64 IRE TRANSACTIONS-ELECTRONIC COM'PUTERS June

A Diode Multiplexer for Analog Voltages*H. J. GRAY, JR.t, M. RUBINOFFt, AND J. TOMPKINSt

Summary-A diode multiplexer switch is described for time- because of high degree of complexity or insufficient ac-sharing 64 analog voltages in a digital computer application. Apart curacy. On the other hand the diode multiplexer de-from its relative simplicity and economy, the multiplexer character- cracy. On the other hand, the diod autiry de-istics of microsecond switching speeds, maximum settling time OI scrbe ei.tIsp erprv tobe aeseatifa tor answe133 microseconds for a 10-volt operating range, and accuracies of to the problem. It bears a close resemblance to a bi-better than 1 per cent full scale are confirmed both by theoretical directional switch, used in a different application.'equations and by experimental results. Static characteristics of a number of similar structures

are discussed elsewhere.7INTRODUCTION

A MULTIPLEXER is a switching device for con- DESCRIPTION OF MULTIPLEXERnecting any one of a number of wires to a single The system as used is diagramed in Fig. 1. Thewire. For example, when a number of analog operation of the multiplexer can be better understood

voltages are to be transmitted over a single wire to a by reference to Fig. 2, which is derived from Fig. 1 by anumber of remote points, a "many-to-one" multiplexer horizontal bisection along a line joining input to output.is used to connect each voltage in its turn to the nearend of the wire, and a "one-to-many" multiplexer is +150

used to connect the far end of the wire to the remotepoints one at a time. A single-pole multiposition switchis clearly a primitive multiplexer, and when used within a o

its limitations, a highly effective one.In the design of a digital real-time simulator' it

proved advantageous to provide for the conversion of TO 5 4 /5many digital signed magnitudes into analog voltages. CONVERTER 3

It was proposed to do this by time-sharing one digital- C-.02 S f

to-analog converter by using a multiplexing device.The requirements to be fulfilled by the multiplexer in CHANNEL d o I

question were as follows: sIENLIOOK

1. Simplicity sufficient to assure economical multi-plexing of 64 voltages; -10

2. Speed sufficient to serve as a component in a real-time simulator. 100 microseconds was set as a goal TO OTHER CHANNELSfor switching time; AS ABOVE

3. Accuracy of at least 1 per cent of full scale withzero drift not to exceed 0. 1 per cent per hour; Fig. 1-Multiplexing system.

4. Compatibility with other simulator components, Assume that -5 . e .5 volts, -5 . v .5 volts, andsuch as the computer gating circuits and instru-

ment servoamplifier serving as outputla, b < -5 volts, c, d > 5 volts. Then 1-4 are nonconduct-investigatederiotlod

ing. The charge on capacitor C will leak off through theExisting multiplexing switches were reverse impedance of diodes 1 and 4. In the digital real-

none of which was satisfactory for the application either time simulator under consideration, C is recharged

* Original manuscript received, October 1, 1954; revised manu- through the multiplexer at 50 millisecond intervals.script received, January 22, 1955. This work was done under contract Based on leakage figures for silicon junction diodesNonr(551)02 sponsored by the Office of Naval Research, Special (<10-8 amperes at - 10 volts) and allowing for theDevices Center, Port Washington, N. Y.

t Moore School of Elec. Engrg., Univ. of Pennsylvania, Phila- amplifier load on the output, leakage current does notdelphia, Pa. exceed 4X10-8 amps. (Note in Fig. I that the diodeI W. H. Dunn, et al., "Universal Digital Operational FlightTrainer," Univ. of Pennsylvania, Moore School of Elec. Engrg., Res. leakage currents oppose one another.) To assure less thanDiv. Rep. 54-45; June 30, 1954. 01vdit( e et u olaaei srqieIta

2F. F. Roberts and J. C. Simmonds, "Multichannel communica- 0. rf 1prcn)detolaae ti eurdtations system," Wireless Eng., Part II (Pentodes, Cyclophon), vol. 22, Itt 4 X 10-8 X 50 X 10-ipp. 567-580; December, 1945. __>__ 8___________

3A. M. Shellet, "The magnetically focused radial beam vacuum C >- = 2 X 10- .tube," Bell. Sys. Tech. Jour., vol. 23, pp. 190-202; April, 1944. - V0.1

4Roberts and Simnmonds, loc. cit., Part I (Cyclophon), vol. 22, pp.538-549; November, 1945. 6 B. Chance, et al., "Waveforms," Rad. Lab. Ser., McGraw-Hill

6J. L. H. Jonker and Z. van Gelder, "New electronic tubes em- Book Co., Inc., New York, N. Y., vol. 19, pp. 374-375; 1949.ployed as switches in communications engineering," Philips Tech. J. Millman and T. H. PuckeLtt, "Accurate linear bi-directionalRev., vol. 13, Part I, p. 49, Part II, p. 82; 1951/1952. diode gates," PROC. IRE, vol. 43, pp. 24-37; January, 1955.

Authorized licensed use limited to: IEEE Xplore. Downloaded on May 13,2010 at 11:52:15 UTC from IEEE Xplore. Restrictions apply.

1955 Gray, Rubinofif, and Tompkins: A Diode Mlulhiplexer for Analog Voltages 65

Note further that the circuit in Fig. 2 (a) is a positive rearrangement,"AND" circuit and Fig. 2 (b), a negative "AND" cir- Cdv/dt =-I tanh (av/2) (2)cuit. Hence if a and b are raised above 5 volts, V will riseto a value slightly exceeding e. Similarly, when c and d -tan1h (av/2). (3)are lowered below -5 volts, V will fall to a value slightly We are concerned only with those cases when vo, thebelow e. Thus, in Fig. 1, if a and b exceed 5 volts, and c initial value of v, is of the order of 1 volt. Then avo»>1,and d are below -5 volts, V will assume a value almost sinh avo e-avo and (2) has the solutionequal to e.

V Zz (2/a) sinh1 {(1/2 exp [(to-t)]} (4)+ ~~~~~~~~~~~~wherea- = aI/2 C and to =cvo/I.

R Case 1: t.<toa o iFor t<to, except for values of t very close to to, a goodb do 4 1approximation of sinh'I may be had by keeping only the

oi 0 V 40-19 ~~~first term of the expansion2 34

e e R 1

I I I ~~~~~~~~~~~~~ ~~~~~sinh-1x=log2x+ 2 -x ;x> 1. (5)(a) (b) --

Fig. 2-Derivation of diode bridge. Hence

Both halves of the multiplexer are needed. The half v V - PI/C; t < to, vo > 0. (6)shown in Fig. 2 (a) charges the condenser C when v is This corresponds to the interval when only diodes 1 andinitially below e; the half shown in Fig. 2 (b) discharges 4 are conducting.C when v is initially above e.

Cs :t=t

Since the multiplexer is derived from conventional Cs :t=tgating circuits used in digital computers, some of the For t = to, (4) becomesgating needed to select a specific instrument can be vt)=(/)sn- 12 .92aperformed within the multiplexer. A double coincidence vI)=(/)sn1( )=092aselection system has been assumed for the preceding. This is only 0.0364 volts for the 1N138A.

DETERMINATION OF SWITCHING TimE Case 3: t > to

The selection of a new channel is followed by an inter- Here it yields a good approximation to keep the firstval during which v makes the transition to voltage e. term of the power series expansion of sinh'1. HenceAn approximate determination of this interval will now V (i/a) exp [-oa-(t -to)]; t > to, Vo > 0. (7)be obtained in closed form.A silicon junction diode such as the 1N138A has a

forward voltage-current characteristic such that in therange of interest i =i3 exp av where 13 and a are con-stants. This is quantitatively correct for the forward v

characteristic of the 1N138A if a=26.5 and f3=6.25X1012. The same equation may be extended to apply toLi e

o

the reverse characteristic in that both the true reverse 4

current and the current given by the exponential func-tion are negligible. V

Consider the simplified equivalent circuit in Fig. 3.The input voltage is assumed for simplicity to be zero.

This does not incur any loss of generality. All diodes Fig. 3-Equivalent circuit.have been assumed identical for the analysis.

The circuitequations are ~The decay time constant for the values in Fig. 1 isCdv/dt + 13 exp [a(v - V2)]-1 eXp [a(vi - v)] 0 1/la = lj.ts. The value of to is correspondingly 133 Mis for a

Authorized licensed use limited to: IEEE Xplore. Downloaded on May 13,2010 at 11:52:15 UTC from IEEE Xplore. Restrictions apply.

66 IRE TRANSACTIONS-ELECTRONIC COMPUTERS June

Equivalent circuits derived from (6), (7), and (8) are equations of Fig. 3 may be solved to yieldgiven in Fig. 4 for the case when the generator has an v Z (vo/2a)(-a, + a2+ a3-4)internal resistance, Rg.

+ (1/2a#)(-#1 + 02 + 03 - 4) + * * *, (9)e2/_ I v e v where vo is such that 1/2 = /.3 exp (avo).

lg rn llFor vo=0.7 volts and a=26.5, which are reasonablefRs 9iRS } 1 values for silicon diodes in the present application, (9)l vs ~~c l g X ^^c becomes

TI I becosv| < 1.4a+0.07b,le-vlj> le-vJ4 where a and b are the maximum anticipated per cent

variations in a and 3, respectively.Fig. 4-Equivalent circuits.

EXPERIMENTAL RESULTSAlthough the last of (8) implies that il goes to zero, The diode multiplexer circuit was breadboarded using

this is not usually so, as demonstrated for a multiplexing four unmatched 1N100 germanium diodes in the multi-switch in steady state (Fig. 5). Solution of the nodal plexer bridge. Despite the random choice of diodes the

error voltage between e and v was less than 0.05 voltover the + 5-volt range.The switching time to swing the output over the full

Rrange of 10 volts was found to be 125 ,us. This wasmeasured by applying a 10-volt p -p sine wave to theinput and observing on an oscilloscope the frequency

e '/V (4 kc) at which the triangularly-shaped output waveinitially became attenuated.

R2 CONCLUSION

|E2 A multiplexing switch has been described which isrelatively inexpensive, which is capable of achieving

Fig. 5-Equivalent circuit in steady-state. accuracies of 1 per cent of full scale or better, has lowdrift, and is microsecond fast. The only fundamental

equation for this circuit yields limitations on the speeds that might be achieved seem

[1 1 1 E2 E1 to be the diode capacitance and recovery time, whichil=i+ et-+- +--R for the silicon diodes in the system described were re-

-R, R2 - R2 RI spectively about 10 ,u,f and 1 ,us.Note there is a current offset i+E2/R2-Ej/R1 and aneffective input resistance R1R2/ (R1+R2).The static error that results when the diodes are not The authors are very grateful to Mrs. E. L. Fishl who

perfectly matched can be estimated. The steady-state typed the manuscript.

C _~5

Authorized licensed use limited to: IEEE Xplore. Downloaded on May 13,2010 at 11:52:15 UTC from IEEE Xplore. Restrictions apply.