Biased Resonance Circuits for Electrooptic Digital Deflectors

C. F. Haugh

A number of circuits for electrooptic digital deflectors is presented. These circuits minimize power dissi-pation by utilizing the novel technique called biased resonance. This technique is based on the coinci-

dence of zero points of a raised cosine and its derivative. Test results are reported for one circuit that

operated at 2200 V, with a load capacitance of 200 pF, and at greater than 100 k baud rate. Dissi-pation for this breadboard model was 10 W. Other circuits are shown; their advantages and disad-

vantages are discussed. Also discussed are some future switching device requirements.

Introduction

In order to obtain half-wave retardation in KD*Pand other electrooptic crystals, a substantial voltagemust be applied to the material. Typically, thesevoltages are on the order of several kilovolts; whilenot extraordinarily high by vacuum tube standards,such voltages are well beyond the rated junction volt-ages of most semiconductor devices. Therefore, thecrystal must be transformer coupled, or a series stringof switching devices must be used.

The crystals themselves are, electrically speaking,capacitors; if high switching rates are to be obtained,one must pay the price of high transient currents. Thecombination of high voltage and high current placessevere power-handling restrictions on any switchingdevice. This paper presents a general method, as wellas several specific examples, of circuit design, whichminimizes the power handling requirements for highvoltage switching devices.

Consider the circuit shown in Fig. 1(a) as a possiblehigh voltage switching circuit. If C is two KD*Peach 1 cm X 1 cm X 2 mm thick and optically in seriesbut electrically in parallel, a capacitance of approxi-mately 200 pF is presented to the switch. Supposethat Si is initially closed and S2 open, so that C ischarged to 2200 V. Therefore, the energy stored on Cis 4.84 X 10-4 J. If the transition from the charged tothe discharged state is to be made in 10 lisec by openingSi and closing S2, there is a resultant power dissipationrequirement of 48.4 W-a rather husky requirement.Figure 1(b) shows the switching trajectory as seen byS2, assuming that it is an ideal transistor driven by aconstant current source at the base.

The author is with the IBM Corporation, Systems Develop-ment Division, Poughkeepsie, New York 12602.

Received 2 May 1966.This work was supported in part by the United States Army

Electronics Command under a contract.

Therefore, the following criteria for switching electro-optic crystals were adopted as goals: (1) all switchesopen and close with zero voltage across them; (2) allswitches open and close with zero current through them.The circuits to be described meet these criteria asnearly as possible with nonideal elements. The switch-ing trajectories used are shown in Fig. 2.

If we examine a raised cosinusoidal wave and itsderivative, we notice that zeros of both coincide.Hence, if switching takes place at even multiples of7r/wc, where co is the radian frequency of the cosinusoid,both voltage (the cosine) and current (its derivative)are zero [see Fig. 2 (b) ]. This is the basic principleof biased resonance.

Circuit Configurations

One of the simplest circuits that operate in thismanner is shown in Fig. 3(a). Here there are twoenergy sources: a sinusoidal ac generator, whose ampli-tude is 1 VX/2, and a battery whose voltage is also w-Vx/2 .As long as Si is opened and closed at negative maxima ofthe ac signal, it operates within the criteria mentionedabove. The waveforms of Vi, V,,, and I are shown inFig. 3(b) for a data sequence 10011. (Here, as in thefollowing, a logical 1 corresponds to a high positivevoltage on the crystal; logical zero corresponds to alow voltage.) Of course, the full voltage is not appliedto the crystal for the entire logical 1 time. If the volt-ages are increased to 1.06 (TVX/2), the voltage is within6% of VX/2 for 78.8° of 3600, or about 21.8% of thetotal time; this insures a polarization efficiency of 99%or better during this time.

An extension of this circuit is shown in Fig. 3(c).Here C' is an ordinary capacitance whose value isequal to the capacitance of the crystal C. Either Si orS2 is closed at any time; hence, the raised sinusoidalvoltage appears across either C or C' at any instant.The next obvious step is to use the transformer-capaci-tor combination as the resonant tank circuit of a Hartley

November 1966 / Vol. 5, No. 11 / APPLIED OPTICS 1777

VX/ C

(a)

IC

VX2 VCE

(b)

Fig. 1. (a) Simple high voltage switching circuit for electro-optic crystals. (b) Switching trajectory for transistor version of

switch S2, driven by constant current base drive.

Ic II

i

I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

VX/ 2 VCE

(a)

V

Experience has shown that if KD*P crystals are op-erated for long periods of time with dc voltage applied,the crystals deteriorate. The circuits of Fig. 3 doapply a voltage with a nonzero average value to thecrystal. Although these circuits can be modified toapply no d to the crystal by suitable biasing, anentirely new circuit, shown in Fig. 4, was designed.Although it is not immediately apparent, this circuitalso uses the biased resonance approach; the waveformof the voltage across the load capacitor is a raisedcosine. In this circuit, the bias is switched to obtainboth zero average voltage and the required totalpeak-to-peak voltage. Because this circuit operationis unique, it is described in some detail.

Assume that there is no initial energy storage. Att = 0, switch Si is closed. Neither voltage nor currentcan change abruptly because of the presence of thecapacitor and inductor, respectively. The voltageacross the capacitor rises, according to the well-knowntransient solution, as

V = 4VX/2(1 - COSCO)

I

S

2 vx/2

(a)

VX/2 -

vc.-

(b)

Fig. 2. (a) Optimum switching trajectory for transistor switch.(b) Raised cosine voltage and its derivative (capacitive current).

oscillator, thus removing completely the need for anyexternal ac source. We only need to operate Si and S2at appropriate times in order to obtain the desiredpolarization of the light beam.

Not only do switches S and 2 operate at times ofzero current and zero voltage, but the circuit of Fig. 3(c)has other advantages also. Note, first of all, that thevoltage across the switches is unidirectional; hence,transistors can be used. In order to eliminate turn-offproblems in the transistor, the switches can be con-structed as shown in Fig. 3(d); the diode can be used toshunt the reverse current. The transistor can beturned on during only the first half of the on time. Thiscircuit [Fig. 3(c)] has been built and operated at lowvoltages. Rather than trying to design the oscillatorsection for the required high-voltage operation, a newapproach was taken.

2nr (2n+2)r (2n+ ), (t -

(M)

(c)

(d)

Fig. 3. (a) Simple biased resonance switching circuit. (b)Voltage on electrooptic crystal, circuit current in simple biasedresonance switch. (c) Self-excited version of simple biasedresonance switching circuit. (d) Unipolar switch that passes

current in both directions as required.

1778 APPLIED OPTICS / Vol. 5, No. 11 / November 1966

_L_-

while

I = -VX/2wC sinwt,

where c = (LC)-/2, cot = r, V = -VX/2 ; at cot = 2r,VI = I = 0. At wt = 2 , then, Si may be left closed,or it may be opened and 2 closed. If the latter ischosen, the capacitor voltage for the next cycle is givenby

V = -VX/ 2(1 - cost)

I = - V/2wC sinw.

The voltage across the capacitor is therefore continuousthrough the cycle; the current is also continuous, al-though its derivative is not. Coupling between thecoils is necessary to eliminate the discontinuity ininductor voltage. Because of the distributed capaci-tance of the windings, it might otherwise be possibleto obtain high frequency ringing across the coil, andswitching at zero voltage and current might not bepossible.

Obviously, a physical circuit has losses; this one isno exception. Consequently, if one switch were leftclosed indefinitely, the voltage across the crystal wouldeventually damp out to a final value of VX/2. There-fore, alternate switching is necessary. The most ad-vantageous scheme is to identify two full cycles of os-cillation with one bit of data. Thus, the resonant fre-quency should be twice the band rate. The second fullperiod within the data period is identified as the datatime, and the switches are always reversed at the startof this time. Thus, logical 1 corresponds to S2 closed,Si open, followed by S2 open, SI closed. This insuresthat the capacitor voltage has its largest swing duringthe data time.

Because of this double frequency operation, the volt-age is within 6% of 2VX/ 2 for 10.9% of a data period;at a 100 k/sec data rate (200 kc/sec resonant fre-quency), this represents about 1 usee. Either the lightsource would have to be shuttered or the detectorstrobed to ensure proper reception of the intended in-formation. If ideal elements were available, the voltagewaveforms would be as shown in Fig. 4(b). Since theseare not yet on the market, there is degradation. Whenthe circuit was built and tested, the waveforms asmeasured on the oscilloscope were as shown in Fig. 4(c).The data frequency involved was 113.5 kc/sec in thiscase. All switching elements in this circuit are solidstate; note that if vacuum tubes are used, thepolarity of the voltage across S when it is open issuch that the filament supply (and possibly a screensupply) must be floated above ground by about 2200 V.Three transistors, each rated at 800 V (VCBO), were con-nected in series as the switching elements. An at-tempt was made to use SCR's, but the dV/dt of thereverse voltage was such that the SCR's turned onerroneously with about 750 V across them. Power lossin this breadboard circuit amounted to approximately10 W; most of the dissipation took the form of heatingloss in the inductor core. Losses could be reducedsubstantially with an improved coil design.

S,

(a)

(1) V - K

-2K

I K

(2) Vc

-IK

0-

V

rD A = 2 f=T 2 2''D:V A A X / X

0 10 I

1 tl 0

V1 1I 0

_ =

V

INPUT "I. I6 __

(3) DATA 'uOI.

(b)

B

D

(c)

Fig. 4. (a) Double frequency self-excited resonant circuit. (b)Voltage waveforms for ideal double frequency: (1) voltageacross switch Si; (2) voltage across electrooptic crystal; (3)output data waveform. (c) Actual oscilloscope recording ofcircuit operation. Traces (A), (B): transistor signal voltages;10 V/cm. Traces (C): voltage across switch S1 ; 1 kV/cm.Traces (D): electrooptic crystal voltage; 1 kV/cm. Horizontal

scale: 5 sec/cm.

Mfore detailed measurements indicated that the volt-age actually switched, in the worst case, was 200 V.The maximum current switch was less than 1 mA.This is close to the ideal criteria mentioned earlier, but

November 1966 / Vol. 5, No. 11 / APPLIED OPTICS 1779

C

(a)

0 - - - L

I I I I

SWITCHES S SI S2 S S SICLOSED: S3 S4 S4 S4 S4 S3

(b)

II

/

S S S S S Sz

S3 S S S S S5

- +

\j S3

S4

5

In many cases, it is desirable to charge the crystal to ahigh voltage for a period of time longer than that possi-ble with the circuit just discussed. Biased resonancecircuits can be used for this purpose as well. Onepossible arrangement is that shown in Fig. 5(a).Capacitors C2 and C3 have capacitances equal to that ofthe electrooptic crystal Cl. Assume that, initially, allswitches are open, and that C2 is charged to +-VX/2, C3

to -2!V/2, and C, is uncharged. Operation of thiscircuit is similar to that of the circuit just discussed;if Si and S3 are closed, the voltage across the capacitorrises. At t = r/co the voltage on C, is +2VX/2 Atthis instant, 3 may be opened and 4 closed. Thevoltage on Cl remains at + VN/2, while that on C2 dropsto zero. Opening Si and closing S2 causes C2 to chargeto -- "-VX/2 and then return to zero. Reversing Si andS2 brings this voltage back to +2VX/ 2 ; at ot = 3 r, S3may be closed and S4 opened. To charge the crystal toa negative voltage, the same sort of thing may be doneusing C3 rather than C2. At every instant of time, onecapacitor is positively charged, one negatively charged,and one swinging, i.e., resonating with the inductor.

A sketch of idealized waveforms is shown in Fig. 5(b).This circuit is completely self-exciting. As long ascapacitors are being switched in and out of resonancewith some regularity, no recharging is required. Anac signal source is never required, though it is apparentthat the idea of swinging capacitors can be extended tocircuits like that of Fig. 3 [see Fig. 5(c) ].

Also, by changing initial conditions and adding bias,this circuit can be made to swing over any voltagerange of V,/ 2 V. Again, all switching is accomplished

(c)II.I

T-IC(a)

(d)

Fig. 5. (a) Double frequency self-excited d resonant switchingcircuit. (b) Capacitor voltage S as a function of time switchoperations. (c) Self-excited simple d resonant switchingcircuit. (d) A possible bipolar switch for switch S3 in Figs.

5(a) and 5(c).

even these could be reduced if the coil design wereoptimized.

If desired, this circuit can obviously be modified bycoupling the crystal through a transformer in order tostep up the switching voltage. It is also apparent thata bias supply can be inserted between the crystal andground in order to obtain a voltage swing between 0and VX/2, rather than between i.Vx/2.

(b)

Fig. 6. (a) Amplitude modulation of the circuit of Fig. 3(c).(b) Amplitude modulation of the circuit of Fig. 4(a).

1780 APPLIED OPTICS / Vol. 5, No. 11 / November 1966

vcs.

�_I/

SI

S3

_,1, E '1

-JIII I1

L1 ,S4 L

S I

(a)

Inn

L, M

I

\JJ

(b)

Fig. 7. (a) Circuit for applying voltages of different magnitudeto electrooptic crystal: L = 2Li. (b) Voltage across capacitor

in Fig. 7(a) for switch operation sequence S2S1S3 S4.

with zero voltage and zero current. The main draw-back of these circuits is that 3 must be a bipolarswitch; C is left in either the up or down state.Switches S4 and S5 are still unipolar. At the presenttime, no bipolar switching element capable of meetingthe breakdown voltage and frequency response limita-tions imposed by this circuit have been announced;a possible bipolar switch is that shown in Fig. 5(d).

In many cases, it is desirable to obtain more than onebias voltage on a crystal. This is the case, for example,when more than one color of light is to be deflected;since the half-wave voltage is a function of wavelength,it may be desirable to have either a continuum or adiscrete set of voltages to apply to the crystal. Onemethod of doing this can be exemplified by the circuitof Fig. 3(c). A modulating voltage can be used toamplitude-modulate the Hartly oscillator. This samevoltage, suitably amplified or transformer-coupled,can be used in series with the bias supply in the tankcircuit. Then the peak to peak excursions of the crystalvoltage will follow this modulation. Transformercoupling of a modulating voltage in series with thebatteries of Fig. 4(a) will have the same effect. Circuitsare shown in Figs. 6(a) and 6(b).

If only a discrete set of voltages is required, as isfrequently the case, the circuit of Fig. 7(a) can be used.Here only a single power supply is required; differentvoltages are obtained by switching in different primarywindings. The primaries have different numbers ofturns, but all have the same coefficient of coupling withthe secondary winding. If the circuit is analyzed, itis found that the capacitor voltage is given by

V = Ek(L2 /L)'/2 cos[L2(1 -k 2)C] -'1t,

where E is the supply voltage, LI and L2 are primaryand secondary inductances respectively, and k is thecoefficient of coupling between primary and secondary.Here again we take for granted that the switches areoperated at the resonant frequency. Typical wave-forms are shown in Fig. 7(b) for the case in which thereare two primaries whose inductances differ by a factorof four. In this circuit, the switches do operate withzero voltage across them; however, there is a nonzerocomponent of current at these times because of theleakage inductance of the transformer.

Summary and ConclusionsIn this paper, a number of circuits for electrooptic

switching have been described. Practical results havebeen obtained that demonstrate the feasibility of thebiased resonance approach to reactive load switching.

The greatest difficulty in exploiting these circuits isin the procurement of suitable high voltage switchingelements; such elements are either unavailable or quitecostly. These elements, whether they are two, three,or more junction types, must be capable of withstand-ing high voltages at high frequencies; yet they need not,in general, support any substantial current or even havecurrent gain capabilities. At the present time, VCBO'sof about 1 kV are available. This should be increasedby at least a factor of four in order to obtain reliableoperation with reasonable light transmission efficiency.If laser-based printers, displays, memories, or thelike are to become economically feasible, such devicesmust be readily available at low prices. The emphasismust be on these components as well as on the laseritself.

The author is indebted to G. A. Hellwarth for manyof the ideas on which these circuits are based. Theencouragement of E. J. Skiko is deeply appreciated.To Paul Frick, who built and tested the high voltagecircuits, and to Harold Fleisher and Werner Kuleke,whose faith in the basic principles never wavered. adebt of gratitude is owed.

November 1966 / Vol. 5, No. 11 / APPLIED OPTICS 1781