ENGINEERING RESEARCH INSTITUTE DEPARTMENT OF AERONAUTICAL ENGINEERING UNIVERSITY OF MICHIGAN DEVELOPMENT OF THE MULTIPLEXED MULTIPLIER Department of the Air Force Contract No. AF 33(038)-19996 E.O. 460-12-16 BR-1 Quarterly Progress Reports Nos. 3 and 4 for the periods October 1, 1951, to December 31, 1951 and January 1, 1952, to March 31, 1952 Project M946 Submitted for the Project by: E. J. Schaefer

PROJECT PERSONNEL Both Part Time and Full Time Robert M. Howe, Consultant Marguerite A. Kemble, Secretary Joseph B. Newman, Technician Henry R. Pentek, Research Associate Lawrence L. Rauch, Project Supervisor Edward J. Schaefer, Project Engineer iii

TABLE OF C ONTENTS Section Page Project Personnel iii List of Figures v 1 Introduction 1 2 Summary 1 2.1 Phototube Output as a Function of Spot Positior 1 2.2 Spot Diameter Measurements 1 2.3 Deflection Amplifiers 2 2.4 Multiplier Phototube Power Supply 2 2.5 Cathode-Ray Tube Accelerating Power Supply 2 2.6 "Millisec" Relay Tests 2 2.7 Appendix I 2 2.8 Appendix II 2 3 Phototube Output as a Function of Spot Position 3 4 Spot Diameter Measurement 8 5 Deflection Amplifiers 11 6 Multiplier Phototube Power Supply 14 7 Cathode-Ray Tube Accelerating Power Supply 14 8 "Millisec" Relay Test 16 9 Future Program 16 Appendix I The Closed-Loop Operation of the Function Generator 17 Appendix II A Note on Necessary Spot Positioning Accuracy 22 iv

LIST OF FIGURES Figure Page 1 Phototube Output as a Function of Vertical Spot Position 3 2 Phototube Output as a Function of Horizontal Spot Position 3 3 Original Function-Generator Optical System 4 Present Function-Generator Optical System 5 5 Dynamic Method of Displaying Phototube Output as a Function of Spot Position 7 6 Typical Oscillogram - Phototube Output as a Function of Spot Position 7 7 Phototube Output vs. Horizontal Spot Deflection Past a Vertical Mask Edge: Low Intensity 9 8 Phototube Output vs. Horizontal Spot Deflection Past a Vertical Mask Edge: High Intensity 9 9 Circuit for Dynamic Measurements of Phototube Sensitivity, Sp 10 10 Typical Oscillogram - Phototube Output as Spot is Deflected Past Mask Edge 10 11 Deflection and Phase-Inverter Amplifier Chassis 12 12 Circuit Diagram: Deflection and Phase-Inverter Amplifiers 12 13 Function Generator Closed-Loop Diagram 13 14 Multiplier Phototube Power Supply 15 15 Cathode-Ray Tube Accelerating Power Supply 15 A The Open Loop of the Function Generator 19 B Useful Tube Area v

- ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN DEVELOPMENT OF THE MULTIPLEXED MULTIPLIER 1. INTR ODUCTION The proposed multiplexed multiplier consists of a wide-band function generator and an electronic commutator. Original plans called for the production of a final unit capable of delivering continuously logarithms of twenty channels and antilogarithms of ten channels. During the present report period, the goal has been modified to the construction of a prototype laborabory model of only three channels. The principles of operation, as well as the development work preceding the period covered by this report, are described in detail in the previous progress reports dated July 29, 1951, and September 29, 1951. 2. SUMMARY 2.1. Phototube Output as a Function of Spot Position The output of the 1P21 multiplier phototube was found to vary excessively as the spot was deflected from the center of the cathode-ray tube. Considerably better uniformity has been achieved by means of a new optical system. 2.2. Spot-Diameter Measurements A dynamic method of obtaining phototube output as a function of spot position as the spot was deflected perpendicularly past the edge of a mask was evolved. The resulting curve was photographed directly from the face of a calibrated cathode-ray oscillograph. Phototube sensitivity in terms of current output per unit spot deflection past the edge of the mask

- ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN was obtained from the tangent to the curve. The sensitivity at several points of the cathode-ray tube was determined. 2.3. Deflection Amplifiers The first models of the deflection amplifiers were completed and installed. Closed-loop operation of the function generator over a limited frequency range was,achieved. Several methods of extending this range are discussed. 2.4, Multiplier Phototube Power Supply An improved power supply for the multiplier phototube was designed and constructed. 2.5. Cathode-Ray Tube Accelerating Power Supply A VR-tube regulated supply for the cathode-ray tube accelerating voltage was constructed and installed. 2.6. "Millisec" Relay Tests The life test of the Stevens-Arnold "Millisec" relay was concluded after approximately 650 million cycles. The relay sustained no apparent damage. 2.7. Appendix I - The Closed-Loop Operation of the Function Generator The closed-loop operation of the function generator is analyzed, and the gain equations derived for the conditions of an auxiliary approximate logarithmic input to the deflection amplifier from a source external to the loop and use of only a portion of the deflection-amplifier output for feedback purposes. 2.8. Appendix II - A Note on Necessary Spot Positioning Accuracy The necessary spot-positioning accuracy of the function generator is analyzed and a maximum spot-positioning error determined. From this value, the minimum necessary open-loop gain is calculated. Positioning errors introduced by phototube noise current and non-uniform output as a function of spot position are compared with the derived criteria. — 2 _____

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN 3. PHOTOTUBE OUTPUT AS A FUNCTION OF SPOT POSITION Reference to Appendix I of this report will confirm the fact that any variation of phototube output as the spot is deflected in the absence of a mask will result in a source of error in the determination of the final spot position. It is desirable, therefore, to realize constant phototube output with varying spot position. Figs. 1 and 2 are plots of phototube output as a function of spot position for two widely different intensities as the spot is deflected along the vertical and horizontal axes respectively. All curves are reduced to a reference value of unity at zero deflection and pertain to the function generator as it existed at the beginning of this report period. Data from which the curves were plotted were obtained through point-by-point meter readings as the spot was deflected. Random fluctuations of output as the spot is deflected are hidden by this method, and the peak value of these fluctuations is unknown. The difference in the shape of the curves for the two different intensities is probably due to the saturation limiting action of the photoF1.6 WD 1.0 -— X,^ —1.8 -H 1. INTENSITY 1. LOW hI- \ lO >I \ -INTENSITY SPOT. 08 <I / -\\ | / \ \ m0 1.2 L.. -5 -1.0 -0.5 0 0.5 1.0. - - 5OS 0* ___ ___ 0.6 DOWNHIGH UP LEFT RGHT > igINTENSITY SPOT F.i e O0 —-— 04.6 ~ ---- Cr 02 0.2 -1.5 -1.0 -0.5 0 0.5 1.0.. -1.0 -0.5 0 0.5 LO VERTICAL DEFLECTION IN INCHES HORIZONTAL DEFLECTION IN INCHES DOWN UP LEFT RIGHT Figure 1 Figure 2 Phototube Output as a Function of Phototube Output as a Function of Vertical Spot Position Horizontal Spot Position......~~~~~~~~

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN From an inspection of Figs. 1 and 2, ana a study of Appendix I of this report, we may conclude that the wide variation in phototube output will result in excessive spot-positioning errors unless high values of Sp' are obtained, where Sp = Sp/ic S = phototube sensitivity in terms of current output per unit spot displacement perpendicularly past the edge of a mask, and ic = phototube current obtained when the spot is centered on the mask edge. Hence, attention was directed toward methods of achieving a uniform output, The optical system of the function generator as it existed when the data for Figs. 1 and 2 were obtained is shown diagrammatically in Fig. 3. The spot of light on the phosphor face of the cathode-ray tube is focused in the plane of the mask by means of an f/4.5, 152-mm Kodak Ektar lens. Light transmitted past this plane is diffused by a piece of frosted glass. A portion of the diffused light falls on the cathode of the phototube, resulting in an output signal. The nonuniform response obtained is due to either, or a combination of a) nonuniform diffusion of light at the frosted surface, resulting in decreasing phototube output as the angle between the normal to the photocathode and the line joining the photocathode and spot image increases, and b) decreasing phototube output as the angle of a constant beam of incident light deviates from the normal to the photocathode. The evolution of the present optical system, shown diagrammatically in Fig. 4, involved trials with several condensing lenses, including Hartley field lenses (a Fresnel type of lens). The basic philosophy throughout was to focus an image of the object lens on the photocathode. Since light comes from the entire area of the object lens, its image is an illuminated circular area which, ideally, remains in a fixed position independently of the spot position. Hence, phototube output should remain constantO The defects of the original system, itemized as (a) and (b) above, might have been minimized by simply moving the phototube to a greater distance from the ground-glass surface. It was felt, however, that the decreased optical efficiency would require unreasonable spot intensitieso -4

FROSTED SURFACE: PLANE OF SPOT FOCUS - 1.1-l1/4'". 12-7/8" —--- -' REFLECTING SURFACES 5RP -15A /OBJECT LENS FROSTED 1P21 MULTIPLIER CATHODE RAY TUBE / KODAK EKTAR GLASS PLATE PHOTOTUBE f:4.5 152mm Figure 3. Original Function-Generator Optical System PLANE OF SPOT FOCUS (AND OF MASK) - -I-/B" = - ~-11-I'" -t - 2. I-7/8" — "1 —— 2-t&" -..... IP21 5RP-15A BJECT LENS CONDNS LENNS MULTIPLIER CATHODE RAY TUBE L KODAK EKTAR 6"DIA.,6" FOCAL LENGTH PHOTOTUBE t:4.5 152mm. Figure 4. Present Function-Generator Optical System 5

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN The advantage of the present system lies in the fact that all the available light is directed toward the phototube. It should be noted that the available light floods the photocathode, thereby reducing the saturation effect which might exist if the light were concentrated on a smaller area. Each trial of this system showed great improvements in phototube output as a function of spot position. The present arrangement, superior to all others tried, utilizes two 12-inch focal length, 6-inch diameter condensing lenses mounted back-to-back, giving the equivalent of a 6-inch focal length lens. These are placed directly behind the plane of the mask. The initial adjustment of the photocell is at the image of the object lens. Final adjustment is made empirically by setting the phototube at a position where the variations in output with changing spot position are at a minimum. Rather than attempt a point-by-point evaluation of the present system such as produced the data for Figs. 1 and 2, a dynamic system, shown diagrammatically in Fig. 5, was used to display phototube output as a function of spot position on the screen of a cathode-ray oscillograph as the spot was cyclically swept parallel to one axis across the useful tube area. The sweep line was deflected along the opposite axis by means of the batterypotentiometer combination shown in Fig. 5, and readings were taken at approximately ten positions of the line across the useful tube area. A second set of readings was taken by reversing the cathode-ray tube axes. The divider at the H-axis input of the cathode-ray oscillograph merely serves to prevent overloading of the H-axis amplifier. Each reading consisted of two components -- the indication of the vacuum tube voltmeter across the phototube output and an observation of the maximum positive and negative excursions on the face of the calibrated cathode-ray oscillograph. Fig. 6 is an oscillogram showing a typical presentation on the oscillograph. Results of this survey showed the outside limits of phototube output for all observed spot positions were -2.4 volts and -5.6 volts, respectively, or +40 per cent about a mean value of -4.0 volts. Comparison of these results with Figs. 1 and 2 indicates a major improvement, which would have appeared even more striking had data been obtained by the same method for both optical systems. While greater perfection is desirable, work on this phase of the project was suspended at this point to concentrate on other equally pressing problems. The random excursions seen in Fig. 6 are probably due to either a nonuniformity in the cathode-ray tube phosphor which intensity modulates the spot as it moves across the surface, or to a shift in light intensity across a non-homogeneous photocathode. An attempt to isolate and correct the cause will be made when work on the function-generator optical system is resumed. ----------- 6 --

CATHODE- RAY TUBE DEFLECTION PLATES BALANCED 1 100 K SIGNAL GENERATOR ouTPUT (60") T (^::IOOK'WLIREVERSING SWITCH 4- K - 1 10 K PHOTOTUBE OUTPUT -_ r (S) 1 V-AXIS H-AXIS VOLTAGE CATHODE-RAY CALIBRATOR OSCILLOGRAPH VI, VS D.Q ELECTRONIC VOLTMETER, II MEG. INPUT V2 * A.C. ELECTRONIC VOLTMETER Figure 5. Dynamic Method of Displaying Phototube Output as a Function of Spot Position Figure 6. Typical Oscillogram - Phototube Output as a Function of Spot Position 7

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN 4. SPOT-DIAMETER MEASUREMENTS The value of phototube sensitivity, Sp, in terms of current output per unit spot displacement perpendicularly past the edge of a mask is inversely proportional to spot diameter if a circular, uniformly illuminated spot of fixed total intensity is assumed. From Appendix I of this report, it becomes obvious that it is desirable to achieve the maximum value of Sp/ic and, therefore, the minimum spot diameter obtainable throughout the region bounding the logarithmic curve. From visual observations it appeared that serious defocusing of the spot occurred when it was deflected toward the edge of the screen under conditions of a grounded second anode and balanced deflection voltages around ground potential. It was found that focus could be improved by raising the second anode above ground potential and making the necessary focus voltage and intensity control settings. However, it was necessary to vary all these quantities to maintain optimum focus throughout the range of possible deflections. The complexity of the circuitry necessary to accomplish this type of focus compension was considered prohibitive. Instead, it was decided to restrict deflections to an area of the tube where defocusing effects were small enough to be tolerable. Following inquiries of the manufacturer's representative and further observations, this region was set as a circular area 2-1/2 inches in diameter, centered at the electrically neutral point. Thus, the lengths of the coordinates of the logarithmic curve are limited to 1.77 inches. The next step to be undertaken was a determination of the spot diameter and the value of Sp directly. Actually, the latter is preferable since it eliminates any need for assumptions regarding spot shape or illumination gradients throughout the spot. Figs. 7 and 8 are graphs of the voltage measured across a 40-k resistor due to phototube current as the spot is deflected horizontally past a vertical straight-edge mask in a number of small steps. The two figures are for two widely different intensities, as will be seen from the values of the ordinates. In each case, the mask edge passed close to the electrical center of the tube, and the horizontal deflection path was approximately 3/8 inch below the electrical center to be at the peak of Fig. 1. By drawing tangents to the curves of Figs. 7 and 8, the following values of Sp were determined: For low intensity S = 1.45 x 10-3 amp/in., Sp/ic = 145 For high intensity Sp = 20.2 x 103 amp/in., S /i = 162 -----— 8 -___

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN < - 0.7 -ue Os LowI" --— 0 y HV I —-- 0.5 0 6 0o.4s fo -oi -o5h rpthu04HORIZONTAL DEFLECTION IN INCHIES.. HORIZONTAL DEFLECTION IN INCHES LEFT T LEFT RIGHT Figure 7 Figure 8 Phototube Output vs. Horizontal Spot Phototube Output vs. Horizontal Spot Deflection Past a Vertical Mask Edge: Deflection Past a Vertical Mask Edge: Low Intensity High Intensity As might be expected, higher values of S are realized with higher intensities. As can be seen from Equation (7) of Appendix I to this report, higher values accompanied by proportional increases in phototube noise current, in, and spotcentered current, ic. Increasing spot intensity, therefore, will result in no improvement in errors due to in or to variations in output with spot position (see Appendix II). In subsequent work, therefore, the spot intensity was adjusted so that the spot-centered current, i, equalled the rated phototube output of 0.1 ma. When passed through a 40-k load resistor, this current gives an output of 4 volts. It can be noted from Fig. 8 that no saturation effects of the phototube exist at this value. Next, the value of S throughout the useful tube area for both horizontal and vertical deflections was investigated. These measurements were made following installation of the latest optical system, described in a previous section of this report. As a reresentative sampling, nine points were selected as follows: each corner of the 1.77-inch square, the center of each side, and the center of the square. Rather than point-by-point determination of data justed-so-that-the-s pot-eneecurn:i:qaldthrtd phtt9 ou — ---------

500 K O.Smf.. | BALANCED 100lK CATHODE-RAY SIGNAL GENERATOR o TUBE OUTPUT (60'V) DEFLECTION'OOK -- PLATES V gT SlOOK OK m 500K.5mf. REVERSING SWITCH PHOTOTUBE OUTPUT r (g 7 < V-AXIS H-AXIS VOLTAGE CATHODE-RAY 1 CALIBRATOR OSCILLOGRAPH VI,V3 ~ DA ELECTRONIC VOLTMETER, II MEG. INPUT V2 ~ A.C. ELECTRONIC VOLTMETER Figure 9. Circuit for Dynamic Measurements of Phototube Sensitivity, Sp Figure 10. Typical Oscillogram - Phototube Output as Spot is Deflected Past Mask Edge 10

- ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN such as resulted in the curves of Figs. 7 and 8, the circuit of Fig. 9 was used to present, directly on the face of a calibrated cathode-ray oscillograph, a plot of phototube output as the spot was deflected past a mask edg. Horizontal and vertical straight-edge masks were prepared with edges passing close to the center and to points 0.88 inch from the center on each side. Steady-state deflections to position the spot at the desired edge were produced by the battery source of Fig. 9, and incremental deflections back and forth across the edge by the sinusoidal signal generator. A similar battery source, not shown in the diagram, was used to produce steadystate deflections along the other axis. A typical oscillogram taken in this manner is shown in Fig. 10. Values of Sp were determined from the slope of the tangent to the curve as before. Values obtained in this manner varied between the limits 24.3 x 10-3 - Sp' 10.6 x 10-3 amp/in. 236? Sp/ic! 103 for the different positions. In all cases, the average value of the output, equal to ic, was kept very nearly constant. Paradoxically, some of the higher values of Sp determined by this method occurred at the corners of the square. This suggests that at least part of the "defocusing" observed visually was actually due to spot motion as a result of hum pickup. Further study of this problem with a view toward extending the useful tube area is indicated. A mu-metal shield for the cathode-ray tube is currently on order. Higher values of Sp for the same total illumination would ease the amplifier requirements and reduce the errors due to noise currents and nonuniform output with spot position. This can be obtained with a spot of smaller diameter. Inquiries have been made of DuMont about such a tube. 5. DEFLECTION ANPLIFIERS During the period covered by this report, the first models of the deflection and phase inverter amplifiers were completed and tested. These amplifiers are almost idential, the only difference being in the method of shaping the frequency-response characteristic. Both amplifiers were constructed on the same chassis and are shown in Fig. 11. The wiring diagram, exclusive of feedback and input resistors, is given in Fig. 12. 11

Figure 1I. Deflection and Phase-Inverter Amplifier Chassis + 300V. IS.7MA. &?MA. 14.6MA. 42lMA \7.3MA +^ WIMA )lMA. --- L —— 24 B t A _.n' _,n MMF. TIOMMF 6ANI6 Nm111 1 3E sa-e X - 6AU6 250K^r 600K 6A05 6AH6.J:', "1 OUTPUT INPUT 200K HAE I NVERTER AMPLIFIER 0.4 -K DEFECTO F0.01 MMMA 12 Om Rm ot OEFLECTION AMPLIFIER O.M upMF 0 -OMMu PHASE INVERTER AMPLIIER O. 004 ME I K 0 Figure 12. Circuit Diagram: Deflection and Phase-Inverter Amplifiers 12

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN Using the hookup of Fig. 13, closed-loop operation of the function generator was achieved. However, because of the inadequate frequency range of the amplifiers, reasonable square-wave operation was limited to frequencies below 1 kc. Three expedients to increase the operating frequency are under consideration: a) the provision of an approximate logarithmic input from a source external to the closed loop, b) the use of only a portion of the amplifier output for feedback to the input, and c) improved physical layout of the amplifiers proper. The first two possibilities are treated in detail in Appendices I and II of this report. Briefly stated, the use of an auxiliary logarithmic input, accurate to 10 per cent, to the deflection amplifier reduces the loop gain requirements by 20 db. Thus the open-loop frequency-response characteristic IP21 MULTIPLIER 5RP-15A CATHOOE-RAY TUBE PHOTOTUSBE...^ D —---— V-o BALANCED /, I/il~~~~ \ \OUTPUT OF i —(0 fm~ l-^J i —-- SQUARE.,:-y T WAVE -~ OENERATOR i DIABOAL MASK WoMMF 500 K 0K 500 K ib A 40K DEFLECTION AMPLFIER PHASE INVERTER 50K AMPLIFIER _- _ Figure 15. Function Generator Closed-Loop Diagram -1 —— 15 K

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN can be shaped to 0-db gain about two octaves earlier, while meeting the condition of less than 12-db/octave fall-off required for stable closed-loop operation. The reduction in the controlled-frequency range eases the design requirements of the amplifier considerably. Feeding back only a portion of the amplifier output reduces the value of R (Fig. 13) required for a given open-loop gain. Hence, phase shifts introduced by the shunt capacity at the amplifier input occur at higher frequencies. With the exception of the frequency-shaping components, the amplifier design of Fig. 12 is believed to be adequate for our purpose. Cathode followers are utilized at both the input and output. Thus a low output impedance of the order of 250 ohms is obtained and the input capacity is essentially reduced to the grid-plate capacity of the 12AX7 input tube (approx. 2.0 mmf). It will be noted that provision is made for a drift-stabilizing input should one prove to be necessary. Initial balance is obtained manually by means of the 300-ohm variable resistor in the common cathode circuit of the 6AU6 stages. 6. MULTIPLIER PHOTOTUBE POWER SUPPLY The dynodes and the anode of the photomultiplier tube each had separate variable supplies. The regulation of the dynode supply was poor and the ripple content high. This condition was corrected by means of the power supply shown schematically in Fig. 14, which supplies current for both the anode and the dynodes. The output voltage is equally divided between the photomultiplier elements, sb that the 1P21 is operated with 100 volts per dynode stage and 100 volts between dynode No. 9 and anode. From no load to a 10-ma load, the RMS ripple content measured 0.005 per cent and the output resistance 40 ohms. 7. CATHODE-RAY TUBE ACCELERATING POWER SUPPLY Fig. 15 is a diagram of the accelerating supply for the cathoderay tube which was constructed when the current capacity of the 20-kv regulated supply was found inadequate to provide the accelerating as well as the post-acceleration power. It will be noted the only regulation is obtained by means of VR tubes. This supply will eventually have to be replaced by one affording better regulation similar to the multiplier phototube supply of the previous section. 14

2A3 REGULATOR\ 6SJ7 56K UTC-S74 CONTROL z z TUBE IOK CTr 866A FREED-F636 160ma 330 20hy y K OA2 235v. I- X AMPERITE 2350w X 66A i 115 NO 30 X 0 2 0A2 xC~~~02 0 @|igure 14 Multiplier OB2od. 2000Poe Supply THORDA N 866A CONL STANCOR DKBILIER 2M OA2 115 V A.C. 5 INPUT OA2 le~oK - 3.2 OA2 -1000o ECT on -,OO0v ~25' OUTPUT OA2 Figure 14. Multiplier Phototube Power Supply THORDARSON 5A. T-79FB4 0-20 115v. A.G ___ INPUT TO 2ND TO 2ND'____ _____ S _3 MEG.I1 ANODE 2^ ^-."T (^ MF 3SME. <3MEG15 TYPE OA2 VR 3 MEG TUBES IN.^^^n sooo;"", o^~ $ jh-i SERIES 2100V. 2O 2ME SR 2000v. s 2X2-A AMPERITE 9,*) 115 NOO O PILOT 10 TO LIGHT 2MF 3 MEG. 3 MEG FOCUSINGT E ~ 2000" | I3MF 2000v. I TO CATHODE 100 v. 2X2-A 9-49 20K ~ ~~ 0 TRIO Figure 15. Cathode-Ray Tube Accelerating Power Supply 15

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN 8. "MILLISEC" RELAY TESTS During the period of the previous report, a Stevens-Arnold "Millisec" relay was started on a life test in which it was operated at a rate of 40 operations per second with an "on" period of 0.8 millisecond. Power supply failure during the present report period brought this test to a close after the relay had undergone more than 650 million cycles without apparent damage. These relays are under consideration for use in the sign-changing circuits of the multiplier. 9. FUTRE PROGRAM Work on the function generator will be discontinued temporarily and development of the electronic-commutator circuits will be undertaken. -------------- ~16 -

APPE DIX I

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN APPENDIX I THE CLOSED-LOOP OPERATION OF THE FUNCTION GENERATOR Two possibilities for easing the design requirements of the deflection-amplifier feedback loop have been suggested: a change in the method of feedback and the use of an approximate logarithm generator as an auxiliary deflection-amplifier input. Both these modifications reduce the magnitude of the feedback resistance necessary for a given accuracy. Stability of the feedback amplifier is thereby more readily achieved. To illustrate the manner in which these suggested modifications affect the feedback loop design and also to take account of the dependence of phototube output on spot position, it is only necessary to elaborate somewhat on the derivation presented as Appendix III of Progress Report No. 2, September 29, 1951. With the exception of the auxiliary input represented by the voltage -zVy in series with R/a, and the feedback tap at aeo instead of at the full output, Fig. A is an exact reproduction of the open loop of the function generator detailed in the previous report. The quantity -zV represents the output of the approximate logarithm generator. The factor z, a measure of the degree by which the output approximates the voltage corresponding to the true logarithm, need not be constant but is assumed to be close to unity within fixed limits at all times. Assuming A1 is large enough to make the voltage e' at the amplifier input negligible, the output voltage e will be given by eo = -(ip+ ib) -+z (1) P a y( The total current output, ip, of the phototube is given by ip = (SpAy + iN + ic) (w) (2) 18

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN where Ay = an incremental displacement of the CRT spot center from the logarithmic mask edge along the axis driven by the phototube and deflection amplifiers (hereafter called the y axis); Sp = phototube sensitivity in terms of current output per unit spot displacement past the edge of a mask parallel to the x axis; iN = noise component of phototube current; ic = phototube current obtained when spot is centered on mask edge; and w = a function of spot position, the ratio of phototube output current referred to that obtained at zero deflection under conditions of complete spot visibility. IP21 MIULTIPLIER B5RP-15A CATHODE-RAY TUBE PHOTOTUBE +Vy Ip R RI f ~^^ o Vy - DJF W~FLE~CTION PHASE INVERTER DEFI.LEI TION AMPLIFIER AMPUFER lb G Figure A. The Open Loop of the Function Generator 19

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN The relations Ay = y - Y (3) V Ys = (4) Ed e = V (5) o y where y = the mask ordinate, Ys = the spot center ordinate, and Ed = the deflection factor in volts per inch, together with Equations (1) and (2), yields the relation Ys: - - SpRw y = ad(lz) L(i+ ic)W ib] 6) 1 SERw [lv1 Sdl j aEd(l-z) L-^ 1- a~a(l-z)_ Since, ideally, y = y, SpRw/aEd(l-z) A 1 and Equation (6) can be rewritten as S Rw - p aEd(l-z) i icw + ib s = y+- +(7) SpRw Sp Spw a1 Ed(l-z) Comparing Equation (7) with its counterpart, Equation (11) of the previous report, 20

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN S R y+ P Ed N c b v -s 1 SpR Sp Sp Ed we note that the coefficient of y can be made sufficiently close to unity with smaller values of the feedback resistance, R, since a is less than unity and z approximates unity. It will be noted, also, that the function w should be ideally constant in the region bounding the edge of the mask, so that the error due to the last term can be eliminated by setting ib = - icw. A large value of Sp/ic will help in minimizing this error as well as that due to the noise component of phototube current, iN. The auxiliary input, - zVy, may be obtained with the use of a logarithmic attenuator manufactured by Kalbfell Laboratories, Inc. and sold under the name of "Logaten." Since the manufacturer claims a linearity within 1 db, the maximum absolute value of the quantity (l-z) in Equation (7) should be 0.12. One such unit is on order at present. 21

APPENDIX II

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN APPENDIX II A NOTE ON NECESSARY SPOT POSITIONING ACCURACY It is of fundamental interest to determine the greatest tolerable error in spot position consistent with the required system accuracy. The function generator is required to deliver at its output either a logarithm of an input number or an antilogarithm, depending on the channel being sampled. Actually, our interest is centered on obtaining a given accuracy in the antilogarithm outputs, and the logarithm outputs must have errors below the maximum value which will just meet the required antilogarithm accuracy. Because of the nature of the apparatus, let us assume the logarithmic curve is plotted with coordinates of equal length. Let the length of either coordinate be Q and the number of decades n, where n is any positive integer. It is readily apparent that, in this case, the logarithms are plotted to a scale expanded by a factor Nmax/n relative to the number axis, where Nma is the full-scale value of N. If the numbers, N, are plotted along the x-axis and the logarithms along the y-axis we have x = N (1) N y -max logN, (2) n and the geometric slope of the resultant curve at any point is tan G = dy = 0.4343 c N, (3) dx nN N where c = 0.4343/n, and 9 = angle made by the curve with the x-axis. 23

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN Now let us assume that we require the final antilogarithm output to be accurate within 0.1 per cent of full-scale. Since the number scale is linear, spot positioning along the x-axis must then be within 0.001 Q of the true value for the case where the logarithm input is precisely correct. As demonstrated in Appendix III of the previous report, the spotpositioning accuracy along the y-axis is proportional to cos 9. In a similar manner, spot-positioning accuracy along the x-axis can be shown to be proportional to sin 9. Hence, the greatest spot-positioning error along the x-axis can be expected at full-scale, where 9 is a minimum. At this point, tan 9m = c (4) cn 0.4343 sinm - + "c2 =/n2 + 0.1886' where Em = angle made by the curve with the x-axis at full-scale. Now let us define Ax' as the greatest equivalent positioning error we can tolerate at a mask edge parallel to the y-axis to obtain the required antilogarithm accuracy for the case when the logarithm inputs are precisely correct. Then, to obtain N within 0.1 per cent of full-scale, 0.4343 Ax' =0.001 Q sin m 0.001 sin =086' (6) n' + o.1886 During the period when the function generator is determining logarithms, its required positioning accuracy is fixed by the maximum error tolerable in the antilogarithm outputs. Let us assume, for the moment, that, given a logarithm, the function generator will deliver the antilogarithm precisely. In this case, the error along the number (x) axis due to the error in the logarithm is Ax = Ay/tan 9, (7) where Ay is the positioning error along the y-axis. Hence, for an accuracy of 0.1 per cent of full-scale in the antilogarithm determination, N Ay = Ax tan 9 = 0.001 Q c-. (8) ____N24

- ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN It is easily apparent that the most stringent requirements occur at fullscale, where Ay must be smallest. At full-scale, Ay = 0.001 Q c. (9) Let us define Ay' as the greatest equivalent positioning error we can tolerate at a mask edge parallel to the x-axis. Since the spotpositioning accuracy along the y-axis is proportional to cos Q, at fullscale Ay' = 0.001 c cos Gm = 0.001 Q (10) = ~.001 ~0.434 - n= 0.001 n 1886 which is precisely the condition imposed on positioning along the x-axis (see Equation (6) above). It can be shown that if the function generator is capable of the positioning accuracy of Equation (10), it will provide antilogarithm outputs accurate within 0.1 per cent of full-scale over the entire range between the limits 0.001 Nmax N' Nmax Unfortunately, when input and output terminals are reversed for the determination of logarithms and antilogarithms, the errors Ax' and Ay' are cumulative. Hence, assuming operation of equal accuracy along either axis, Ax" = Ay" 0.001 0. 4343 (11) 2 /n2 + 0.1886 for an overall accuracy of 0.1 per cent of full-scale. It should be noted, however, that the foregoing figures are based on operation at the upper end of the scale, where the most rigid requirements exist. Because of problems of spot focus and uniform phototube output sensitivity outlined in previous sections of this report, let us restrict our useful area to a circle 2-1/2 inches in diameter centered at the electrically neutral point on the cathode-ray tube. The length of the coordinate axes are thereby limited to 1.77 inches. Since the present goal is to _ —----- ~~25

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN Y 2-1/2" 1.77" L- -- 1.77 - Figure B. Useful Tube Area achieve operation over three decades, let us assume n = 3. Substituting these values in (11), we have Ax" = Ay" = 0.000127" (12) From (11) it can be noted that Ax" (or Ay") is approximately inversely proportional to n if n - 1. Thus, the positioning requirements can be eased by a factor of three if three function generators were employed, one for each decade. To see what the foregoing result means in terms of the functiongenerator loop performance, let us rewrite Equation (7) of Appendix I as -k iN icw + ib Ys S1 -ki S +.' (13) ------------------ 26........

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN where S Rw k aEd(l-z) and investigate it term by term. a) The term, (-k/l-k)y. If we neglect all other terms, Equation (13) becomes ~~~~~-k Y ~(15) Ys = k-, from which k = + 1 Ayt Since no loop output is required for the condition where the spot comes to rest at the electrical center of either axis, the effective value of y at full-scale, where k is a maximum, is 1.77/2, or 0.885 inch. Hence 0.885 k = 000127 + 1 = 6970 (16) Now, from recent measurement: S (min) = 10.6 x 103 ampere/inch (page 11) w = 0.6 (page 6) Ed = 80 volts/inch; also, assume (l-z) = 0.12 (page 21) Substituting these values into (14) R = 10.7 x 106 a If a is made equal to 0.1, the feedback resistor, R, falls in the neighborhood of one megohm. 27

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN b) The term, iN/Sp. From recent measurements iN = 0.0038 x 103 ampere peak Thus, the error in ys introduced by this term is 0.00036 inch. By comparison with Equation (12) this random error is seen to be about three times the maximum positioning error required for 0.1 per cent accuracy in antilogarithm determinations. An improvement may be realized by obtaining a cathode-ray tube having smaller spot size, thus increasing the value of Sp/iN. The noise current may also be reduced by eliminating any component that may be due to intensity modulation of the spot. c) The term, (iew + ib)/Spw. Let ib = -ic Then the above term reduces to ic(w 1) Spw -3 Now, if ic = 0.1 x 10-3 amperes, the maximum rating of the 1P21 phototube, we see the positioning error introduced by this term is 0.1 x 10-3 (0.6 - 1) o.o64 in. 10.6 x 10-3 x o.6 which is a factor of 50 higher than allowed by Equation (12). The best possibility for realizing this factor lies in obtaining a value of w much closer to unity by means of a better optical system. The value of Sp may also be increased with smaller spot size on a better cathode-ray tube. A reduction in ic would be accompanied by a proportional reduction in Sp; hence, no gain can be realized in this direction. 28