOT OBTAINED TO OESIREO TOLERANCE//! FORMAT! 6*i NCCE S , 15X , 19H CURRENT UNBALANCES /) KMAX-NNODE IND-6 GO TO 100 00 42 I»1,NNAX CCSAVI2,II*CURR(I) IF 4JX4 .GT. C) GOTO 900 GO TO 1399, 399,399, 900), NTR CALL BCDBN1I3,1,IDW0RDI4) ) IF(IOWORO(5) .GE. 1) I0HOR0(73) ■ IDWORDI731 ■ I0W0RDI73I ♦ 1 IDWORDI73I ■ 1IDWOROI731 ♦ l)/2 WRITE (6, 8011 I IOWOR0IIK), IK"7, 72 ) , IOWORO ( 3) , I DWORD! 4 ) , I DWORD J 73 ) WRITE (6,8001 IF (NMAX-NNGCE) 4C0,5C0,401 MAX«NNODE MIN*NMAX GO TO 402 MAX=NMAX MIN=NNODE 00 403 I=1,KMAX XI I |= 1 .0/Y< N WRITE (6,e5C) I I,E( I), AMP! ll.XI 1 1 , ICCSAVIJ , I ) ,J = l,6) ,1,1 = 1, MINI IF JMIN-MAX) 4C4,«5CC,900 MIK=MIN*1 WRITE (6,8511! I, El I), AMP! I ),X(I ),ICCSAV( J, I), J = l,5), 1= MIN.MAX) IF IIDW0RCI74) .LE. 0) GOTO 900 TEST DC251310 DC251320 DC251330 0C251340 DC251350 DC251360 DC251370 OC251380 DC251390 0C251400 DC251410 DC251420 DCA25104 DCA25105 DCA25108 DCB25U7 DCB251 DCA25121 DCA25122 WRITE (8,852) (lOWORO(I), 1-1, 73) WRITE! 7,652) (ICWORD(I), 1*1, 73) WRITE (9,8521 (IDWORDII), 1*1, 73) WRITE! 10,852) (IOWORDII), 1*1, 73) WRITE ( 1 1,8521 (IDWORDII), I>1, 73) WRITE I 7, 853* ( I DWORD I 3) , ID WORD! 73) , I ,E ( I ) , AMP! I ) ,x( I I , ( CCSAVI J, I ) , 1 J=l,6), 1=1, MAX) WRITE (8, 8 54) ( I DWORD ( 3 ) , I DWORCI 73 ) , I ,E 1 1 1, AMP ( I ) , X I I ) , ICCSAVIJ, I ) , 1 J=i,6), 1=1, MAX) WRITE 1 9, 8 55) ( I DWCRD ( 3 ) , IOWCRC! 73 ) , I ,E( I), AMP (I ) , X I I ) , COS AVI 1 , 1 ) , 1CCSAVI I, 1 1, CCSAVI 2, I >, CCSAVI 5,1 ),CCSAV(6, I) , 1 = 1, MAX ) WRITE I 10,8 551 ( 1CW0R0I 3) , IOWOROI 73) ,I,EII),AMP( I ) ,X ( I ) , CDS AVI 2, 1 ) , 1CCSAVI 1, II, CCSAVI2, II, CCSAVI 5,1 1 .CCSAVI6, I ) , 1 = 1, MAX ) WRITE 1 11, 855 1 I I DWORD! 3 I , I DWORD ( 731 , I ,E({),AMPI I ) , X I I ) , CDSAVI 2 , 1 ) , 1CCSAVI 1,1 ),CCSAV(2,I) ,CCSAVI5,I ),CCSAVI6,I) , 1=1, MAX I GO TO 900 800 FORMAT !• BRANCH ■ ,3X, 'VOL I AGE ', 5X, • CURRENT ' ,7X ,' BRANCH' , 7X , DCB25121 1* BRANCH •, 8 X,'eRANCH',7X,' ELEMENT ',7X, 'ELEMENT ', 5X ,• EL EMENT •, 7X DCB2512? 2'N0DE',6X,'NODE'/' NUMBER •, 3X, • SOURCE « ,6X , 'SOURCE •, 6X ,• RES I STANCE 'DCB25 12 3 3, 5X,« VOLT AGE ',7X, 'CURRENT', 6X,' VOLT AGE ',7X,' CURRENT «,4X, DCB25124 4 • POWER LOSS », 4X, • VOLT AGE «,3X,' NUMBER '/10X,' I VOLTS) • ,6X , • 1 MA) • ,9X, 0CB25125 5MOHMS)',7X, '1V0LTS)',8X,'1«IA)',8X, • I VOLTS) ',8X,'(MA) • ,7X, DCB25126 6' I WATTS )',6X,' I VOLTS) •//,/) DCB25127 801 FORMAT! • 1' ,4OX,66Al/'0',40X, 'PRCBLEM NO. = • ,2X , A I , A 1 , 10X, ' SOLUT ION 118 1 NO. « ' 13,////) 650 FORMAT!' ' ,4 4.2X.F 10 .3 t 3PF 1 2 .4, 3X , 0PF12.2 , 2X ,F 1 1 .6 , 2X , 3PF 1 2 .6, 12X,CPFll.fc,PX,3PFl2.6,2X,0PF 10.4 , 2X ,OPF U .6 , 2X , I 5 ) 851 FORMATI • ' , 14, 2X , F 10. 3 , 3PF 12 .4, 3X,0PF12 .2 ,2X ,F 1 1 .6 , 2X , 3PF1 2 .6 , 12X,OPF11.6,2X,3PF12.6,2X,0PF10.4) 852 FORMAT ( 1 X , • C ' , 1 X , 72A I , I 3 » 853 F0RMATI'P',Al,«-S',I3,«-B»,I2t F7 .3 ,3PF8. 2.0PF 1 1 . 2,F7. 3, 3PF8.3, 10PF7.3,3PF8.3,0PF6.3,0PF7.3I 854 FORMATI' P • , Ai , '-S« , I 3 , «-B • , I 2, F7. 3 , 3PF6.2 ,0PF 11 .2 ,F7. 3, 3PF8.3 , 10PF7.3,3PF9.3,0PF6.3,0PF7.3I 855 FORMAT< • P • , A I, «-S • , I 3, «-B • , I 2, F8. 3, 3PF8.2 ,OPF 1 1 . 2, F9.3,F8.3, 13PF9.3, 0PF7.3,CPF8.3) 856 FORMATI • P* ,A1 , '-S* , I 3, «-fl • * I 2, IX , F 7. 3, 3PF8. 2 , OPF 1 1 .2 ,F7.3 , 3PF 10. 3 1 ,0PF6.3,0PF7.3) 860 FORMATI • • , 5X , • P • , A 1 , «-S • , I 3 , '-B' , 1 2 , 5X , • ECB25 • ,10X,« ICCLTP, 13,' ) 1 *•» I4.10X, MPOhTI • ,13, • ) =«,I4 I C DC251520 C OUTPUT ROUTINE DC251530 C 0C251540 100 LASI=0 DC251550 150 K*LiAST*l DC251560 LAST=LAST*4 0C251570 IF ILAST-KMAX) 200,200, 201 DC251580 201 LAST=KMAX DC251590 200 WRITEI6, 2C3)K, LAST, ( X|JI ,J*K, LAST) 0C251600 203 F0RMATI1X,I3,1H-, I3.2X.4I 3X,E15.8) ) DC251610 IF(KMAX-LAST)5CC,5CC,150 DC251620 C DC251630 500 GOTO 106 900 RETURN DC251650 END 0C251660 AUG 1 6 1958