LIBRARY OF THE 
 
 UNIVERSITY OF ILLINOIS 
 
 AT URBANA-CHAMPAIGN 
 
 510.6-1 
 no.212-2-20 
 
Digitized by the Internet Archive 
 in 2013 
 
 http://archive.org/details/hybridcircuitdes220ober 
 
Report No. 220 
 
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 HYBRID CIRCUIT DESIGN OF THE ARTRIX GRAPHICAL PROCESSOR, 
 
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 by 
 
 PETER ERNST RUDOLF OBERBECK 
 
 January 7> 19^7 
 
 DEPARTMENT OF COMPUTER SCIENCE • UNIVERSITY OF ILLINOIS • URBANA, ILLINOIS 
 
 THE UoRARV GF Tr,E 
 
Report No. 220 
 HYBRID CIRCUIT DESIGN FOR THE ARTRIX GRAPHICAL PROCESSOR 
 
 by 
 
 PETER ERNST RUDOLF OBERBECK 
 
 January 7 > 196" 7 
 
 Department of Computer Science 
 University of Illinois 
 Urbana, Illinois 6l801 
 
Ill 
 ACKNOWLEDGEMENT 
 
 The author wishes to express his gratitude to Professor 
 W. J. Poppelbaum who conceived the basic Artrix System, and whose 
 efforts made the actual construction possible. His enthusiasm even 
 during difficult times was greatly appreciated by all. 
 
 Special thanks is also given to William Kubitz and 
 David Rollenhagen for their design of the display and memory system, 
 and to John Esch for his design of the digital processor. Furthermore, 
 the author wishes to thank Al Irwin for his efforts in building the 
 main frame and his help in debugging the system. 
 
IV 
 
 TABLE OF CONTENTS 
 
 ACKNOWLEDGEMENT iii 
 
 LIST OF FIGURES v 
 
 1. INTRODUCTION 1 
 
 2. CAPABILITIES AND OPERATION OF THE SYSTEM 3 
 
 2.1 Line Construction 3 
 
 2.2 Circle Construction 3 
 
 2.3 Erasing h 
 2.h Freehand Construction 5 
 
 3- BASIC SYSTEM LAYOUT 6 
 
 3-1 Display and Storage System 6 
 
 3.2 Local Erase System 9 
 
 k. GRAPHICAL PROCESSOR 10 
 
 h.l Generation of Circles 10 
 
 h.2 Generation of Lines 11 
 
 U.3 Digital Processor l6 
 
 h.k Hybrid Processor 17 
 
 k.k,l Circle Operation 20 
 
 U.if.2 Line Operation 21 
 
 5- HYBRID CIRCUIT DESIGN AND DESCRIPTION 23 
 
 5 .1 DC7GLA (Digitally Controlled Variable Gain Linear 
 Amplifier) 23 
 
 5.2 D/A Converter 27 
 
 5.3 DC and AC Mixer and Amplifier 31 
 5.^ Plus and Minus Sine and Cosine Generator 35 
 
 5.5 Comparator 39 
 
 5.6 Q,06k MEz Clock lH 
 
 5.7 DC Adder and Amplifier h2 
 
 6 . CONCLUSION kk 
 
 BIBLIOGRAPHY ^7 
 
LIST OF FIGURES 
 
 FIGURE PAGE 
 
 1. Block Diagram of System. 7 
 
 2. Storage -Display System. 8 
 
 3. Erase Operation 8 
 
 k. Generation of a Circle with Sine and Cosine Functions. 12 
 
 5 • Generation of a Line "with a Positive and a Negative 
 
 Sine Function. 15 
 
 6. Counter Scheme Used to Obtain Digital Positions 
 
 of Points. 18 
 
 7o Hybrid Processor. 19 
 
 8. Basic Scheme of DCVGLA. 25 
 
 9. Schematic Diagram of DCVGLA. 26 
 
 10. Basic Scheme of D/A Converter. 29 
 
 11. Schematic Diagram of D/A Converter. 30 
 
 12. Basic Scheme of DC and AC Mixer and Amplifier. 32 
 13« Schematic Diagram of DC and AC Mixer and Amplifier. 33 
 1^. Schematic of Plus and Minus Sine and Cosine Generator. 36 
 
 15. Schematic of Comparator. 38 
 
 16. Schematic of 8,06k MHz Clock. l K) 
 
 17. DC Adder and Amplifier. hj> 
 
1. INTRODUCTION 
 
 As computer systems have "become bigger and bigger it has become 
 increasingly difficult for people to communicate 'with the computer effect- 
 ively. Ideally one would just like to talk to a machine, and tell it 
 about ones problem, and then have a reply come back in the form of a 
 printed output, or a picture on a graphic display, or a spoken answer. 
 
 The printed form of question and reply is the most commonly 
 used today. Some systems are capable of giving a spoken reply, but are 
 not capable of receiving a spoken command. Graphical input and output 
 have become a reality over the last few years and have shown great promise 
 as being an efficient way of communicating with a computer , 
 
 Most graphical consoles used to date will generate or recognize 
 a drawing or symbol on a point by point basis. Elaborate calculations 
 and logic must be performed with each point in order to determine what to 
 do with it. This type of processing obviously requires a great deal of 
 computational equipment to process even the most trivial drawings, e.g., 
 a straight line . 
 
 It seems, therefore, that the price one pays in "talking" to a 
 computer through a graphical terminal is to use another computer as an 
 interpreter. It seems to be a waste of expensive equipment to tie up a 
 big machine with possibly trivial problems, and one begins to look for 
 simple means to do graphical processing. 
 
 The Artrix Graphical Processor is a high speed, on-line graphi- 
 cal processor capable of doing all Euclidian constructions . (those construct- 
 ions that can be done through the use of a compass and straight-edge only) 
 without the use of a large digital computer. It was conceived with the 
 
idea in mind that graphical processing could be done rapidly and 
 effectively through the use of both analog and digital circuitry, 
 For graphical displays an accuracy of «3 percent is sufficient, 
 hence simple digital and analog circuitry could be used. By making 
 effective use of the best features of analog and digital circuits a 
 minimum of total equipment was used, and high-speed graphical pro- 
 cessing without the use of a large digital computer became reality. 
 In order to make use of both digital and analog circuitry 
 one has to overcome the interface between the two. The design of 
 hybrid digital-analog circuitry enables one to make the best use of 
 each and becomes therefore a very important part of the design con- 
 siderations of the Artrix system. Of particular interest is the 
 DCVGLA (Digitally Controlled Variable G-ain Linear Amplifier) whose 
 function is to control the amplitude of a sinusoid in response to 
 a digital input. The de\~ice is capable of digitally changing the 
 amplitude over the range of 512 points at a speed of about 2 MEz. 
 Response of the entire system is such that all drawings appear 
 flicker -free and instantaneous as far as the operator is concerned. 
 The effective use, need, and design of this and other practical 
 hybrid circuits as regards graphical processing will be discussed 
 in this thesis. 
 
3 
 2. CAPABILITIES AND OPERATION OF THE SYSTEM 
 
 2.1 Line Construction 
 
 The operator is capable of constructing a line between any 
 two points on the screen. First the construction points used are 
 indicated with a light pen and appear on the display screen as dots. 
 The operator now presses a button to put him in the line construction 
 mode. Now, by pointing the light-pen in the neighborhood of a point 
 and pressing an "enable" button on the pen he will store the coordin- 
 ates of this point as point one. Similarly a second point is indic- 
 ated. As soon as both points have been indicated an "execute construct" 
 button will light up, and upon depressing it, a straight line will 
 appear between the two points indicated. The operator can now trans- 
 late this line to any other point on the screen by resetting and 
 reindicating point one. This feature enables the operator to draw 
 a series of parallel lines on the screen. 
 
 In actual Euclidian constructions one has to "construct" a 
 parallel line using a compass and doing several operations before such 
 a line may be drawn. Since it is often desired to construct parallel 
 lines it was felt that this feature is essential to the system, 
 although it is not a primary Euclidian construction. 
 
 2.2 Circle Construction 
 
 As in the line construction the operator can indicate a 
 series of construction points on the screen with a light pen. He 
 then goes to the circle construction mode by pressing the approp- 
 riate button. The first point he now indicates will correspond 
 
k 
 
 to the center of the circle. Indicating a second point on the 
 screen will correspond to indicating a point on the circumference 
 of the circle. Again as in the line construction the circle "will 
 be drawn when the ''execute construct" button is depressed. 
 
 The operator can now translate the circle with the same 
 radius to any point on the screen, by reindicating point one. 
 Similarly the radius can be changed by reindicating point two. This 
 will result in constructing a circle with a new radius and using 
 the previously indicated point one as the center. These two basic 
 circle operations correspond to the actual operations one can carry 
 out with a compass. 
 
 For both line and circle operation the construction points 
 used to indicate the position and size of the lines can be erased by 
 pushing a button marked "erase point". (Note that no constructions 
 can be made without these construction points) . This is done to 
 avoid confusion between the construction point and a construction 
 line or circle segment. 
 
 2.3 Erasing 
 
 If one wants to erase part of a line or circle, one first 
 goes into the erase mode. The part of the construction that is now 
 to be erased is traced over by the operator with the light pen. 
 The part to be erased will appear black on the screen until the 
 "execute erase" button is depressed. At this time the black lines 
 and the "underlying" lines to be erased will disappear. 
 
5 
 2 oh Freehand Construction 
 
 Should one encounter a drawing where it is necessary to 
 draw something other than a circle or a line, one can go to a "write 
 display" mode where it is possible to do freehand sketching or 
 writing. All one has to do is to keep the enable button on the 
 light-pen depressed as long as one wants to write. 
 
 This feature is especially useful for filling in gaps, 
 and for lettering. 
 
3- BASIC SYSTEM LAYOUT 
 Figure #1 shows a basic block diagram of the Artrix System. 
 
 3.1 Display and Storage System 
 
 The basic method used to store and display constructions and 
 construction points is to have a vidicon look at a storage tube, which 
 is simultaneously scanned (in synchronism) with a standard television 
 monitor, and to gate the storage tube on each time the scan on the monitor 
 intersects the light -pen. The light -pen is a photosensitive device, 
 that will produce a short pulse each time the beam on the monitor scans 
 past it. The point that occurs on the storage surface is then displayed 
 on the point indicated by the light -pen on the monitor. This point will 
 remain displayed until the storage tube is erased. It is interesting to 
 note, that the vidicon merely provides an optical feedback path" necessary 
 to view what was written on the storage tube. One could still write on 
 the storage tube even though the vidicon were not turned on. All construct- 
 ions are done and stored on one storage tube. All construction points are 
 stored on another storage tube . They are called display and point memories 
 respectively. This enables the distinction of construction points from 
 actual constructions by the processor, and also allows complete erasure of. 
 all construction points without indicating each one of them beforehand. 
 One can also do freehand construction in either one of these storage tubes. 
 
 Figure #2 illustrates the vidicon-TV monitor-storage tube combin- 
 ation. 
 
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 Figure #3. Erase Operation, 
 
3.2 Local Erase System 
 
 In order to perform local erasure (which is not a feature of the 
 storage tube) two more storage tubes are needed. One storage tube contains 
 the information regarding the areas that should be erased (erase memory) . 
 The other temporarily stores the display information minus the points to 
 be erased before it is transferred back to the display tube (Tempo memory) . 
 During erasing the following things take place. The parts of the drawing 
 to be erased are traced over by the light pen, and are stored in the erase 
 memory. Upon "erase execution" the negative of what is stored in the erase 
 memory is now added with the display memory and the result is stored in 
 the temporary memory. One can see that those parts stored in the erase 
 memory and those that were also in the display memory have now cancelled 
 each other out „ As soon as the transfer to the temporary memory has taken 
 place, the display memory is erased. Then the information in the temporary 
 memory is transferred to the display memory. At the end the erase and 
 temporary memory are erased. The result is that only these portions that 
 were originally in the display memory and not traced over will reappear 
 on the display memory ° Figure #3 illustrates this operation. 
 
10 
 k. GRAPHICAL PROCESSOR 
 
 The graphical processor of the Artrix system essentially consists 
 of two main parts. One is the digital section, and the other is the hybrid 
 digital-analog section. The operation of each of these sections may "be 
 subdivided into two more parts » One for the construction of lines, the 
 other for the construction of circles. 
 
 The digital section essentially provides digital magnitudes for 
 the size and translation of the analog signals. The hybrid circuitry uses 
 these digital signals to provide actual analog signals corresponding to 
 lines of proper size, slope and position as well as circles of proper size, 
 and position. The actual analog signals are first sent to the display 
 memory, from which they are shown on the display. 
 
 h .1 Generation of Circles 
 
 The storage tube employed in the Artrix System is essentially 
 an oscilloscope with the property that any waveform displayed on it may 
 be stored at the user's command. The problem then consists of supplying 
 a waveform to the storage tube that will look like a circle. A sine and 
 a cosine wave of equal amplitude and frequency applied to the vertical 
 and horizontal deflection plates respectively will generate a circular 
 pattern. Such a pattern is a very simple example of a Lissajous Pattern. 
 Figures of a more complicated nature are usually encountered when dis- 
 playing combinations of sinusoidal waveforms of different phase and fre- 
 quency relationships. Using the two functions R sin (cot) and R cos (cot) 
 a circle of radius R will be generated. If R is made variable, circles 
 
11 
 
 of any size may be generated. If one wants to translate the circle in 
 the vertical and horizontal directions, one merely adds a DC component 
 to the R sin (act) and R cos(cot) functions. We therefore concentrate on 
 functions of the form* 
 
 V - R sin(cot) + VP 
 
 H - R cos(oot) + HP 
 
 which generate a circle of radius R translated vertically VP units and 
 horizontally HP., units from some zero reference. The actual generation 
 of such a pattern is graphically illustrated in Figure #4 « We now have 
 a mechanism by which we". can generate a circle of any radius and any trans- 
 lation, provided we can accurately control the values of R, VP , and HP-. 
 It will be shown later how digital values of R, VP_ , and HP are generated 
 and used to control the amplitudes of the sinusoidal functions and their 
 respective DC offset component. 
 
 4.2 Generation of Lines 
 
 The generation of a line at first sight is even more trivial 
 than that of a circle. This seems so because one only has to use the 
 function R sin(a)t) or R cos (cot) . In fact, any two sinusoidal functions 
 that are in phase will generate a straight line. The function R sin(ajt) 
 applied to both horizontal and vertical plates of an oscilloscope will 
 generate a line of length 2R sloping at -:-^5 to the right. One can now 
 see the difficulties involved in constructing a line between two points. 
 If the slope should be variable (as is desired in this system) one must 
 be able to control the magnitude as well as the sign of each sinusoid 
 independently. For instance, lines with negative slope must have a 
 
12 
 
 OSCI LLOSCOPE 
 
 VERTICAL INPUT 
 
 Figure #4. Generation of a Circle with Sine and Cosine Funct 
 
 ions 
 
13 
 
 -R sin(o)t) component. And lines of slope other than ^5 must have 
 different amplitudes. Another problem that enters at this point is 
 that a line generated by this method extends in two directions from 
 the zero reference. That is to say that a line generated by 
 + R., sin(cot) and + R cos(cot) will extend from the zero reference 
 (0 , 0) to a point (R , R p ) and also in the opposite direction to a 
 point ( -R, , -Rp) . The first thought to correct this phenomena was to 
 rectify the sinewave, so that only the positive "humps" would reach 
 the deflection plates. This method would work theoretically. However, 
 in practice it was found that one would have to have the negative hump 
 for one type of line and the positive hump for another line, depending 
 on its slope. Also rectification would have to be done not with respect 
 to ground as is usually done, but with respect to some DC offset used 
 to translate the line. These two difficulties, plus the nonlinearities 
 that would create very high-frequency components once the sinewave was 
 rectified, was our reason not to use the rectification approach. 
 
 The alternate approach was to add a DC component equal in 
 magnitude to the peak amplitude of the sinewave to the sinewave itself, 
 thereby translating it by exactly the amount it would extend in the 
 undesired direction. This method proved particularly desirable, because 
 digital signals corresponding to the amplitude of the sinewave have to 
 be present, and it was not difficult to generate the corresponding DC 
 offset from the same digital signals. The functions that would now 
 generate a line was of the following form: 
 
 V = R sin(a)t) + P 
 
 H = R„ sin(ajt) + R 
 
14 
 
 ■where R, and R p would also be negative if a line of negative slope was 
 desired. It can now be seen that a line generated by the above two 
 functions would extend from the zero reference (0, 0) to (2R , 2R ) , 
 and the undesired extension in the opposite direction is eliminated. 
 Consequently by specifying R-,/2 and Rp/2, one can draw a line from the 
 origin to a second point. This, as in the use of the circle merely 
 corresponds to adding on two DC offsets corresponding to the vertical 
 and horizontal displacement of the first point. The forms of the 
 functions that now describe the generation of a line between any two 
 points (HP,, VP, ) and (HP, + R ? , VP, + R,) is given by 
 V = R (sin (cot) + l)/2 + VP 
 
 H = R (sin(ttft) + l)/2 + V? 2 
 
 It should be noted again that R and R can be either positive or nega- 
 tive depending on the slope of the line. Figure #5 shows a graphic 
 illustration of the actual generation of a line . 
 
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16 
 4.3 Digital Processor 
 
 We can now construct any circle given digital information 
 about the location of its center and the magnitude of its radius . We 
 can also construct any line given the coordinates of the first point 
 of the line and the horizontal and vertical distances to the second 
 point o The problem is how to obtain these digital signals corresponding 
 to the position of points and magnitudes of distances. Since the display 
 used in the Artrix system is of the TV type it was thought to divide the 
 TV raster into a 512 by 512 matrix. In doing so^ a "horizontal counter" 
 counted down the 512 points on a horizontal line., and a vertical counter 
 would count down the 512 lines in a frame.. Hence the content of the 
 horizontal and vertical counter would contain the digital coordinates 
 of the beam that sweeps out the raster at any time . It should be pointed 
 out that the resetting (or spilling over) of the horizontal and vertical 
 counters are used to provide the horizontal and vertical synchronization 
 signals for the raster that sweeps the TV monitor., the cameras and the 
 storage memories. A 512 by 512 matrix was chosen since this is close to 
 the 525 by 525 resolution that should be found in a "500" line TV system. 
 Furthermore^ 512 is the count that can be obtained in a 9 bit counter. 
 If one now controls a second set of counters by the master counters and 
 stops them at some particular time^ the count contained in them will corres- 
 pond to the position of the beam at the time the count was stopped. By 
 detecting the position of the beam with a light sensitive device and 
 using its output to stop the second set of counters one will store in these 
 counters the digital position of the point indicated by the light sensitive 
 device (light -pen) . By this method a convenient way of obtaining the 
 
IT 
 
 digital position of a point indicated by a light pen has been found. We 
 will call the coordinates of these points horizontal point one (HP ) and 
 vertical point one (VP , ) . 
 
 Next, one would like to generate the difference of the coord- 
 inates to the second point (clearly those are needed in the equations 
 that describe the lines) . This is done by simply starting a third set 
 of counters at the time point one (HP,, VP, ) "was indicated, and stopping 
 them with the second output from the light pen, called point two (HP p , 
 VPp) . Since the counters spill over and start again from zero once a 
 511 count has been reached, the magnitude of the count they contain will 
 always be relative to the point one counters and be equal to the difference 
 between point two and point one. An illustration in Figure #6 will clarify 
 this procedure. 
 
 As we shall see later the circle operation requires the direct 
 coordinates of point two (not relative to point one) . This is done simil- 
 arly to obtaining point one by using a different gating sequence in start- 
 ing and stopping the third set of counters. 
 
 h ,k Hybrid Processor 
 
 We have discussed the production of lines and circles and various 
 digital signals corresponding to coordinates and differences of coordinates 
 on the display. We shall now investigate how these are put together to 
 form lines and circles as indicated on the display. A block diagram of 
 the hybrid processor is shown in Figure #7 and will be helpful in the 
 forthcoming eirplanations . All control inputs are from the digital proc- 
 essor and are in digital form. All outputs (excepting the one from the 
 
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 comparator) are analog, and go directly to the display storage tube. 
 Solid arrows represent analog signals and open arrows represent digital 
 signals , 
 4.U.1 Circle Operation 
 
 Let us consider the operation of constructing a circle. First 
 the processor is switched into the circle construction mode. This selects 
 by means of relays and logic signals CR, CV, CH, a sine and cosine wave. 
 The cosine wave is then applied to the vertical channel and the sinewave 
 is applied to the horizontal channel. The wave manipulations are performed 
 in each channel, except that one uses horizontal digital inputs and the 
 other vertical digital inputs. It should also be noted that the gain of 
 the vertical channel is only 3/h that of the horizontal channel. This is 
 done to preserve the 3° ^ aspect ratio of the TV monitor. 
 
 It was shown in Section ^t-.l that in order to generate a circle 
 one has to generate the analog signals 
 
 R sin (cot) + HP 1 
 
 R cos (cut) + VP 
 
 HP, and VP. are the EC offsets that provide the translations, and are the 
 digital coordinates of the center of the circle. These two digital signals 
 are generated as described in Section U.3 and are now applied to the digi- 
 tal to analog converters (horizontal and vertical D/A converter #2) . The 
 output of these D/A converters are then two DC voltages corresponding to 
 the two DC offsets HP, and HP p . Next the radius of the circle must be 
 found. This is done by a coincidence scheme. The sine and cosine waves 
 are applied to an amplifier whose gain is proportional to a given digital 
 input. (DCVGLA Digitally Controlled Variable Gain Linear Amplifier). 
 
21 
 
 The digital input to the horizontal and vertical DCVGLA is the same and 
 is stepped from to 511 as long as only the center of the circle has "been 
 indicated . The output of the DCVGLA is then a sinusoid that increases 
 "with time. This output is then mixed in the DC and AC mixer and ampli- 
 fier -with HP, and VP in the horizontal and vertical channel respectively. 
 The vertical and horizontal D/A converters #1 are at this point disabled 
 by CR and OR. The output of the mixer is then an increasing sinusoid 
 with a DC offset. Next a point on the circumference of the circle is 
 indicated and similarly converted by a D/A converter (#3) "to a DC level 
 corresponding to the coordinates of that point. These two DC levels are 
 then compared "with the two increasing sinusoids. The desired radius is 
 reached "when both sinusoids are equal to the second DC levels (or coord- 
 inates of point two) at the same instant. When this coincidence is 
 obtained a logic signal causes the radius counter to stop. In other 
 "words: the circle expands about its center until the indicated size 
 
 (HP„ and VP,-.) has been reached. 
 2 2' 
 
 h. h .2 Line Operation 
 
 Again, as in the circle logic signals CR, C7, and CH select 
 sine or minus sine functions to generate a line. (Actually not all 
 logic signals are available until both endpoints of the line have been 
 indicated since point two determines the slope. This is of no conse- 
 quence since nothing can be displayed until point two is indicated and 
 settling time of the circuits is much faster than the operator can push 
 the construct button) . CR and CR signals now enable both #1 and #2 D/A 
 converters that go into the DC and AC Mixer and Amplifier. When point 
 one is indicated, VP and HP are available and are applied to the D/A 
 
22 
 converters and fed into the mixer. These then correspond to the 
 coordinates of the first endpoint of the line. Remembering the 
 form of the functions needed for a line from Section h.2 
 (HP 2 -HP )(sin(ojt)+ l)/2 + EP ± 
 
 (VP 2 -VP )(sin(cot)+ l)/2 + VP 1 
 
 we see that -we must next indicate point two., which gives us 
 (HPp-HP,) and (VP -VP ) as shown in Section k.J. 
 
 These are now applied to the DCVGLA to give the sinewave 
 the proper amplitude and to the #1 D/A converters to give the proper 
 DC offset to keep the line from extending through point one . The 
 output of all three signals are then indeed of the form needed to 
 generate the line and are applied to the deflection plates of the 
 display storage tube. No use is made of HP p and VP p alone in the 
 line mode., and also no comparison methods are needed. 
 
23 
 
 5 . HYBRID CIRCUIT DESIGN AND DESCRIPTION 
 
 In the folio-wing chapter, the hybrid circuits and their design 
 ■will be discussed. Their implementation and purpose has been described 
 to some extent in Section h, -while this section will deal more -with the 
 design considerations. 
 
 5-1 DCVGLA (Digitally Controlled Variable Cain Linear Amplifier) 
 
 In the hybrid processor need existed for a device that could 
 
 control the amplitude of a sine-wave proportional to a digital input . 
 
 Specifically a device was needed that would control the amplitude in 
 
 512 increments corresponding to 9 digital bits. A mathematical transfer 
 
 function for this device would be as follows: 
 
 X = K. sin(o)t) a 2 + a-, 2~ + a ? 2 + .... + an2 
 
 where a . . . .a fi are the binary inputs, K is an arbitrary gain constant 
 and X is the output. 
 
 It was decided that the output should have a peak to peak 
 variation from zero to + 10 volts in order to maintain compatibility 
 with established voltage levels. A gain constant of V ~ 1.5 was found 
 convenient since this would require a 6.67 volt peak sinewave for an 
 input, and this was a convenient value to generate. 
 
 The scheme that was used to obtain the above function was 
 
 one of summing currents through resistors whose values were in the ratio 
 
 o 1 ? ft 
 of 2 ; 2 ': 2 \2 , and whose presence in the circuit was determined 
 
 by a transistorized switch. The scheme is similar to a D/A converter, 
 
 except that an AC voltage is converted instead of a DC voltage. The AC 
 
2U 
 
 must also be able to be changed in phase and in amplitude yet retain 
 the digital control over the signal. A basic diagram of the scheme used 
 is sho-wn in Figure #8, and the actual circuit used is shown in Figure #9- 
 In the actual circuit the constant controlled voltage source -was imple- 
 mented by an emitter follower which used the digital resistance chosen 
 as the emitter resistor. A Darlington configuration for the transistors 
 was chosen to make the source as "stiff" as possible. This would give 
 the circuit a current gain of about 3-, . 3 P where 3, and 3o are the respect- 
 ive betas of the 2N2102 and 2AJ305^. This proved to be adequate for the 
 change in the emitter resistor from R/2 to AC open circuit. A DC bias 
 current had to be present to keep the transistors in the active region. 
 An 8 Hy coil was put in series with the bias resistor to make it look 
 like an AC open circuit at 10 KHz. 
 
 Current sensing is done in the collector of the Darlington 
 pair. A transformer was chosen as the current detection device. It 
 provides complete DC isolation from the rest of the circuit, it gives 
 great voltage gain, and provides the needed impedence match. The AC 
 resistance in the collector should be small compared to the minimum AC 
 resistance found in the emitter. The load on the secondary of the trans- 
 former is 10K. Its turns ratio is such as to present 3 ohms in the 
 primary: 3 ohms in the collector is small compared to a minimum of 
 
 100ft in the emitter. Using this value as a standard, the R in the 
 
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 digital emitter chain was chosen close to 200 ohms. Since it is difficult 
 to get precision resistors such that the R is 200ft + .1$, and since the 
 saturation resistance of the transistor switch would add an even greater 
 error, it was decided to use adjustable resistors in the first six most 
 
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 significant bits of the chain. For the last three bits 1$ resistors were 
 found adequate, and at this value (2 R ) the saturation resistance of the 
 transistor was also negligible. The resistance chain was adjusted such 
 that any two adjacent bits would provide an output voltage in the ratio 
 of 2: 1. The switching in and out of the resistor was accomplished by a 
 two stage switching circuit. Two stages were needed to provide compati- 
 bility with the logic levels of the digital system, and to provide the 
 high gain needed to drive the first two most significant bits . Peak 
 currents of the order of 200 ma are expected to flow through the trans- 
 istor turning the most sifnificant bit on and off. The accuracy of the 
 system is one part in 512 or about .2$. The limiting factor in adding 
 on more bits is that the resistance of the least significant bit be less 
 than the total parallel resistance of the backbiased collectors of all 
 the other legs- Another way of looking at this is to note that the 
 current flowing in the least significant leg be greater than the total 
 leakage currents in all the other legs. The other limiting factor is 
 that the AC open path in the bias drive indeed look large compared to the 
 resistance of the least significant bit. 
 
 It was this factor that limited the accuracy of the circuit. 
 We used an inductance of 8 Hy to provide an AC impedance of about 500K 
 compared to about 50K in the path of the least significant bit. 
 
 5.2 D/A Converter 
 
 The D/A converter is essentially a much simplified version of 
 the DCVGLAo There are several things that simplify its design consider- 
 ation. For one thing, we are only concerned with DC levels; There are 
 no AC components. This eliminates bias problems and AC isolation immed- 
 
28 
 iately. The detection mechanism can now be a differential amplifier 
 sensing current through a resistor. The need for a constant controlled 
 AC source is eliminated., since the DC supplies can essentially perform 
 this function o The need for high power levels,, and hence a two stage 
 switch is also eliminated,, because there is no AC open circuit bias 
 chain that puts a limit on the resistance of the least significant 
 bit o The limiting factor is now the leakage current in the rest of 
 the chain,, which can be made extremely small;, by choosing low leakage 
 transistors. A basic diagram of the D/A converter is shown in Figure 
 #10 and Figure #11 shows the actual circuit configuration. Conversion 
 accuracy of the circuit is one part in 512^ and maximum conversion 
 frequency was about 2.5 megabits per second. That is to say that 
 any bit can be switched at a 2.5 MHz rate and the output will produce 
 a 2.5 MHz waveform. The limitation of the uppermost conversion rate 
 is governed by the RC time constant of the least significant bit. 
 The value of the summing resistor R should be small compared to the 
 resistance R in the most significant bit of the binary resistance 
 chain. The output variation for a zero to 511 digital input variation 
 was -10 volts for zero and -1^ volts for 5H» These levels had to 
 be amplified again in the mixer stages in order to be compatible with 
 the + 10 volt swings required for full screen deflection. Zero volts 
 horizontal and vertical would represent the center of the screen. 
 Performance of the D/A converters proved excellent throughout the use 
 in the system. 
 
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31 
 5.3 DC and AC Mixer and Amplifier 
 
 Another analog circuit with digital control is the DC 
 and AC mixer and amplifier. It was designed to perform several 
 functions , two of which depend on the presence or absence of a 
 digital signal. The operations the circuit can perform are the 
 following. First, the circuit is a precision adding or subtract- 
 ing circuit of DC levels <> Second., it is a compensated differential 
 DC amplifier. Third, it is a mixer which takes the DC level 
 (DC offset) of a D/A converter and mixes it with one of the sinus- 
 oids . As mentioned above it can be digitally controlled to perform 
 addition of two variable levels, or addition of one variable and 
 one fixed level. The circuit is also an output buffer for the 
 hybrid processor. Figure #12 gii^es a complete schematic of the 
 circuit. Operation of the circuit is as follows. 
 
 First let us consider the digitally controlled DC adder 
 and subtracter. The digital control signal corresponds to either 
 line or circle operation. For the line operation (Section h .2) a 
 DC offset of the same magnitude as the sinusoid is added in to prevent 
 extension of the line through point one. Also, another DC offset 
 was needed that would translate point one to the proper point on the 
 screen. The digital signal for line operation selects current source 
 I„ in this mode. Both current source I and I are controlled sources. 
 I is controlled by the D/A converter that determines translation, 
 and I is controlled by the D/A converter that determines the addit- 
 ional DC offset to prevent extension of the line through point one. 
 
 These two currents are then summed through R and the voltage across 
 
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 currents is negative with respect to a ne"W reference, subtraction 
 will t ake p lac e . 
 
 When the system is in the circle operation, the additional 
 DC offset due to source I is not wanted. The digital control then 
 selects I , which is a fixed current source that is equal to the 
 zero reference mentioned above. Since it is at zero reference it 
 does not add on any translation to the center of the circle. It is, 
 however, necessary, since zero reference differs from ground or zero 
 current at this point. This fixed current reference can be adjusted 
 by means of a potentiometer to the correct value. The controlled 
 current sources are essentially emitter followers, whose collector 
 currents are summed through a 2.2K resistor (R ). The output of the 
 adder is then applied to a compensated DC amplifier whose gain is 
 such that a + 10 volt variation occurs at its output. The compen- 
 sation circuit was designed to prevent drift due to supply variations 
 The reference to the differential amplifier is essentially of the 
 same configuration as the DC equivalent of the signal source. Hence 
 through common mode rejection the supply variations are eliminated 
 at the output . 
 
 The other function is the mixing of the sinusoids with the 
 DC levels. This is done by applying the DC to our emitter follower, 
 and putting in series with the output the output transformer of the 
 DOVC-LA. The AC is developed by the DCVGLA across the 10 K resistor 
 and added on to the DC present on the emitter resistor of the emitter 
 follower. The output of this series circuit is then tied to another 
 
35 
 emitter follower, -which serves as a high input impedance to the mixer 
 and a low output impedance to the rest of the system „ This is the 
 output buffer mentioned before. The performance of the circuit in 
 the system proved excellent. Variations in switching from one mode 
 of operation to another were not noticeable by eye on the display 
 screen. Temperature and voltage stability proved excellent compared 
 to an uncompensated previous circuit. 
 
 5 .^- Plus and Minus Sine and Cosine Generator 
 
 In order to generate the lines and circles for the processor 
 it was necessary to provide the + sine and cosine functions. These 
 had to be extremely linear and practically void of all higher harmon- 
 ics. The phase relationship between the functions had to be controll- 
 able and fixed to within onehalf of one degree: Otherwise circles 
 would appear elliptical and lines would look like an extremely long 
 or narrow ellipse. Phaseshift had to be controllable to compensate 
 for phaseshift in the amplifiers of the rest of the system., Any higher 
 harmonic distortion would cause circles to have bumps in them and lines 
 would exhibit figures that resembled a profile of a twisted pair of 
 lines. It turns out that Lissajous patterns are an excellent measure 
 of linearity for sinusoidal waveforms _, so in checking linearities the 
 desired end product was used as a measuring tool. 
 
 The entire circuit consists of four sections. First a 
 sinusoidal oscillator, second an amplifier, third a phaseshifting net- 
 work., and fourth, an output buffer network with amplitude control of 
 each sinusoid. A schematic diagram of the circuit is given in Figure 
 
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37 
 For the oscillator a Colpitts configuration with emitter 
 feedback was used. Since frequency stability is of no consequence 
 a freerunning LC tuned configuration proved adequate. To get the 
 greatest linearity the loop-gain was adjusted such that it is as 
 close as possible to one. A frequency of lOKHz was chosen so that 
 the response time of the comparator would not be exceeded. Also 
 at this frequency any third harmonic distortion., which was prevalent } 
 did not pass through the transformer used in the phaseshifting network 
 and the DCVGLA. The amplifier used was a simple single ended class A 
 configuration with transformer output . The only caution that had to 
 be observed was not to saturate the transformer. This transformer 
 also served as the heart of the phaseshifting network. By grounding 
 the center of the transformer^ the two ends of the winding have two 
 signals that are 180 degrees apart. These provided the + functions. 
 By taking a resistor P. and a capacitor C whose reactance at lOErlz is 
 equal in magnitude to R one can obtain a signal exactly 90 degrees 
 out of phase with either end of the transformer by applying this 
 series combination of R and C across the transformer. This signal 
 was then the cosine function. By making R variable the phase of the 
 consine function could be adjusted separately. The outputs of the 
 transformer and phaseshift networks are controlled by potentiometers 
 and fed to emitter followers to provide a buffer for the next stage. 
 A Darlington configuration was used for the cosine function since 
 its phase stability was more dependent on the input -impedance into 
 the emitter follower. The circuit exhibits excellent linearity 
 at this point and perfect lines and circles can be obtained. 
 
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39 
 5 .5 Comparator. 
 
 It was explained in Section h.l that radii of circles were 
 determined by a comparison method. The expanding sinusoids were 
 compared to the DC levels of the horizontal and vertical portions of 
 point two. Upon coincidence of both vertical and horizontal Aroltages 
 the radius was stopped from increasing. 
 
 The circuit configuration is shown in Figure #15° It con- 
 sists essentially of three sections. First the differential amplifier, 
 second a "NOR" circuit to sense two equal voltage levels, and third a 
 single -shot to provide an output pulse of fixed width. 
 
 In considering the differential amplifier, one must realize 
 that it must be able to compare any two voltages in the range of + 10 
 volts. Since it is conceivable that one input can be + 10 volts while 
 the other might be -10 volts, a differential voltage of this magnitude 
 will break down the base to emitter junction of most transistors, so 
 special precautions must be taken. A diode "with a high breakdown 
 voltage must be used in series with the base. The diode is forward 
 biased by a 100K resistor tied to -25 volts. A constant current 
 source is used in the emitter circuit of the differential amplifier 
 to provide high sensitivity. When both inputs are equal, current 
 splits evenly between the two legs of the amplifier, and the "NOR" 
 circuit is such that it changes state when the voltage in both legs 
 of the circuit are equal. This change indicating equivalence is used 
 to trigger a single shot of ,2}j,s duration. Since accuracy of 1 part 
 in 512 is desired the period of the TOKHz was divided by 512 to arrive 
 at the .2us duration. 
 
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 The circuit will respond to a differential offset of 30 mv. 
 This falls within the desired sensitivity of 40 mv. (This was obtained 
 by dividing the maximum voltage variation by 512 which is the quantized 
 voltage change) . It was found that the sensitivity of the comparator 
 could be maximized by adjusting the value of the current source. This 
 would essentially set the threshold for the " NOR " circuit. Perform- 
 ance of the circuit showed good results in as far as radii of circles 
 could be determined accurately and consistently. 
 
 5.6 8,064 MHz Clock 
 
 In order to divide a horizontal line of 62.5 l-ts duration 
 into 512 points a fundamental clock frequency of 8,064 MHz was needed. 
 This clock would provide the synchronization signals for the entire 
 system. To get the best stability and frequency accuracy a crystal 
 controlled circuit was designed. A schematic of the circuit is given 
 in Figure #l6. The configuration is a crystal controlled Colpitts 
 circuit with tuned collector and emitter feedback with the crystal . 
 The circuit is driven hard to provide good stability. Since a square 
 wave is needed to drive the logic circuits of the processor, two 
 transistors are used in a squaring circuit. The tuned collector has 
 a secondary winding which feeds directly into the base of the first 
 transistor. This transistor in turn drives the output transistor 
 of the circuit. The output is a square wave with rise and fall trans- 
 itions of less than 20 ns . At these speeds decoupling of the supplies 
 through the closest physical path is of primary importance in main- 
 taining a clean waveform with fast rise-time. Without this precaution 
 severe overshoot and ringing took place. Layout of the circuit on 
 
1+2 
 the printed circuit card was done in such a way as to obtain 
 short interconnections. 
 
 5-7 DC Adder and Amplifier 
 
 This circuit is basically similar to the one shown in 
 Section 5«3j> but with some simplifications. It only amplifies DC 
 and mixes it with the sinusoids., rather than mixing two DC voltages 
 together also. The circuit configuration is shown in Figure #17 • 
 The first section takes the DC voltage of the D/A converters and 
 amplifies it by a factor of four. This is done with a differential 
 amplifier whose second input is the zero reference of the D/A convert- 
 ers. It can be adjusted by a potentiometer in the emitter circuit. 
 This merely allows one to change the effective zero reference of the 
 D/A converter input. The next section is an emitter-follower and 
 level changer. The level is changed such that the DC output is 
 centered with respect to ground. It is also used to provide a source 
 for the mixer. Mixing is done in the same way as in the circuit of 
 Section 5«3« That is,, the transformer output of the DCVC-LA is put 
 in series with the emitter follower of the previous section, and 
 then fed into another emitter follower. This last stage provides an 
 output-buffer to the rest of the system. Through use of a differ- 
 ential amplifier, good stability is obtained. Also a low gain factor 
 makes the circuit insensitive to drift. 
 
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 6 . CONCLUSION 
 
 It can now be seen that through the effective use of hybrid 
 digital-analog circuitry, (on which the most effective use of the desir- 
 able properties of each technique is made)., one can perform all euclidian 
 constructions without the use of a large scale digital computer. 
 
 The digital processor of the graphical display, and its assoc- 
 iated counters divide the screen into 512 x 512 points and provides a 
 digital output for indicated positions or distances. Obviously a digital 
 counter can perform these functions very well. To generate the lines and 
 circles in a trivial manner analog circuitry is used to form Lissajous 
 patterns. To use digital techniques at this point would require a great 
 deal of computational equipment. Analog circuitry is the only simple way 
 out. Now the analog information must be combined with the digital infor- 
 mation. This is done with the newly developed hybrid circuitry. It 
 digitally controls the amplitude phase as well as the routing of the 
 analog signals. It is this close merging technique which allows one to 
 perform seemingly complex operations in a simple manner. The speed of 
 the system is also very high, since the display of constructions is done 
 by a continuous analog wave form rather than a point by point plotting 
 routine . Once the shape of the waveform has been determined by a set of 
 counters and a digital-analog interface, no more calculations have to be 
 done to continuously display a construction. Again one can see that the 
 advantageous points of each system are used and then merged together. 
 
 Unfortunately, one also inherits some of the disadvantages of 
 each system in this type of operation. These difficulties, however, 
 
^5 
 are not insurmountable, and usually just represent an upper limit to 
 speed and precision. Analog information is limited in accuracy since 
 it is hard to differentiate between two nearly equivalent voltages 
 (or currents) over a large range. For a 512 by 512 point system 
 this was no problem, but for a 1000 x 1000 point system the problems 
 of accuracy would become more severe. A digital system is usually 
 more accurate in the sense that even a very small digit is still 
 represented by a "0" or "1" condition which is readily recognized. 
 The disadvantage of a digital system however is that one would need 
 as much circuitry as one wants accuracy in digits. For instance, 
 one can store an analog number on a capacitor, and if the detection 
 circuit is accurate, one can resolve this level to a certain accuracy, 
 To store this voltage by digital means to the same accuracy would 
 obviously require more than a capacitor and a detection circuit. 
 Again these difficulties can be overcome by more elaboration in the 
 involved circuitry o 
 
 Another problem that was noted in the design of the Artrix 
 system was that of drift caused by aging, temperature variation, etc. 
 Great care should be taken to have all analog signals as stable as 
 possible.. In most cases drift tends to be a cumulative rather than a 
 canceling effect, and when an accuracy of one point in five hundred 
 has to be maintained, this can become significant. Again, the high 
 resolution is somewhat limited by the drift that might occur due to 
 temperature variations and elaborate precautions should be taken for 
 higher resolution systems. 
 
 Despite these minor difficulties hybrid processing offers 
 many advantages and shortcuts over present all-digital or all-analog 
 
1+6 
 systems. It is felt that hybrid systems are very worthwhile and 
 should be used wherever high speed, simplicity, and limited accuracy 
 are called for . 
 
^7 
 
 BIBLIOGRAPHY 
 
 "Quarterly Technical Progress Report", (Hardware Systems Research), 
 Department of Computer Science, University of Illinois, Urbana, 
 Illinois. July-September, 19^5 » 
 
 "Quarterly Technical Progress Report", (Hardware Systems Research), 
 Department of Computer Science, University of Illinois, Urbana, 
 Illinois. October -December, 1965* 
 
 "Quarterly Technical Progress Report", (Hardware Systems Research), 
 Department of Computer Science, University of Illinois, Urbana, 
 Illinois. January-March, 1966. 
 
 "Quarterly Technical Progress Report", (Hardware Systems Research), 
 Department of Computer Science, University of Illinois, Urbana, 
 Illinois. April-June, 1966. 
 
 Pulse ? Digital, and Switching Waveforms , Millman, Jacob, and Taub, 
 Herbert. McGraw-Hill Book Company, 1965. 
 
 Selected Semiconductor Circuits Handbook , Schwartz, Seymour, Editor. 
 John Wiley and Sons, Inc. i960. 
 
APR 5 1967