Contains reports on two research projects

Guillemin, Ernst A.

Maartmann-Moe, R.

Pantell, R. H.

Scott, R. E.

Wallman, Henry

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IX. MISCELLANEOUS PROBLEMSA. ELECTRONIC DIFFERENTIAL ANALYZERProf. Henry WallmanR. Maartmann-MoeA new main gate generator has been designed and built. It employs acathode follower output with cathode resistor center-tap grounded, and afloating power supply. A delayed feedback circuit is used to get the pulsetops flat within 20 myv (0.07 percent). This is still not quite satisfactorywith the present method of obtaining initial condition voltages, as thepercentage deviation from flatness increases with decreasing initial condi-tion voltage setting. New potentiometers employing a grounded center tapare expected to clear this trouble.The long-time drift of the power supplies has been investigated. Thenegative (-110 volts) supplies have an initial drift rate of one volt perhour, final voltage being reached after about 5 hours. The positive (+250volts) supplies have no appreciable drift. Minor alterations to the negativesupplies are hoped to reduce the drift to more tolerable levels. All sup-plies show occasional jumps of about one-tenth volt due to mode changes inthe voltage regulator tubes (VR105). The drifts of the supply voltagescause the zero settings on the function-generator-multiplier units to change,as these units employ d-c amplifiers without feedback.Five new function-generator-multiplier units have been tested and someminor changes made to obtain better linearity of the magnetic channel ampli-fiers, and to make the zero settings more easily accomplished.One function-generator-multiplier unit has been sent to Evans SignalLaboratories, Belmar, N.J. for use with the analyzer being constructed therewith this analyzer as model.Mr. Robert H. Cannon, Mechanical Engineering Department, M.I.T., con-tinues to use the analyzer on a speedboat design problem which requires theuse of every component of the machine. The problem also required the addi-tion of more function-generator-multiplier units to the machine, so as toenable two waveforms to be generated, and two multiplications to be per-formed simultaneously. About 200 different conditions of the boat construc-tion have been studied, and about 500 pictures taken.-90-(IX. MISCELLANEOUS PROBLEMS)B. ANALOG DEVICES FOR NETWORK PROBLEMSProf. E. A. GuilleminR. E. ScottR. H. Pantell1. An Automatic Impedance-Function AnalyzerA new buffer amplifier and integrator unit has been designed and builtfor the automatic impedance-function analyzer. A block diagram of thesystem is shown in Figure IX-1.Fig. IX-I Block diagram of buffer amplifier and integrator.The system is a novel one which uses a-c amplifiers throughout,but still retains the full duty cycle. This is accomplished by adding thed-c component to the output. For the magnitude, this involves merely theaddition of a direct voltage to the output or alternatively the settingof the zero db line. The method of obtaining the phase is slightly morecomplicated, since an integrated constant, or a sweep wave, must be addedto the output. The amount of the sweep wave which must be added is deter-mined from the fact that the phase curve must be flat at very low frequenciesand at very high frequencies.In the magnitude position, the outputs from the two commutators areidentical. The filters remove the 1000-cycle hash, and the output isaveraged and displayed on the cathode ray tube. In the phase position, theoutputs of the two commutators are slightly different. One of them is in-verted and then added to the other. The result is the difference betweenthe two commutator voltages. This difference is the derivative of the phasewith respect to frequency. It is integrated and a sweep wave is added to it.The final result is the phase.For stability and accuracy, active integrators, adders and invertershave been used. The general scheme is well known and is illustrated inFig. IX-2.-91-(IX. MI5CELLADOUS PROBLEMS)RR8 I o--..I\,/Iwf\,--9"""---I\I'V'J----,R82 0---'''''',.-+--4RINVERTER ADDER INTEGRATORFig. II-2 The inverters, adders and integrators.The requirements on the ampli.fier are stringent. It BlUst have a highgain and a large bandwidth but it IllUst not break into oscillations whenlarge amounts of feedback are applied. In addition the output impedanceDlUst be low. A design which satis.fies these requirements is shown inFig. IX-3..-----------------o150V.-----+-------y--......--------1------0250 VFig. IX-3 The basic amplifier.The output impedance of this ampli.fier is about 100 ohms. The ampli-.fication is about -1000. The high-frequency phase shift is controlled bymeans o.f the O.02-ufd shunting capacitor at the grid o.f the .first 6.16 tube.The lov-~equency phase shlft ls controlled by means o.f the coupling capaci-tor between the 6AGS and the 6J6.Bome experimental results of magnitude, delay and phase .for s1ngle-tuned circults are shovn in Fig. IX-4.Fig. IX-4 Experimental results. Quadratic factor. i2-s2+22CTs + 1s~ft, log magnitude vs. log frequency; center, negative phase derivative vs. log frequency;right, negative phase-va. log frequency (final value & 0). --92-(IX. MISCELLANEOUS PROBLEMS)2. The Electronic Isographa. TheoryA problem frequently encountered in various engineering problems isthe solution of polynomials of the fourth, fifth, sixth degree or higher.The process of solution can be quite tedious. Thus there is the apparentdesirability for a device that would obtain the roots of a polynomial in arapid, simple manner. The electronic isograph performs this function.To comprehend the construction and performance of the isograph, expressthe polynomial:0 = a + ax + a2 x 2 + ax 3 + ... +anxn (1)in polar form. Letx - r(cos a + J sin 9) (2)The polynomial then becomesn0 (akrk cos k + jakr k sin k) . (3)k=OIn essence, the isograph produces a summation of sine and cosine terms ofmultiple frequencies with the proper coefficient values in accordance withEq. (3). The sine terms, which have been shifted 90* out of phase with thecosine terms, are placed on the vertical plates of a CRO; the cosine termsare placed on the horizontal plates of a CRO. In this manner, a plot ofthe polynomial is viewed on the oscillograph. Variation of the parameter rcauses the plot to pass through the origin thereby indicating that thesetting of r is a root of the polynomial.b. DesignMultiple frequency square waves are obtained from flip-flop circuitsthat operate at integral sub-multiples of a master crystal oscillator asin Fig. IX-5.The isograph illustrated in Fig. IX-5 is capable of handling polynomialsup to the sixth degree.A square wave is a composite of a series of sinusoids, where the funda-mental component is at the frequency of the square wave. Therefore, a high-Q circuit tuned to the frequency of the square wave yields the desiredsinusoid.The magnitude of cos kG must be equal or proportional to rk . This is-93-(IX. MISCELLANEOUS PROBLEMS)6 KGFig. IX-5 Block diagram ofmultiple-frequencysquare wave synchron-ization.KCLrealized if the output from the flip-flop circuit is clipped at the valueof rk (Fig. IX-6). As indicated in Fig. IX-6, the powers of r are obtainedfrom ganged potentiometers. All the resistors move as a unit, and so eachrheostat is set at the same relative position. Hence if the first resistoris 1/2 of Eb (for r - 1/2), the second resistor is 1/2 of 1/2 or r2; and soon. In this manner the powers of r are obtained by the movement of one shaft.Fig. IX-6 Block diagram ofsquare wave clipping.-- r4--- r5The value of ak is introduced by means of a voltage divider. Since akmay be either positive or negative, a double-throw switch is used to connectthe circuit to the cathode or plate resistor respectively of a cathodefollower.With the polynomial plotted on a CRO, and r adjusted so that the plotpasses through the origin it is then essential to find the 0 for which thepolynomial is zero (Fig. IX-7). The fundamental frequency component isFUNDAMENTALFREQUENCY VARIABLE CLIPPER I_SINUSOID PHASE AND : TO Z-AXIS OF(2000 KC) SHIFTER PEAKER OSCILLOGRAPHFig. IX-7 Block diagram forevaluating 0 .~"v~(IX. MISCELLANEOUS PROBLEMS)fed into a variable phase shifter and subsequently into a clipper and peaker.This resultant pulse can thus be placed at any point along the time axis.The setting of the phase shifter indicates the desired value of 9 when thepulse occurs coincident with the passing of the polynomial plot through theorigin.By varying r continuously, a plot of the polynomial for all values ofthe variable appears simultaneously on the oscillograph. Applying a voltageto the Z-axis at the proper time interval will indicate the region of thepolynomial for which x is positive and real. This information is necessaryto predict the response of numerous electrical and mechanical systems.Mechanical isographs are now in operation which produce multiple frequencysquare waves by rotating brushes. The latter are limited to a maximumfrequency, thereby precluding a simultaneous plot of all values of thevariable without the use of a long-persistence screen. In this respect,the electronic isograph is superior.* *-95-

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