Reference / Paper · 1958
Generating Characters (Electronics, 3 January 1958)
The MIT Lincoln Laboratory article on drawing characters on a CRT from sine and cosine waveforms, the method behind the Wyle Scientific's display.
Reference / Paper · 1958
The MIT Lincoln Laboratory article on drawing characters on a CRT from sine and cosine waveforms, the method behind the Wyle Scientific's display.
Generating Characters ~ UMMARY - - Analog device displays alphabetic or nume1'ic characters on face of cathode-ray tube by deflecting spot to trace out each desired character smoothly and continuously. Necessary X and Y deflection voltages for scope are obtained by Fourier synthesis technique that involves combining sine and cosine terms of first five harmonics of 30-kc fundamental frequency. Each character is traced in about 30 microseconds. Transistorized gated oscillators, flip-flop serial counter s an d emitter-followers feed ten toroidal transformers having one set of secondary windings for each character desired By KENNETH E. PERRY and EVERETT J. AHO Lincoln Laboratory, Massach uRetts In8tl tute J(LTHOUGH MANY PLANS have ,&'1 been devised in the past for scribing numeric and alphabetic cnaracters qn a scope face by spot deflection, a new analog circuit recently developed for this purpose has some advantages in both simplkity and versatility. The Arabic octal numerals zero through seven each may be represented as a segment of a continuous closed curve given in cartesian coordinates by the equation y f (x). In general, y is a multivalued function of x, but the curve can be represented by two parametric equations : y f, ( t), x f, (t) where t. < t < t, and where f, and / . are single-valued functions of t. If t is the t ime, then these functions define the continuous motion of a point along the curve. They must be single-valued funetion s, since the spot cannot be in two different pos itions at the same time. If the tangential speed of the point is known at all times (specifically, if it is constant), then the parametric ·equations a re defined by y f(x). Thus, if /1 (t) and f,(t) represent the voltage waveforms that a re applied to the y and x deflection amplifiers, the desired curve will be t raced on the scope face. Since most of t he symbols are not closed curves, an unblanking function must be pro- or Techno logy, Lexington , Massachusetts 3 6 8 -- ,2 I , I I 12 II = 72 = 1.2 1.0 I 2 13 •• +O 8 •t.2 +0. 15 • 0 .2 ·o +0. 2$ 0 .8 + o.e +I +I + I + I 0.6 0.4 •• _, _, 0.2 0 • -' 2 " e 4 ,. 6 - 0 .03 - 0 .2 -0.6 7 8 .. .. 10 •0.7 +0.3 0 -I - 0 .6$ + 0 .2 -0.2~ 13 +0. 1 19 (A) + 0~) +0.29 +0.29 +0.2 +087 16 +0,99 - 0.4 17 +0.7 9 - 0 . 73 +0.43 -0.9) ,. .. · - 0 20 - 0 . 46 - 0.95 -0.7 21 - I = = COORDINATES ' 0 + 0 .11 22 -1.3 23 -0.6 {BJ 8 1.2 - 0.3 - o. i 1- (Cl FIG. I- Waveforms a l riqht. obtained by measurinq coordinates of numeral five as c left. wlll qenerate this numeral when applied to X and Y inputs of oscillocsope vided to segment. intensify the desired Equations for Nu m erals A funct ion of the type just desc.ribed can be expanded into a Fourier series of sine and cosine terms: f,(t) A . + A1 sin wt + B, cos wt + A , sin 2 rut + .... where w = 2 rr (t1 - t.) and t 0 = 0. T he expr ession (t, - t 0 ) is the time required for the spot to trace the entire closed curve. The procedure for finding the coefficients A~, B. is as follows : The desired character is d rawn on graph paper as in Fig. lA, including a retrace segment which closes = the curve. To ensure t hat all cha acters can use the same unblanki1 function, closed figures like ze and eight have redundant retn1 segments tacked on as an append Twenty-four points are laid along the curve at roughly eq1 intervals the actual number bei arbitrary. These points divide t time ( t, - t.) into 24 equal int vals. The x and y coordinates each point a re tabulated as in F lB, with t. taken as the center the reb·ace segment. These ta· lated values represent the t functions f, (t) and /,(t), as pl ted in Fig. l C. These functi1 may be analyzed by any one several graph ical and numer January 3, 1958- ELECTRONICS engineering . edil for C athode-Ray Readout integration methods. The method now used' is a purely graphical one where each x or y value is laid off as a vector at a n angle equal to (nwt). When these vectors are added head to tail, the projections of the resultant vector g ive the coefficients A., B... When the coefficients have been determined it is possible to synthesize desired waveforms by elect r ically adding sine and cosine waves of correct frequency and amplitude. Synthesizing System The circuit for synthesizing the desired voltage waveforms from a rtificially generated sine and cosine waveforms uses five harmonics with a fundamental frequency of 30 kc. Ten tuned circuits (five sine and five cosine) a re simultaneously sh ock-excited in to oscillation by a gate 33 m icroseconds wide to give one cycle of 30 k c, two cycles of 60 kc, three of 90 kc, four of 120 kc and five of 1 50 kc. These ten signals a re fed through emitter-follower b uffers to the primaries of ten toroidal transformers. Secondaries are wound on these toroids, with direction of winding and numbe1· of turns determined by t he s ign and magnitude of the Fourier coefficients. When t hese secondaries are connected in series and one end of ~he series circuit is grounded, the iesired volta ge waveform appears !lt the other end. Figure 2 is a complete block dia?'ram of the prototype system. The :ircuit as depicted here will display :he numerals 0 through 7, four ·ows deep (32 characters). This :an be displayed on any oscilloscope iaving an external unblanking con\ection. A 120-kc sine wave is fed into a :lock generator which shapes the .ignal into a square wave. The >rime s ide of t he clock generator •utput is commutatively coupled to lip-flop F,, t hP. first of a chain of ight serial counters'. The logic :vels used are +5 volts and -5 olts. The unblanking function is Harmo nic qenerator. with ten chara cter-lonninq toroidal translonne rs In vertical row al left. Transistorized shock·excited oscilla to rs are a t riqhl. buffer.emitters at center. a nd control a nd cyclinq circuitry is on pluq·in cards slid in9 into qrooves of lower compartment FIG. 2- J!lock diagram of Fo urier.sy nthesis cha racter qe nerator LECTRONICS engineering edition - January 3, 1958 73 FREQ FlJNCllON 30KC cos 85 SIN SIN As 60KC cos 84 90KC cos 3 SIN S.3MH 2..65MH l.7 7MH TO X OEFL SECON OARY TURNS FOR ·=---'"-"",......OF SCOPE CHARACTERS 0,1,2,3,4,5, 6AND7 c, 5.IC>01'1LF +200~p.f 2.400>',.F tZ40,.,.F 1,600;a~F .+160'°'"' 120KC cos l.33MH eot<C SIN l.06MH 1pco,.,.f COS .. 56,-~F A4 B SIN ... 1.,300,..,.._F ALL FIVE PAIRS Of RIN GING CIRCUITS ARE I DENTICAL EXCEPT A3 FOR VALUES OF L1 ANO C1 C2 the operation is not duty-cycle sensitive. In other words, at the instant of turn-off the voltage on the capacitor and the current throu gh the inductor are very near to the quiescent values. This would be exactly true except fo r the losses during ringing. It is only n ecessary to leave the circuit off long enough for this small amount of lost energy to be replaced. The values of L and C in Fig. 3 are deter mi ned by setting vL/ C R where R is the crit ical damping resistor, arbitrarily chosen as 1 k, L and C are unknown. Solving first for L in terms of C and substituting this result m the equation v LC 2"1Tf, then solving for C, L can then be found from either equation. Trimmer C, has a range of from 100 µµf to 500 µµ,f and is adequate for adjusting the ringing circuit for any L and C inaccuracies. Each ringing circuit is followed by an emitter-follower buffer amplifier which also drives the base of a power transistor in an emitter-follower amplifier configura- = ONE SET OF SECONDARIES, ONE Z·TRANSISTOR ~A~~~:,s:6'H ,_•~·-- ~·~•._o_,_,__~''-' -' ONE PAIR Of SOOPEi--~ '."~ ' --<t--'-<'"'----1 INPUT DIODES :;:~, :;:; (AS ABOVE) NEEDED 0 1 • 4 b .,,1 1 FOR EACH CHAR- • • ,...3 b.-1 ACTER -+"'-'-'-"'~ 1-•_,,_-',-"(:",'-. . BA -6.SV -30V MINUS SIGNS INDICATE REVERSEO CONNECTION S TO WINDING ZERO MEANS NO WINDING NEEDED IOK -6.5V - 30V FIG. 3-Circuit of harmonic g e ne rator for p roducing o ne character. Each addiUonal character requires a dditional selector switch and additional set of toroidal transformer secondaries feeding scope input terminals as at top of diagram gener ated in the intensity flip-flop, controlled by F,. F ,, F a and the clock generator. The intensity pulse starts one-h alf clock cycle or about 4 microseconds afte1· the prime side of flip-flop F, gbes up and ends 4 microseconds before the same point goes down. This unblanks that segment of t he Lissajous pattern which forms the desired character. One-fourth of this continuous closed curve is blanked. Harmonic Generator Flip-flop Fa, which shock-excites the r ingin g circuits in the harmonic generator of Fig. 3, is operating at exactly one-h alf the rate of the fundamental frequency used in t he synthesis. The ringin g period of the shock-excited oscillators occurs during the time the prime side of flip-flop F. is high. Since the fundamental frequency of 30 kc is twice the frequency of flip-flop F •• one complete cycle goes into the slot before the r inging is ended by a change of state in F •. In like manner, t here are two cycles of the second harmonic, 74 three of the third, etc., all initiated and terminated at the same time. The sine waves and the cosine waves are generated in parallelresonant and series-resonant cfrcuits r espectively. Input A in Fig. 3, which is connected to five sinewave ringing cir cuits, is controlled by counter output C.'. When C,' goea up, the five inpu t transistors connected to point A are cut off and the parallel resonant circuits composed of L ., C, and c. in Fig. 3 ring at their respective frequencies (30, 60, 90, 120 and 150 kc). The output is a positive sine wave. Damping of oscillations is s mall because of t he high-Q powdered iron cor es used for L,. Input B, which is connected to five cosinewave series ringing circuits, is controlled by flip-flop counter output C,. T hese circuits oscillate at their resonant frequencies when the input t ransistor is on (point B low) . Output is a negative cosine wave. Since the r inging circuits are cut off at a point in the cycle exactly corresponding to the turn-on point, there is no damping transient and = x ALL POTENTIOMETERS 250 OHMS FIG. 4-Simulator circuit in which potentiometers d uplicate changing of turna or. toroidal transformer secondaries, for try ing out effects of various combinations o· coefficients before putting windings or transformers permanently January 3, 1958 - ELECTRONICS engineering editio tion. The output of the power transistor is coupled through a 1-/.lf capacitor to t he primary of a toroidal transformer. Referring to Figs. 2 and 3, X. and X.', X, and X,', etc, or Y , and Yo' or Y, an d Y,', etc, on the harmonic generator block are the terminals to t he series secondary windings on the toroidal t ransformers. Every time fti p-ftop F . cycles, these circuits have f, (t) and f, (t) waveforms on them. These secondary waveforms will not, however, be passed through the OR diodes to the scope unless the X and Y inputs are high. The d-c levels of the unprimed ends of the seconda ry windings (X and Y in Fig. 2) are controlled b y the state of their associated switches. When a switch output is h igh, the corresponding OR diode (Fig. 2 ) is for ward-biased and the signal on that particular secondary is transferred to the scope. Transistorized Switch Circuit The switches are rmP transistors in t h e g r ounded-emitter configuration shown in Fig. 3. The collector controls the d-c level of the associated secondary wind ing in the h armonic generator. T he base inputs have two states. When the base is high the collector is at - 6.5 v a nd its associated secondary winding sees an open diode in the OR circuit preceding the scope (Fig. 2). When the base is low, the collector will be at ground or some small negat ive voltage, determined by the fixed resistor at t h e emitter. The purpose of t h is resistor is to adjust t h e level of the synthesized waveform f,(t) and f,(t) . In the original g raphical a nalysis for f,(t) and f,(t), no attempt was made to compute the d-c Fourier coefficient A, since the zero frequency cann ot be accommodated in the t ransformers. Therefore, some of the numerals would be displaced from their proper relative positions on the scope face. It is this discrepancy in the d-<: level t hat is adjusted by the res istors. The diode matr ix selects the number to be displayed under control of ftip-flops F ,, F . and F,. A different number will be displayed during each unblanking pulse. Only Waveforms involved in qeneralion nf eiqht Arabic numerals by synthesis one output is low at any time. This voltage turns on a pair of switching t ransistors in t he selectionswitch package. The four resistors on the X input of the scope ( Fig. 2) are used to generate an eight-step ladder of voltages at the same rate as the unblanking function, thus displacing each n umeral consecutively. T he t hree resistors on the Y input, in conjunction with the slowerrunning flip-flops F, a nd F ., displace the whole row of eight numbers vertically four times. Toroid Construction The ten toroidal transformers in the harmonic generator each consist of a General. Ceramics F-108 fer rite core with 100 turns machine-wound evenly around the entire toroid, then covered with i nsulating tape. With th e ten cores mounted at right angles to the panel, the secondaries can be p laced on by hand as t hey a1·e needed. A set of series secondaries consists of ELECTRONICS engineering edition - January 3, 1958 a single leng th of No. 24 Formvar wire wound through and around the ten toroids. Ample space is available to accommodate additional windings on the toroids for generating other characters. A simulation device was built to try the effect of various combinat ions of coefficients in generating various cha racters. The circuit is shown in Fig. 4. The toroid primaries are substituted for the tor oids in the harmonic generator, and the 250-ohm p otentiometers are adjusted to the proper coefficient values. The resulting character can then be observed. The research work on this project was supported join tly by the Army, Navy and Air Force under contract wit h Massachusetts Instit ute of Technology. REFERENCES (1) T . C. Blow, G r aph ical Fourier Analy•is, E LECTHON ICS, IJ 194, Dec. 1917. ( 2) R. H. Raker, Boosti ng T ransistor Switching Speed, EL&(."l"RON!CS, p 190, March I, 1%7. 75