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A polarcardiograph computer 1954

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A POLARCARDIOGRAPH COMPUTER by WILLIAM KEITH RAE PARK A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE i n the Department of E l e c t r i c a l Engineering We accept t h i s thesis as conforming to the standard required for candidates f o r the degree of MASTER OF APPLIED SCIENCE Members of the Department of E l e c t r i c a l Engineering THE UNIVERSITY OF BRITISH COLUMBIA November 1954 1 ABSTRACT Vectorcardiograms have proved useful i n the diagnosis of heart disorders. However, such information as the v a r i a t i o n of the magnitude and angle of the vector with time i s not d i r e c t l y obtainable from a vectorcardiogram. An electronic device which would present the magnitude and angle of the vector as continuous functions of time, or "polarcardiograph" as i t i s named, would be useful i n electrocardiographic research. It i s shown that such a device, which must compute the polar co-ordinates of points from their respective Cartesian co- ordinates, can be constructed i f analogue m u l t i p l i e r s , subtract-, ors and adders are available as well as a two-phase sinusoidal voltage source and a device for generating a voltage proportional to the phase difference of two sinusoidal s i g n a l s . A search of the l i t e r a t u r e revealed that a similar de- vice had already been constructed, the major difference between i t and the present machine being the manner in which m u l t i p l i c a - tion i s achieved. The p r i n c i p a l d i f f i c u l t y involved i n the design of the computer was the development of a simple and accurate m u l t i p l i e r using a pentagrid tube. A mathematical analysis of the dependence of the plate current on the two control-grid voltages was made to determine the operating conditions under which such a tube has an output voltage proportional to the product of the two input v o l t - ages. The polarcardiograph was b u i l t using the pentagrid-tube mu l t i p l i e r s , and when tested proved to have an overall accuracy- well within that required f o r normal electrocardiographic pur- poses. i i TABLE OF CONTENTS PAGE I Introduction 1 II P r i n c i p l e of the Polarcardiograph 8 III The M u l t i p l i e r ' 11 IV The Complete Computer C i r c u i t t 22 V The O s c i l l a t o r 29 VI Magnitude and Phase Outputs 30 VII Input C i r c u i t s 34 VIII The Complete Instrument v 36 IX Accuracy Tests 40 X Conclusion 42 XI References 43 • • « 111 ILLUSTRATIONS FIGURE PAGE 1, Schematic Electrocardiograph Arrangements 5 2» Schematic Computer 10 3o Pentagrid Tube C i r c u i t 10 4. Transconductance Bridge 20 5» Subtraction C i r c u i t 20 6. 6SA7 Characteristics 21 7o Two possible Computer Arrangements 24 8. Resistive Addition 24 9 0 Computer C i r c u i t 26 10o Schematic Phasemeter 31 l l o Cathode-Coupled Clipper C i r c u i t 31 12o Computer Outputs 44 13o Complete C i r c u i t Diagram 45 • i v ACKNOWLEDGMENT The author expresses his indebtedness to members of the Department of E l e c t r i c a l Engineering at the University of B r i t i s h Columbia, especially to Dr. A-D. Moore f o r his guidance through- out the research project and to Dr. F„ Noakes for arranging f o r assistance whenever i t was needed. The polarcardiograph was developed with the assistance of Dr. G.E. Dower£, following his suggestion that such a device might be useful i n electrocardiographic research. The major portion of the project was supported by the Medical Board Fund of the Vancouver General Hospital. The author's post-graduate studies were made possible through the B r i t i s h Columbia E l e c t r i c Railway Company Limited Graduate Scholarship, which he was awarded i n 1953. A POLARCARDIOGRAPH COMPUTER I INTRODUCTION The device to be described i s an electronic analogue computer which converts the Cartesian coordinates (x,y) repre-. sented by the input voltages to the equivalent polar coordinates (r,6) represented by the output voltages. Since the (device i s spec i a l l y designed for eledtrocardiographic work, a short,descrip- tion of electrocardiography i s i n order. Probably l i t t l e can be said about the e l e c t r i c a l v o l t - ages which can. be measured on the surface of and inside a human body (or animal body for that matter) during a heartbeat without r a i s i n g some' controversy. Certainly one can state that these voltages and the i r associated current f i e l d s are generated i n the heart, i f only because t h e i r magnitudes r i s e as measurements are made closer to that organ. Since the only known form of current i n l i v i n g tissue i s ionic movement, i t can also be stated that the voltages which produce an electrocardiogram are due to ionic cur- rents originating i n the heart muscle c e l l s . Potential measurements made on l i v i n g c e l l s indicate that i n the resting state the i n t e r i o r of a c e l l i s negative with respect to i t s external environment, and that the potential d i f - ference across the c e l l membrane i s about 80 m i l l i v o l t s . This 2 figure i s of the same order of magnitude for nearly a l l l i v i n g c e l l s . When the c e l l becomes activated the potential across the c e l l membrane reverses, with the i n t e r i o r of the c e l l becoming about 40 m i l l i v o l t s positive with respect to the external environ ment. A study of the ion concentrations inside and outside of a resting c e l l y i e l d s the following information: Ion Concentration Outside Ion Concentration Inside K + „oo 2.5 mEq K + „oo 120 mEq Na + ... 120 " Na + ... 20 " C l ~ ... 120 " CI" o o . 10 " and organic anions 130 m i l l i e q u i v a l e n t s / l i t r e . ' It has been found that potassium and chloride ions are free to cross the c e l l membrane of the resting c e l l whereas sodium and the organic anions are not. Due to th e i r concentration d i f - ference, potassium ions w i l l leave, making the c e l l i n t e r i o r negative. When the negative potential of the i n t e r i o r of the' c e l l i s s u f f i c i e n t to hold the potassium ions against the pres- sure created by t h e i r concentration difference, equilibrium re- sults . The calculated value of this equilibrium potential for the known concentration differences agrees f a i r l y well with the experimental value of -80 m i l l i v o l t s . Activation of the c e l l i s thought to involve a change i n permeability of the c e l l membrane which allows sodium ions to cross i t at about two hundred times the speed with which potas- sium 'ions may cross i t . Sodium ions then rush i n , causing the i n t e r i o r of the c e l l to become pos i t i v e . This positive condition i s maintained for a short period during which the membrane permea b i l i t y to both ions i s r e l a t i v e l y low^ then the permeability to potassium ions r i s e s and potassium ions leave the c e l l thus re- t i establishing the negative potential difference across the c e l l mem- brane. In muscle c e l l s the changes i n the c e l l potential seem to be d i r e c t l y related to changes i n the tendency of the contractile elements (actomyesin) to contract. In order that the c e l l may be returned to the exact state that i t was i n before activation, the sodium ions that entered during the activation period must be re- moved. The removal of these sodium ions against the concentration pressure difference i s accomplished by some metabolic process known as a "sodium pump11.^ The sodium pump thus provides the energy of activation, although not necessarily the energy of con- tr a c t i o n . The ions flowing into and out of a c e l l constitute an e l e c t r i c current. This current, i f allowed to flow through the remainder of the body, would produce voltage drops across i t s various parts. Although the genesis of these electrocardiographic voltages i s controversial, i t i s agreed that they must ultimately arise from these ionic currents i n the heart muscle c e l l s . The normal electrocardiogram, as shown i n Figure 1, consists of a slow small-amplitude P wave, a more rapid QRS com- plex, and a slow T wave. The P wave arises from auricular a c t i - v i t y and the QRS from ventricular a c t i v i t y . The T wave i s as- sociated with the recovery process of the v e n t r i c l e s . An electro- cardiogram, such as the one i l l u s t r a t e d , i s obtained by amplifying the voltage obtained between two electrodes attached to the patient and recording the voltage variation as a function' of time. Elec- trode connections are normally made to each arm and to one leg (usually the l e f t leg) as well as to the front of the l e f t chest and occasionally to the back of the right chesto Electrocardiograms obtained from these leads are used to diagnose disorders of the heart. The most accurate information present i n an electrocardiogram i s the rate and rhythm of the heartbeat. Any other information obtained must come from com- parison of the wave shape under consideration with the shape of waveforms whose corresponding heart disorder has already been correlated with c l i n i c a l and post-mortem studies. Such co r r e l a - tion has been carried out over a period of more than t h i r t y years and the results are useful i n determining such information about the heart as the o r i g i n of the i n i t i a t i n g pulse or "pacemaker", the speed and di r e c t i o n of propagation of the activation poten- t i a l s to the ventricles and the state of the ventricular muscle. Disorders of the ventricular muscle diagnosed by such means i n - clude enlargements of either of the v e n t r i c l e s , death or injury of portions of the muscle and abnormalities of the muscle physio- logy such as deficient oxygen supply, which might result from impairment of the c i r c u l a t i o n to the heart muscle, or electrolyte 2 disturbances, which might be produced by kidney disease. Since improved correlation can be obtained by placing more leads on the patient, the best results might be expected from the greatest number of leads. A vectorcardiogram, which may be thought of as being equivalent to an i n f i n i t e number-of electrocardiograms, does i n f a c t y i e l d information not present i n an electrocardiogram. A vectorcardiogram i s generated by suitably choosing two patient leads and considering one lead voltage to be the Figure I Schematic E/ecfpGCctrdicorapf) Arrangements 6 horizontal and the other the v e r t i c a l component of a vector drawn from the o r i g i n i n Cartesian coordinates, as shown i n Figure 1. 3 The locus of the t i p of t h i s vector i s c a l l e d a vectorcardiogram„ The logic for such a procedure i s supported by the heart-vector theory, which considers the p o s s i b i l i t y of replacing the heart's e l e c t r i c a l a c t i v i t y by a current dipole of variable strength and orientation,. The dipole, of course, may be replaced by. a vector. The conduction of the current of t h i s dipole throughout the re- mainder of the body i s then considered to give r i s e to the voltage drops which produce an electrocardiogram. A vectorcardiogram i s obtained at the present time by driving the horizontal and v e r t i c a l deflection plates of a cathode ray tube with the horizontal and v e r t i c a l components of the vector respectively. The resulting vector locus displayed on the face of the tube i s photographed during one heartbeat. One disadvantage of the vectorcardiogram obtained i n t h i way immediately becomes obvious when i t i s considered that there i s no time separation of the events of the tracing. Much over- lapping occurs, especially near the o r i g i n , so that valuable i n - formation about the recovery phase of the heart cycle, which i s characterized by lower frequency components and lower voltages, i s l o s t . Another disadvantage i s that only one cycle i s obtained, giving no opportunity to study changes that might occur from heart beat to heartbeat. A device whose outputs are the polar coordinates of the vector locus .as functions of time might possibly have the advan- tages of vectorcardiograph without i t s disadvantages. There i s also the p o s s i b i l i t y that the c l i n i c a l and post-mortem c o r r e l a - tions might be improved by displaying the information obtained i n x 7 1 a new way and by displaying new information such as the angular ve l o c i t y of the vector,. Whether or not such a "polarcardiograph" w i l l be of value must be determined by experiment. The develop- ment of the polarcardiograph i s the subject of the*present thesis. Some idea of the need for a device which w i l l give new information about electrocardiography may be obtained by consider- ing that there are about 8000 electrocardiograms taken annually at the Vancouver General Hospital. Of the abnormal tracings ob- tained, about 60$ are interpreted as "nonspecific". It i s hoped that the use of the polarcardiograph w i l l reduce the size, of t h i s nonspecific group. 8' II PRINCIPLE OF THE POLARCARDIOGrRAPH For the purpose of analysis, assume that there exists a heart-vector voltage whose instantaneous magnitude i s H (when measured at the surface of the body) at some instantaneous angle cLo Further, assume that electrodes positioned correctly on the sur- face of the body w i l l carry the horizontal and .vertical component voltages G and V respectively 9 which are given by§ C = H cos d. V = H sinoC „ It i s desired to construct an electronic device which, with C and V as the input voltages, w i l l compute output voltages proportional to 8 H = / c 2 + T 2' and o{ = tan 1 ^ • The problem i s solved by f i r s t generating two sinusoidal signals which are equal and constant i n amplitude but 90° out of phase*. Denote these signals by8 e^ = E sin(U>t+9) e 2 = E sin(cut+e+90°) = E cos(CJt+Q) «, Multiply e^ and eg by C and V respectively and add the products« The resulting sum S i s given byg 9 S = C e l + V e 2 • • = E sin(Cu t+0) o fl cosoL + E cos(u;t+0) » H sin oC = HE sin(CO t+0+od ) . This i s the desired r e s u l t since the magnitude of S i s propor- ti o n a l to the magnitude of H and the phase of S i s d i f f e r e n t from that of e^ by the heart-vector angle cL 0 The form of the computer i s shown i n the block diagram of Figure 2, where for convenience 0 has been chosen as 45°, A search of the l i t e r a t u r e revealed that a similar de- 5 vice had already been constructed by R„ McFee0 The difference i n the two devices l i e s i n the manner i n which mu l t i p l i c a t i o n i s achievedo M u l t i p l i c a t i o n i n McFee's computer i s performed by tubes with a single control-grid i n a transformer-coupled c i r c u i t nor- mally known as a balanced modulator, whereas the present device uses tubes with two control grids and hence does not require i s o - l a t i o n transformerso It i s hoped that the use of this form of m u l t i p l i e r w i l l r e s u l t i n a device which, while being more com- pact and less costly to b u i l d , w i l l at the same time be more ac- curate. > Mulf-zol/er HE COS* V 4GJ IT •£ Qicr//a /of y Ey,nu> + AM C/jcr/i/J?/ /2 lO A —•——> — Schematic Ca/wpuJ-e* Mac^m-hitie 1 Pc nfay wc/ Tube 8uf I rf I „ e. F/jure 3 Pen M7~u6<? Circu/f 11 III THE MULTIPLIER Pentagrid tubes of the type normally used for frequency conversion i n radio receivers have e f f e c t i v e l y two control grids, c a l l e d G^ and Gg i n conventional notation as shown i n Figure 3(a}< If an operating point exists where the transconductance of the f i r s t g r i d i s l i n e a r l y dependent upon the signal applied to the t h i r d g r i d , e,^, as i l l u s t r a t e d i n Figure 3(c), then the use of the tube" as an analogue m u l t i p l i e r i s possible,. The equivalent c i r c u i t of the pentagrid tube with a r e s i s t i v e load R^ i s shown i n Figure 3(b) 0 The output voltage, e , for constant e (=E._0) and f o r constant screen-grid (grids o c$3 C C 3 2 and 4) supply voltage, i n response to a signal voltage e , i s 81 given by8 6o = -gm! e g l R L R L r w h e r e ^ = _ J £ . If gffl^ follows the linear law i l l u s t r a t e d i n Figure 3(c), then g m^ may be expressed by the relations g = s + K(e -E ) *mi s m i 0 . v C3 ccq' = g + Ke *mi 0 g3 • Inserting t h i s expression f o r g , i n the expression for e yields; mi o 12 % =-<eml0 +  K°g3 V L = - gmlo 8 g l hr ~ K e g l eg3 " l • The second term i n the above expression,) - Ke , e R T 9 i s the g l g3 desired product output,, When there i s no signal applied to the th i r d g r i d an output voltage -g e R» remains. This zero m l o g l « signal output voltage must be cancelled by a second signal. If a second similar tube i s operated with the same signal applied to G^, and i f the outputs of the two tubes are then subtracted, only the product term w i l l remain. The signal applied to G„ of o the second tube could obviously be zero f o r satisfactory per- formance, but a more detailed analysis shows that making i t equal and opposite to that applied to G^ of the f i r s t tube gives optimum performance. A mathematical analysis i s required to determine what effect the dependence of g m ^ on e c^ w i l l have on the output and what shape the g m ^ surface must have i f accurate mu l t i p l i c a t i o n i s to be obtained. With a plate resistance r such that r >> R T . P P L and with the screen-grid voltage a constant, the plate current i i s a function of e_„ and e only. That i s . - Cl C3 1 7 ? t Define E , E , as the operating-point g r i d voltages and ex- C C ̂  C-C Q press the functional relationship above i n the form? lb = i b ^ c c i + 6 g l ' E c c 3 + e g 3 ) where e and e are the signal voltages applied to G, and G„ g l go •*• « respectively. Expanding the above expression as a Taylor series 13 expansion of a function of two variables yields8 iv = i v (E «E ) + e - 5 , - " — +e «rr~ b bx c c i ? C C 3 g l ^ e c l S3 d e C 3 + ?e — T T " + e e - + 2 g l ^ e 2 81 S 3 ^ e c i e ^ c 1 2. 2 Q T * o o o o o o o o o aeg3ae2 + ° c 3 a ib a 1 * The quantities <3ec^ a n d- ^ e c 3 a r e transconductances g and g f o r grids G, and G« respectively„ The incremental com-ffll m3 J. o ponent of the plate current i i s the only part that i s of i n t e r e s t . Inserting the d e f i n i t i o n s for transconductance i n the expression for i givess i = e s + e g P g l &m g3 sm3 2 A A + i e ™ g + e e ~ — g g l a e c l *mi g l g3 ^ e c g *mi + i e „ „ A — g m o + i e 3 83 ra3 6 g l £ 2 6mi a ei" , 2 a 2 J . i 2 a 2 6S3 ae e «ni + a e g l e g 3 $jT gmi a 2 o o o o o o o o + 6 e| 3 a e2 gm 3 + C3 The voltage output from the tube i s given by8 e =-i RT = - i RT p L, p i L 14 A second similar tube i s required to cancel the zero signal out- put voltage -s , e , RT obtained when e „ = 0. The signal applied r ml g l L g3 to G, of thi s second tube must be e , i f cancellation of the out-1 g l put from the f i r s t tube i s t.o be achieved. The signal applied to Gq of the second tube i s yet to be determined but i t w i l l be related to that applied to G^ of the f i r s t tube and hence w i l l be denoted by ke . The plate current of t h i s second tube w i l l S3 be i i = e„. gm_ + ke g P2 g l m l g3 m3 + i e g i s * i + k e g i eg3 &r~z fimi . 1.2 2 a „ g 3 O ec3 m 3 If the two output voltages are subtracted the resultant voltage i s expressed ass ».! " % 2 " " " L ( i p i " V ,/, ,2v 2 <)gm3 , . v 2 gml + i ( 1 - k ) 9 g 3 ^ + i ( 1 - k ) e g i e g 3 J v ^ i /- i 2\ 2 c) 2 + i ( l - k ) e g l e g 3 j j - g m l C3 1 3 3 ^ 2 1 + 6 eg3 U " k ) a X *m3 + " - • • * ' e J ' C3 Obviously, the output voltage w i l l be a product of the input voltages only i f the term e , e • (1-k; *r— — g „ exists and i f a l l • g l g3 & cq 1 other terms i n the above expression vanish. The requirement that this term exist means that the transconductance g must be de- °m]_ pendent upon e at the operating p o i n t o If a l l of the remaining 0 3 terms are to vanish.independently of the form of e and e , 81 S3 severe r e s t r i c t i o n s w i l l be placed on the required tube character- i s t i c s at the operating points. - In pa r t i c u l a r , i t i s necessary that g m ^ =0, which i s never true f o r a pentagrid tube. There- fore, some r e s t r i c t i o n s must be placed on the allowable frequency components contained i n e and e . For the purpose of analy- 81 83 sis considers e = E, sin tx> t g l 1 e = E Q s i n et. 83 3 . The difference voltage becomes: e - e 0 1 . 02 R L J E 3 sin 0t 8 m 3 ( l - k ) + E, sin U) t E 0 sin 0t (l-k) ̂ — g 1 3 £ e c 3 smi + i ( l - k 2 ) Eg s i n 2 9t + i ( l - k ) E? sin a)t E 3 sin 6 t v ^ • — g u c i 0 3 1 + i ( l - k 2 ) E± sin60t E 2 s i n 2 et P-g- g m i c 3 + ±(l-k 3) E 3 s i n 3 et J ^ - g m 3 + . . . . . } C 3 16 After s i m p l i f i c a t i o n , the output voltage is? % 1 " %2 = - M ( l - k ) g m 3 . E 3 S l n 9 t + |(l-k)E 1E 3[cos (6Jt+et)-cos(a> t+et)J - g + i ( i - k 2 ) E 2 ^ c o s 2 e t | ^ 5 s d ... \ 2 + i ( l - k ) E 2 E 3 [ l - c o S 2ft*] sin 9t Sm± + -Hl-k^E-jE 2 sinOJt [l-cos 28t] g m i 6C3 + 2 I ( l - k 3 ) E 3 [ 3 sin et-sin 3©t| gj- g ^ e C 3 o o o o o o o o } Assume that 6 l ) » 0 and that a bandpass f i l t e r with band centre at Co can be b u i l t to attenuate voltages at frequencies repre- sented by 0, 6, 2@, 38«, and 2iOs 3£U, and so fo r t h , to neg l i g i b l e values. The voltage output from t h i s f i l t e r i s given by? e = - Rj^ i d - k ) E ^ g f c o s ^ t - e t ) - c o s ^ t + e t ) } ^ — g m l \2 + i ( l - k 2 ) E ^ [_sinu)& —cos 20^"sin&> t| c ~ g m ^ 6C3 q ^ 3 + i E p 3 sin £0 t sin et(l-k) - ~ g ^ e c i 6 C 3 17 + 2 ~ E ^ g d - k 3 ) s i n O J t [ 3 sin et-sin 3et]>y-g~ g m l O O O 0 O O o 6C3 The signal applied to Gg of the second tube i s given as ke . If no signal were applied to this g r i d , k i n the above S3 expression for the output voltage would be zero. This form of operation might be called unbalanced operation as opposed to the balanced or double-ended operation obtained when the signal ap- p l i e d to Gg of the second tube i s equal and opposite to that applied to Gg of the f i r s t tube ( i . e . , k = - l ) . For unbalanced operation, i t i s required that 32 _ £ 3 ^ _ 2L!L ^ e 2 g m l "<5e3 ~den *»! " ° v C 3 C3 C3 where n i s an integer greater than unity. This condition w i l l be s a t i s i f i e d i f the curves of g_ plotted against e f o r con-mi c 3 stant values of e are straight l i n e s . These lines need not be c i p a r a l l e l nor equally spaced with respect to e , but, i f they are c 1 not p a r a l l e l , some additional requirements are placed upon the shape of the g m ^ surface or upon the form of the signal voltages - by terms such as the t h i r d term of the above output voltage ex- 3 5 3 pression, i ^ E g sin CO t sin et(l-k) ^ e 2 " ~ ^ — It i s ea s i l y <• c 1 c3 shown that this term i s one of the general set of terms repre- sented by \'e'n' ' I \'e,M"7, n an even integer, and that i f g varies O c i C 3 ' m l l i n e a r l y with e Cg> i t i s the only type of term which remains i n the f i l t e r e d output voltage which does not necessarily c o n t r i - bute to the product. Vanishing of t h i s type of term would be most easily obtained by requiring that the curves of g m ^ versus . 18 e for constant values of e c^ be p a r a l l e l , although t h i s i s not necessary. A l l that i s required i s that the slope of the gffl^ curves be l i n e a r l y dependent upon e - In practice such an operat-es ing region would be d i f f i c u l t to locate. However, f o r the special case i n which e contains only SI one frequency component of constant amplitude, the set of terms represented by r—g—\ — — I contribute to the product because 3 5 ^ e c l \ O c 3 / E., E., and so f o r t h are just constants. If e i s not of con- -L -L SI stant amplitude the error introduced by these higher order d e r i - vatives w i l l be small i f the gffl^ surface i s reasonably smooth over the operating range, since the product of the value of the derivative and i t s Taylor series expansion c o e f f i c i e n t rapidly ^ 8mi becomes negli g i b l e with respect to <r as more terms are con-o e C 3 sidered. For balanced operation (k = - l ) a l l terms containing 2 4 ( l - k ), ( l - k ) and so f o r t h , vanish. Under this condition, i n order to obtain an output proportional to the product of the two inputs i t i s required only that E^ be constant and that for n an odd integer greater than unity. That i s , f o r balanced operation, the g m ^ curves plotted against e Q need not be straight l i n e s , a simple square law curvature, f o r example, being s a t i s - factory. Certainly balanced operation w i l l give greater accuracy than w i l l unbalanced operation, as might be concluded from com- parison of the m u l t i p l i e r pair with a push-pull audio amplifier. Maximum accuracy w i l l be obtained from.the tubes by operating them balanced i n the most linear portion of t h e i r \ - 19 characteristicSo A bridge for measuring the transconductance of a tube was constructed following the c i r c u i t of Figure 4. At balance (no signal output) the r e l a t i o n —g- = g~ e~ holds, or R m S 1 gm ~ R 0 Plate voltage had l i t t l e e f f e c t on the measured value of the transconductance over a swing of more than 100 v o l t s , so an operating value of approximately 250 volts was chosen. A large number of measurements covering the useful working'range of a type 6SA7 tube were made and the useful por- t i o n of the r e s u l t s are displayed on the graphs of Figure 6. A suitable operating point i s seen i n the region e , = -3 to -6 c x volts and e = -1.5 to -7.5 vol t s for a screen-grid voltage C 3 between 90 and 100 v o l t s . The l i n e a r i t y and allowable signal levels were considered s u f f i c i e n t to warrant the construction of a complete mu l t i p l i e r consisting of two m u l t i p l i e r tubes and a subtracter. This unit when constructed and tested proved to be accurate enough for the polarcardiograph application. BO B5 Amp/ifiet" y • \6r,a6/e ffefjkied 'scope fatia&fc Bias * V-n . 7~istm s cor? cft/c Ayr/ c e ~ Sr/cfqQ -o A / ? * - 0 . 3 J 0 figure v5" <$u(>Fr<tcf'/on C/rcu/ f  IV THE COMPLETE COMPUTER CIRCUIT Subtraction of the outputs from the two m u l t i p l i e r tubes i s accomplished by the cathode-follower type of subtrac- t i o n c i r c u i t shown i n Figure 5. If R-̂  = /*! ~ ̂ 29 r p i = r p 2 and i f the capacitor impedances are neg l i g i b l e , the output volt- age . is i ,w+2 ( eo.r eo2 ) o If r ji r j ;u, 9* j i 2 $ R, ji R2, th.e Output voltage i s given bys • = -P2eo2 [ ( R l + R K ) ( l + ^ l ) + r p J + A e o i P R2 + RK ) ( l +^ 2) + r p 2] o 6o — R P 1 + R P 2 + V » I + 1 H » M *2+RK ) For subtraction to be achieved the c o e f f i c i e n t s of e and e 01 02 must be equal. This condition is- s a t i s f i e d when H < B l + V ( 1 + ^ l ) + r p i = ( R 2 + R K ) ( l + ^ 2 ) + r p 2 ' Rewritten i n terms of R̂  t h i s expression requires that ^(1+^2) ^ l r p 2 ^ 2 r p i R i = ̂ d - ^ n j R2 + ^ 2 T i ^ q T ** + ^ u - ^ ; If R̂  i s made adjustable the above condition can be s a t i s f i e d . In practice t h i s adjustment i s made when e 0 ^ = e o 2 S ) ^^ a * *-s* when the two subtractor inputs are equal. The adjustment of R^ to give zero output voltage i s referred to as "balancing the subtractor". 23 Because the above c i r c u i t i s of the cathode-follower type, i t i s inherently stable against c i r c u i t parameter'variations. Calculations indicate that$ f o r the c i r c u i t values used, an un- balance of 10$ between the /l's or B's produces less than 1$ error i n the output. Moreover, less than 10$ of the input signal at any g r i d appears as grid-to-cathode swing, and therefore the as- sumption of tube l i n e a r i t y used i n the above analysis i s j u s t i - f i e d even when the signal approaches ten times the operating bias. The complete computer would require two subtractors and one adder following the m u l t i p l i e r s . However, the i d e n t i c a l pro- cess can be carried out by using two adders and one subtractor as i l l u s t r a t e d i n Figure 7. The advantage i s that addition can be accomplished without the use of vacuum tubes as shown i n Figure 8. The two voltages to be added are represented by e ^ and egg l n series with t h e i r associated internal impedences R . The two sources are coupled through i s o l a t i o n r e s i s t o r s R̂  to a common r e s i s t o r R . The voltage across R i s given bys g g R e° = ( e 2 2 + e l l * R+R.+2R i g which i s the required addition. The r e s i s t o r R̂  i s made approximately 100 times larger than the internal resistance R so that the voltage sources are independent of each other. The common r e s i s t o r R̂  must be made large to prevent excessive attenuation of the signal. In the present case, the input impedance of a cathode-follower i s o l a - t ion amplifier serves as the re s i s t o r R̂ . This amplifier was also required i n order to present a low-impedance source to the subtractor. When a high-impedance source i s presented to > j j ii o 1 — \e» ) Ri i " Figure 8 the subtractor i t cannot be balanced solely by a variable r e s i s t o r , as assumed previously, due to the effects of stray capacitance be- tween the subtractor grids and groundo This capacitive unbalance can be compensated for. by a trimmer condenser on one of the sub- tractor grids, but the setting of this, trimmer condenser i s depend- i ent upon the setting of the variable r e s i s t o r R̂  i n the subtractor c i r c u i t , as well as upon the setting of trimmer condensers required i n the mu l t i p l i e r plate c i r c u i t s . L i t t l e capacitive balancing i s required on the subtractor when i t i s operating with a low-imped- anc e input. In the comput er c i r c u i t of Figure 9, i t i s seen that one jvi&te load r e s i s t o r of each m u l t i p l i e r pair i s variable. When no signal i s applied to Gg of either tube i n a pair, the out- put voltages from both tubes should be equal so that cancellation can take place i n the-subtractor. The variable plate load re- sis t o r on one tube allows the outputs to be adjusted to equality. This adjustment i s referred to as mu l t i p l i e r balancing. Due to phase s h i f t caused by stray capacitance, exact mu l t i p l i e r balancing cannot be achieved solely by a variable r e s i s t o r . A small trimmer condenser i n one plate c i r c u i t of each m u l t i p l i e r pair i s required to achieve an accurate balance. The settings of these trimmer condensers are somewhat dependent upon the settings of the variable r e s i s t o r s , but should normally re- quire changing only when a m u l t i p l i e r tube i s changed. The mathematical analysis predicted the necessity of a band-pass f i l t e r with a pass band extending from U) -9 to u) +9 radians per second, where LO represents the frequency of the o s c i l l a t o r and 6 represents the maximum frequency contained i n Z6 figure 3 27 the patient voltages used for the horizontal and v e r t i c a l inputs to the computer. The electrocardiographic voltages contain f r e - quencies from about one cycle per second up to about 300 cycles per second, although a frequency response up to 100 cycles per second seems to be adequate f o r recording equipment. To allow 100 cycles per second for the electrocardiograph frequencies and — 100 cycles per second f o r o s c i l l a t o r frequency d r i f t requires a pass-band width of 400 cycles per second. The f i l t e r , as shown i n Figure 9, consists of a pentode- driven, double-tuned c i r c u i t whose design centre frequency i s that of the o s c i l l a t o r . Because the phase-measuring equipment becomes increasingly d i f f i c u l t to b u i l d as the frequency of the input signals i s raised, the o s c i l l a t o r frequency should be kept as low as possible. Four k i l o c y c l e s per second was chosen as the lowest frequency f o r which a double-tuned f i l t e r c i r c u i t could be b u i l t with a reasonably f l a t response (-2*$) over the 400 cycles per second pass band. From the mathematical analysis, the difference voltage from one m u l t i p l i e r pair i s given by8 eo 1 " e o 2 " " R L { E 3 s i n 9 t gm 3 ( l- k ) + E 1 sin U)t Egv sin 6t(l-k) ^ — g C3 O O O O O O O 1 The f i r s t term of the above expression i s the amplified electro- cardiograph input voltage. Because the transconductance g i s d gmi m 3 considerably greater than the quantity • a , this amplified • ' 6 c 3 electrocardiograph voltage i s greater than the desired product 28 voltage. To prevent the large low-frequency voltage from over- driving the f i l t e r amplifier a high-pass R-C f i l t e r was placed at the subtractor output as shown i n Figure 9. Since the low-frequency components of the electrocardio- graph input signals makes ac bypassing of r e s i s t o r s impractical, bias i s supplied to the m u l t i p l i e r tubes from a battery, and screen voltage i s supplied from voltage-regulator tubes. One regulator tube was used for each m u l t i p l i e r pair to prevent coupling through the screens, which results i n high-frequency o s c i l l a t i o n . 29 V THE OSCILLATOR The o s c i l l a t o r , a res i s t i v e - c a p a c i t i v e twin-T type, features good frequency s t a b i l i t y and low harmonic content.. The output from the i s o l a t i o n amplifier i s adjusted to approximately 20 volts rms by means of the potentiometer i n the feedback path. The phase s h i f t e r , as shown i n Figure 9, uses a centre- tappod audio-frequency transformer with a suitable transformation r a t i o . Ninety-degree phase s h i f t i s obtained when the voltages across the r e s i s t o r and condenser are equal. The o s c i l l a t o r out- put (see Figure 9) for the phasemeter i s obtained d i r e c t l y from the cathode follower through an R-C phase s h i f t e r . Phase s h i f t i s required at this point to compensate for phase s h i f t i n the R-C high-pass f i l t e r i n the subtractor output. 30 VI MAGNITUDE AND PHASE OUTPUTS The voltage appearing at the output of the tuned c i r - c u i t , which i s given by HE sin(o>t + 45 0 + cO, i s a sinusoidal signal of radian frequency CO whose rms value i s d i r e c t l y pro- portional to the magnitude of Ho If t h i s signal i s r e c t i f i e d and averaged, the result i s d i r e c t l y proportional to Ho Half- wave r e c t i f i c a t i o n i s performed by a vacuum diode and averaging by the electromechanical recorder, since i t can respond only to the quasi-dc component of the r e c t i f i e d sine wave. One type of phasemeter which i s not ambiguous about 180° i s that which u t i l i z e s an Eccles-Jordan trigger c i r c u i t , 6 T 8 or f l i p - f l o p , i n i t s output. 9 ' As shown i n the schematic diagram of Figure 10, the two signals whose phase i s to be com- pared are f i r s t amplified and clipped u n t i l they are "square waves". Di f f e r e n t i a t i o n then produces negative- and positive-going pulses' marking the sides of the square waves. The positive-going pulses are removed by a vacuum diode and the negative pulses are applied to the f l i p - f l o p . The f i r s t negative pulse w i l l cause one tube of the f l i p - f l o p to conduct and the next negative pulse w i l l cause i t to cease conductions hence the average conduction time of either tube w i l l be proportional to the phase difference of the two input waves. In practice, connections are made to the plates of both tubes for balanced output since the recording instrument i s equipped for balanced input. Again, no f i l t e r i n g i s required 31 Different/ah o—>— A mp. Amp- r \ _ r \ _ n _ n i i Ret t't] Amp. i i V 1 Clip Clip Clip p/lp- Flop O • > Amp. Amp. Amp. a n i . i Rpc/ify i • Chp Cl,p Chfi ~ i — r JUL ~1 — — o U IT Figure IO •Scherncthc. F^hetsemefer tn/owr Figure II CctMocfe-Coup/eel C//pper C/rcc/// 32 since the recorder i t s e l f i s e f f e c t i v e l y an electromechanical low- pass f i l t e r . Four k i l o c y c l e s per second corresponds to a phase change of 36Q° i n 250 micro-seconds. That i s , one degree of phase change corresponds to roughly 0.7 micro-seconds." If the phase i s to be measured within ^2° of 180°. the f l i p - f l o p must be capable of d i s - tinguishing between two pulses less than two micro-seconds apart and the pulses themselves should be less than a micro-second wide. Further, i f the phasereading i s to be accurate, the negative trigger pulses must mark the exact point where the sinusoidal waves cross the zero axis, going negative. This l a s t condition can Dfc achieved by insuring that the clipping action i s balanced, that i s , that both halves of the square wave are equal i n width. Q The cathode-coupled clipp e r , shown i n Figure 11, i s easily adjusted to give symmetrical clipping by changing the positive bias E c c ^ . The regenerative feedback r e s i s t o r i n - creases the amplification of the c i r c u i t , thus causing c l i p p i n g to take place at lower input l e v e l s . Since i t i s desired to have no output signal when there i s no input signal, the li n e a r and non-linear gains of the clipp e r must be less than unity. Three stages are cascaded i n order to provide a reasonably square output wave with about 0.5 volts rms input. Decoupling of the f i r s t two stages of each channel i s necessary to prevent zero- signal o s c i l l a t i o n of the system. D i f f e r e n t i a t i o n i s accomplished by using a series R-C d i f f e r e n t i a t o r with a time constant of -7 1x10 seconds. A high-gain pentode amplifier with a low plate load resistance raises the pulse l e v e l to approximately 50 v o l t s . The resulting pulse width, as viewed on an oscilloscope, appears to be less than one micro-second. 33 The positive pulses from the d i f f e r e n t i a t o r are, removed by a diode, the cathode of which i s biased positive with respect to the plate so that the pulse generator i s e f f e c t i v e l y discon- nected from the trigger c i r c u i t except when a negative pulse i s being applied, as shown i n the complete c i r c u i t diagram, Figure 13, This arrangement prevents the low impedance of the pulse generator from loading the f l i p - f l o p . The trigger c i r c u i t i s designed for dc s t a b i l i t y * ^ , the. values of the r e s i s t o r s and cross-coupling condensers being chosen as low as possible so that minimum switching time can be obtained. 34 VII INPUT CIRCUITS If the phase output i s to be correct, the angle must be measured from the correct o r i g i n . Since the f i r s t stages of the electrocardiograph amplifiers are ac coupled and the average of the heart vector components i s not zero, the ori g i n must be re-established at the input to the computer. For this purpose, the computer has been equipped with a cathode-ray tube, the h o r i - zontal and v e r t i c a l d e f l e c t i o n plates of which are driven by the horizontal and v e r t i c a l components of the heart vector, respect- i v e l y . With no signal applied to the computer input, the spot on the cathode-ray tube i s centred. This rest point i s marked on the face of the tube and the computer i s balanced to give zero output. The m u l t i p l i e r inputs are taken from tap points on a r e s i s t o r connected between the deflection plates of the cathode- ray tube. When the electrocardiograph amplifiers and a patient are connected to the computer, the cathode-ray tube displays a vectorcardiogram, the o r i g i n of which i s c l e a r l y v i s i b l e as a bright spot since the beam i s stationary during the resting period between heart beats. The centring controls on the input ampli- f i e r s are then used to bring the ori g i n back to the marked point on the face of the cathode-ray tube. If a noise signal i s present, i t may be p a r t i a l l y masked by deflecting the o r i g i n of the vectorcardiogram s l i g h t l y to the 35 right of the marked point on the cathode-ray tube. This procedure results i n a large error i n the angles associated with a- small signal and correspondingly smaller error i n the angles associated with a larger sig n a l . For t h i s reason a magnitude recording should be taken simultaneously with a phase recording so that the probable v a l i d i t y of the phase readings may be estimated. 36 VIII THE COMPLETE INSTRUMENT Controls for balancing the subtractor, the m u l t i p l i e r s , the input amplifiers and for equalizing the overall gains of the two channels are available to the operator. Balance i s checked v i s u a l l y by observing an electron-ray tube which i s connected to the tuned-circuit output. A rotary switch makes suitable connec- tions f o r balancing purposes. The balancing procedure i s carried out with no signal applied at the input, that i s , the spot on the face of the cathode-ray tube must be centred. In position "1", the rotary switch t i e s the two sub- tractor grids together. The variable r e s i s t o r i n the subtractor i s then adjusted u n t i l the electron-ray tube indicates zero out- put. In position "2", the rotary switch connects the o s c i l - l ator grids, that i s Gr̂  of both tubes of channel one, to bias. Channel two i s then balanced by adjusting the variable plate load r e s i s t o r of one of i t s tubes u n t i l there i s zero output indicated by the electron-ray tube. In position "3", the rotary switch interchanges the connections to allow for balancing of channel one by a similar procedure. In position "4" of the rotary switch, the o s c i l l a t o r grids of both channels are t i e d to one side of the phase s h i f t e r , and at the same time, equal but opposite standardized dc signals -are introduced to the input amplifiers. If the input amplifiers 37 have equal gains the spot on the face of the cathode-ray tube w i l l move away from the origi n at 45° to the horizontal. The input amplifiers are adjusted to equal gain by ganged variable r e s i s t o r s i n the plate c i r c u i t s of the input amplifiers. A l i n e at 45° to the horizontal has been drawn on the face of the cathode-ray tube for this purpose. When the input amplifiers have been balanced ( i . e . , the spot on the cathode-ray tube face l i e s at some point on the 45° l i n e ) , the overall gains of both computer channels are equalized by means of ganged variable r e s i s t o r s i n the g r i d c i r c u i t s of the m u l t i p l i e r s . At balance the electron-ray tube indicates zero output. Position "5" of the rotary switch returns a l l connec- tions to normal and the machine i s then ready f o r operation. The preceding balancing procedures are ess e n t i a l l y i n - dependent of each other and need be carried out only during the warm-up period. Balancing checks should be made before every re- cording during the f i r s t half-hour of operation. Aside from focus and intensity controls on the cathode- ray tube, no other controls were available to the operator on the o r i g i n a l device. However, a few t r i a l runs showed that the machine was quite d i f f i c u l t to use and could not be expected to v give accurate results when operated by an average technician. When o r i g i n a l l y designed, the input amplifiers were direct-coupled to the electrocardiograph amplifiers. D r i f t i n the electrocardiograph machines was thus amplified, and centring of the vector o r i g i n became almost impossible when d r i f t was worse than usual. Capacitive coupling from the amplifiers, with variable time constants, was substituted for the d i r e c t coupling. When there i s l i t t l e d r i f t a time constant of 16 seconds can be 38 selected. When there i s a comparatively large amount of d r i f t , a time constant as low as * second can be selected enabling some results to be obtained at the expense of the low-frequency com- ponents i n the electrocardiograph waveform. The operator w i l l be required to record the time constant used. In order to check that the operator has centred the vector o r i g i n , a push switch which temporarily s h o r t - c i r c u i t s the magnitude output has been i n s t a l l e d . The operator w i l l be re- quired to hold t h i s switch down f o r one or two heartbeats when making a recording. The zero value of the magnitude w i l l then show on the recording, and i f the baseline of the magnitude t r a c - ing i s discernible, i t w i l l be possible to t e l l i f the machine has been zeroed correctly by inspecting the recording. The error i n zeroing w i l l also be obtainable and can be used to determine the worth of the corresponding angle recording. The angle recording i s marked at il80°, ^90°, 0° by means of the "angle ca l i b r a t e " switch which applies a dc signal to each g r i d of the input amplifiers i n the appropriate order. Usually either +180° or -180° w i l l be calibrated. However, i n - s t a b i l i t y of the f l i p - f l o p i n this region may occasionally pre- vent either point from being marked on the recording. The angle i s calibrated by holding the switch b r i e f l y i n each of four p o s i - tions. This can only be done after the computer has been balanced and only i f no signal i s being applied from the patient. The re- corder, of course, must be running. The "angle calibrate" switch must be returned to the " o f f " position when a recording i s taken. Any angle from 0° to 360° can be subtracted from the angle output by means of a quadrant selector and a calibrated 39 phase s h i f t e r . The quadrant selector changes the output angle i n steps of 9G° by interchanging the horizontal and vertical, inputs and t h e i r p o l a r i t i e s , the rotation of the vectorcardiogram being v i s i b l e on the cathode-ray tube. The calibrated phase s h i f t e r varies the angle from 0° to -90° by advancing the phase of the comparison signal. This rotation i s not evident on the vector- cardiogram. Angle s h i f t i n g i s helpful i n avoiding the f l i p - f l o p switchover point at ̂ 180°. The operator can record the amount of phase s h i f t used, although i t i s possible that the waveform of the angle output i s more important than the numerical value of the angle.. 40 IX ACCURACY TESTS The overall accuracy of the machine was checked by applying sinusoidal signals from a two-phase source to the i n - put terminals. Since the vector locus for such voltages i s a c i r c l e whose centre i s at the o r i g i n , the angle output should be a "sawtooth" waveform as shown i n Figure 12(a). Actual machine outputs for c i r c u l a r inputs are shown in Figures 12(b) and 12(c), representing the maximum and mini- mum allowable signal levels respectively. The maximum signal l e v e l of 4.5 volts rms i s determined by non-linearity of the magnitude output, although the angle output waveform remains substantially the same up to 6 volts rms input. Satisfactory performance i s also obtained with signal levels as low as 0.1 volts rms, indicating a dynamic range better than 45gl. As the lowest test frequency available was 20 cycles per second, the f i l t e r required to remove the 4 k i l o c y c l e s per second c a r r i e r frequency reduced the transient response of the output s u f f i c i e n t l y to prevent the triangular wave from extend- ing over the f u l l range of -180° to +180°. It i s f e l t that at the normal fundamental input frequency of one cycle per second the transient response i s adequate. As a further check on the transient response, voltages representing a small c i r c l e with centre displaced from the o r i - + o gin on the -180 l i n e were applied to the input terminals. The 41 resulting angle output waveform i s shown i n Figure 12(d). The time required to switch from -180° to within 5$ of +180° i s of the order of 0.01 seconds, or about \f» of the duration of the heart cycle. The f l i p - f l o p switchover w i l l therefore appear as a nearly v e r t i c a l l i n e oh a polarcardiograph tracing. The magnitude output versus input i s plotted i n Figure 12(e) and shows reasonable l i n e a r i t y from 0 to 4.5 vol t s rms i n - put. The non-linear portion at low signal levels may be due to a small amount of unbalance. In operation, t h i s non-linearity w i l l be small with respect to error produced by noise and i n - correct centring. These tests indicate that the overall accuracy of the machine i s s u f f i c i e n t for normal electrocardiographic purposes, provided i t i s used with a recorder having a frequency response of at least 300 cycles per second. 42 X CONCLUSION The polarcardiograph i s an electronic analogue computing device which computes voltages proportional to the magnitude and angle of the heart vector from voltages proportional to i t s com- ponents i n Cartesian co-ordinateso The computer was designed using analogue m u l t i p l i e r s , adders, a subtractor, a l o c a l o s c i l l a t o r producing a two-phase sinusoidal source and a phaseraeter capable of generating a voltage proportional to the phase difference of two sinusoidal signals., The device was designed to use the output voltages of standard electrocardiograph machines for input voltages and i t s output can be recorded by any s t r i p recorder of s u f f i c i e n t bandwidth. The device i s d i f f e r e n t from a similar one ci t e d i n the l i t e r a t u r e i n the manner i n which mu l t i p l i c a t i o n i s achieved. M u l t i p l i c a t i o n i n the present machine i s performed by pentagrid type vacuum tubes. The operating conditions under which a penta- gri d tube w i l l perform m u l t i p l i c a t i o n were derived mathematically. Such operating conditions were achieved and were incorporated i n the design of the computer. The complete instrument when tested proved to have an accuracy well within that o r i g i n a l l y required. 43 XI REFERENCES 1. Hodgkin, A.L., "The Ionic Theory of Membrane Potential," B i o l o g i c a l Reviews of the Cambridge Philosophical Society'V" 26„ p. 339, November 1951. 2. Lepeschkin, E., Modern Electrocardiography. Volume 1, Williams and Wilkins Company, Baltimore, 1951. 3. Grishman, A. and Scherlis, L., Spatja1 Vectorcardiography. W.B. Saunders Company, Philadelphia, 1952. 4. Frank. Ernest, "The Elements of Electrocardiographic Theory," Communication and Electronics, p. 125, May 1953. 5. McFee, R,, "A Trigonometric Computer with Electrocardio- graphic Applications," Review of S c i e n t i f i c Instruments. 21, p. 420, May 1950. 6. Kretzmer, E.R., "Measuring Phase at Audio and Ultrasonic Frequencies," Electronics, 22, p. 114, October 1949. 7. Florman, E.F„, and Tait, A., "An Electronic Phasemeter," Proceedings of the L R X , 37, p. 207, February 1949. 8. Tu, X.P., "Zero Intercept Phase Comparison Meter," Electronics,, 26, p. 178, November 1953. 9. Goldmuntz, L.A., and Krauss, H.L., "The Cathode-Coupled Clipper C i r c u i t , " Proceedings of the I.R.E., 36, p. 1172, September 1948." 10. Pressman, R„, "How to Design Bistable Multivibrators," Electronics, 26, p. 164, A p r i l 1953.  Po/arcarc//oQraph Coropurer j - ' / C i rcwl Dfajrq n? qz Bur/I A/or. - Allre$t$'-farice values ore megohms im/ess Qtteru/rse All capo cdancp wives r •• fndfcafed- /A'= fcooo'n/ns un/pss olfi^tovsc 'ftol'C?t-/'ed Ufnver^i ly ar <£y rif/sh Co/t//?-.• 3/<\ j / L<, -• ( rr?/c r o £ arret cl Pea'cfyfrnrrrfcf £."/€ cMm 1 f^oroeet- /no / J J , , I

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