Choudhury, A K

Nag, B R

English

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a n a l o g u e  m u l t i p l i e r  a n d  f u n c t i o n  g e n e r a t o rW ITH CATHODE R A Y TUBEA. K. OHOUDHUUY am d  B. U. NAGI nstitittji: or R ajjioi'Jiysics & JClbcthonics, CJmvETisiTY or Calcutta (Rcceit^eil for pubhadton, H(^j)teinbn 18, 11)57)A B S T R A C T . A inultiplior and a liinGlion ^^ oiioralor umng a oalhodc ray tube with u (’npricil ativn pick Ufi device are desculnd. M’ho devdee Hiinplifloh iJio confstnicl ion of the iuultij)lior and function generator without impairing the sjaMjci of leaponHo oi the accuracy of the iiiatrmnont.r N  T n  O D U  C T I  O NFiiiictiou generators and nmltiplicrs using cathode ray tubes have been described by many autliors (MacNco, 11)41), Mackay, 1947; Deely and Mackay, 1949; Simstein, 1949). Use of the electron beam of the C R. tube as the tlynamic eleinent in these functiou generators and multipliers results m high speed and makes them specially suited for apjilieations in high speed analogue computers. However, in all such function generators and multipliers, the voltage giving the lunction or the product is obtained with the help of photocells placed in front ol the C. It. tube, instead of the photocells as the pick up device, MacNcc sug­gested the use of metallic pick up plates mounted inside the C. Tt tube. Evidently, tins IS only suited foi the multiplier i f  it is to bo used fur the function generat-or a separate 0. it. tube is reipiired for each new function. Tn this paiier a multi­plier and function generator with a new pick up device is desciibetl.Thc device is simple and can be easily replai'ed so that the same 0 . 1 1 . tube can be used for till* multiplier oi' for generating different typos of functions.■ 9r  R I N  C I P  L  E  O F  T H E  M U L T I P L I E RThe electron beam in a cathode ray tube, when subjected to an electric field m the -direction and a magnetic field Hg in the Z-direction, is deflected in the y-direction and the deflection is given by ?/, wherey ^  iCiEa,xH,Since, velocity of the spot m the F-direction is proportional to14ie deflection in the Y-direiition is proportional to the product of the electric, and magnetic field intensities. One of the voltage to be multiplied (Fj) is applied to the X-plates (figure 1). Thus E^ . is made proportional to Fj. The other voltage Fg is applied to an amplifier which sends a current proportional to Fg through a1415142 A . K . Chovdhury and B. B. Nagcoil mounted coaxially on the neck of the tube between X  and Y  plates. The resulting F-defloction is proportional to the product of Fj and Fa.On the face of the cathode ray tube is mounted a pick up device. J t  gives an output voltage which varies as the spot is deflected from the zero-F Hue, I f  the output voltage of the pick up device is proportional to the spot deflection, it is also proportional to the product of F  ^ and F.^  Usuallj'^ this is not so, and to obtain a voltage proportional to the product, the outimt of the pick up device i.s amplified and applied to the F-plates, in such a phase that it tries to bring the spot back to its initial position, whenever it is deflected due to the appheations of Fi and Fg. Let the pick up device give an output voltage v per unit F  deflec­tion and bo the F-plate deflection sensitivity of the tube. Then, evidently the volt ago. appearing at the output of the amplifier, when voltages F^ and F, are applied, is where^0 vA(1 )LvAA  is the gain of the amplifier and is a constant related to K^, the JC-plato sensiti­vity and the constant relating Fg with V .^ I f  the gain of the amplifier is made solarge, th a t ^ v A  small compared to 1 . Vgut is proportional to the productof Fj and Fg.Analogue M ultiplier and Function Gentrqior, etc. 143P I C K  U P  ] D E V I C EThe pick up device consists of metallh; plates mounted on the face of the cathode ray tube as shown in the figure 2. One of the plates is directly grounded and the other is connected to ground through a high impedance element. The electron beam of the C. B. tube is intensity modulated. As a result the charge appearing before the plates varies with time and thereby induces charges on theTOJMPUnEPFig. 2 . Shape of tho  pickup p la tes for th e  m ultip lier.plates which also vary with time. The varying charge on tho metallic plate con­nected to ground through high impedance causes a voltage to be developed across the impedance. Evidently the magnitude of this voltage depends on tho position of the cathode ray spot relative to this pick up plate and decreases as the spot recedes from its edge. The presence of the grounded plate onhan(;es this rate of variation.C I R C U I T R Y  O F  T H E  M U L T I P L I E RThe amplifier circuit following the pick up device is shown in figure 3. The high impedance element connected to tho pick up plate consists of a heavily damped paiallel tuned circuit. I t  is tuned to the frequency a t which the electron beam is intensity modulated, which is 400 kc/s. The oscillator supplying the intensity modulation voltage is crystal controlled. Tho voltage developed across the pick up device is amplified by R -0 coupled amplifiers in two stages, and then rectified l)y a thermionic diode. The rectified voltage is applied to the input of a d.c. amplifier. The output of the d.c. amplifier is adjusted to be zero when the spot is on the zero-T line by the zero adjustor. Also the phase of the output voltage is so adjusted th a t as the spot tries to leave the zero- Y  fine, the amplifier output voltage, when applied to the F-plato, brings it back. Tho gain of tho amplifier such th at v8yA is equal to 1000. Thus error introduced from this source is loss than 1 in 1000.144 A . K . Choudhury and B. E. NagFig . : C ircuit arrangem ent o f th e  am plifier.Tho cirimii arraiifremeiit oftlie amplifiev supplying the current to the magnetic deflection coil is shown m figure 4. The frequency response of this amplifier is flat up to 3 Kc/s. The magnetic dellection (’oil (‘onsists of 5000 turns of 4(5 gauge copper wire and has a rosistanec of 1 K  n . The C-R tube used inr the multiplier is of the type 5BP1.M U L T I P L I E R  C H A R A C T E R I S T I C SThe measured d.c. eharacteristies of the multiplier is shown in flgure 5. ft shows an accuracy of 2% of full output. The frequency response of the nmlti- phor is flat up to 5 Kc/s for voltages applied to tho X-jilates and up to 3Kc/s lor voltages applied to tho magnetic-deflection coil.Analogue M ultiplier and Function Generator, etc. 145The accuracy of the multiplier is limited by limitatious of mechanical align- nieiits. The edges of the pick up plates are not iierfccily parallel to the zero-F dellcction lino and also the axis of the magnetic deflection coil caiiuol be accurately aligned Mdth the tube axis. W ith bettor mechanical aTTangomoiits the aiu-uracy flgurc can be further improved. In  this connection, it may be noted th at as theS[)ot is deflected from its centre position it gets defociisscd. This defocussing is liirUier iiicreasi;d when the magnetic field is applied. However, defocussing only reduces the output of the pick-up plate and thereby affects the overall gain. The reduction in the gain does not affo(;t the accuracy much since oven the reduced gam is well over 700 and this may contribute an erior of only 1 in 700.The Ireipicncy response of the multiplier for voltages applied at the F-x)lato may be further imxiroved by using a higher frcqueiKiy for beam intensity modula­tion and increasing the bandwidth of the xiarallel-tuned circuit. The freipiency res]iunsc for voltage applied a t the magnetic deflection coil also may be imjiroved by mcieasing the bandwidth of the magnetic deflection amplifier. This reipiires the use of a magnetic-di^flection coil with smaller number of turns and therefore involves greater power consumption. Since, howT.ver, the differential analyser of wduch the multiplier forms a part has a fixed value of OR equal to 1/4, further, improvement of the frequency response was thought unnecessary. fSuhitum of an equation with the multiplierThe performance of the multiplier in its actual use in the comiiuter is illustrated by solutions of Mathiou equation obtained by the differential analyser using the multipher.Mathieu equation in its general form is written as146 A. K . Choudhury and B . R. Nag(l?y^2 [a — 2q cos 2z)y =  0 (2)The set-u]j ol the computer lor solving the equation is shown in figure 6. Cos is generated in a different jiart of the analyser. The computer set-up solves the equationwhere- ^ +  -  «ii cos Mi% =  0=  IK G Rf.^  f  -I (a —  2q cos 2z)y = 0. <lz-‘On substituting 2z for tiiji Eqn. (^) reduces to dhjHence, [ 4oio2 261„2 1+  - ”, a ^ - 2 .  I  a2C08 22 h y  =  0 .dz^ L (i)i“ coj“ J4fOo^  1 2cOft2a — — y a,, and q — — a,. ^  ^ coi  ^ -(3)In  figure 7 is given the solution of the equation as obtained by the analyser for a =  3, O' =  2 and 3/ =  0.F U N C T I O N  a F N E H A T O HLet the function to bo generated be given by /(F i). The pick up plate mounted on the face of the O.H. tube is replaced by two other plates with their edges shaped to the form given b y /(F i). The form of the pick up plates fo r/(F i) — V-^ is shownAnalogue M ultiplier and Function Generator etc. 147% 0  ^  #HB’ig. 7 ! Computer solution of Mathiou equation for « -= 3, gr =  2, 0.. yXF ig , 8 : Shape o f the p ick u]j plaboH for gonem iing F ,- .Fig, 9 : Plot of Fx  ^ generated by tho function generator against V^ t148 A, K . Choudhury and B, B. Nagin figure 8. Now for generating Fj®, Fg is made zero and Fj applied to the X — plates. A h F i ih aj)j)licd, the spot moves along the AT-axis, hut the feed hacik device keeps it m between tln^ edges of the two plates. As in the ease of the multiplie]' if the gain of the amplifier is large, the spot moves along the centre line between the edges, aiifl since the plate edges are shaped to F^ ,^ the voltage ajjpearing at the output- of the amplifier is proxiortional to F,^.Fj^ plotted against as generated by the function generator is shown in figure t). The freipiency response of the function generator is flat up to 5 Kc/s, whiclij however, can be improved further as indicated before by ni(;reasing the beam intensity modulation frequency.C O N C L U S I O N  ,The new pic;k up device described in this paper can be used successmlly for coiiHtructing a multiplier or a function generator employing a C. E-. tube. The use of this device does not affect the s]ieed of response. The aijcuraey is Wainly limited by me(3hanical mis-ahgnments.A C  K N O W  L E D  C M  E N T SThe authors are deeply indebted to Frof. iS. K. Mitia for his constant help and guida-nce in ihe work. Thanks are also due to Prof. J. N. Bhar, Heail of the De|iartment of Radio Physics and Flectroincs, (Calcutta tlniversity, for his land interest in the work.R E Ji’ E R E N C E SJlcoly, E. M. and Mbickdy, D. M., 104?), Nature, 163, 6J)0. MacNoo, A. H., 1040, /Voc. l.inC ,, 37, 131.Mackoy, D. M., 1047, Nature, 159, 40G.SuiiPt-niii. D. E., 1940, Blcctronics, 22, 100.

Analogue Multiplier and Function Generator with Cathode Ray Tube

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Analogue Multiplier and Function Generator with Cathode Ray Tube

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