TIl{ approximation of 110nliwar flu/(ti()1J~ 'n arlalog eonlpuffrs i' (llrrodifJ a con plir{hui bIn tans nf fmution gUtfrators vf dt.tfuOll tIJPU!, of uhie/! the diode fun tior guurator is I O. t eOmmf)]1ZI tI (d. C. J. Nisson Disa(/1 (lI/tag£;'; of tlH' an I nt/ tr tYPfS of s {ti, (;quipmUlt art Ol'aCOHlt to a {flrge f.rit nt blJ tid triode­ diodt flme/ion genua for da'doped ftl .1P L for u; ill tlu /.aborator /s analog (on puta farilitUs. A Triode-Diode Function Generator

o "build a better mousetrap" is the goal of in order to study such a system completely it is T every engineer. In analog computers, the necessary that the computer generate the correct "mousetrap" may take many forms, but the device nonlinearities. These, unfortunately, may differ that has had the most imagination applied to it considerably from one another, depending upon is the general-purpose function generator that can the system. It is therefore desirable to have a single simulate, with a high degree of accuracy, the function generator that will generate all possible nonlinear functions that are characteristic of types of functions, or at least all of one class. modern physical systems. Two recent entries in The breakdown below shows the groups of this field are the triode and triode-diode gener­ general-purpose function generators now In use.

ators, the principle on which they are based having GROUP ACCURACY BANDWlDTH been described first by L. V. Medredev et aU Electromechanical high low The reason for so much activity in the search Photoformer low high for more efficient function generators is that Gain-swi tching medium-high medium Digi tal or hybrid medium-high medium-low existing devices suffer from such disadvantages as limited frequency response, low precision, ex­ The gain-switching group contains the popular cessive drift, limited range, or difficulty of ad­ diode function generator and the triode and triode­ justment. Diode function generators, which are now diode function generators. the most generally used, are limited in the change of slope of the output that can be generated without Gain -Switching Function Genera tors seriously increasing drift and noise. Triode function Gain-switching function generators use as their generators are essentially unlimited in maximum basic unit an operational amplifier whose closed­ slope and the change of slope. loop gain is changed abruptly at selected values A triode-diode function generator that overcomes of the input voltage. Thus, the output voltage as a the more serious drawbacks of earlier designs has function of the input appears as a continuous recently been developed, built, and evaluated at curve made up of straight-line segments. Members APL for use in the Laboratory's analog computer of this group can generate only single-valued 2 facilities. The principle of operation, based on functions of one variable. that of the triode function generator, together The operational amplifier is the heart of the with some of the characteristics of this equipment, function generator as well as being one of the will be briefly discussed. Operation of the diode most important parts of the analog computer. and triode function generators will be explained I t is a device whose output voltage is equal to the as an aid in this description. input, multiplied by the negative ratio of the feed­ One of the major uses of the analog computer is back and input impedances. When these imped­ to simulate a physical system, as, for example, a ances are resistors, as shown in Fig. 1, the closed- missile control loop or guidance system. Because most physical systems are by nature nonlinear,

1 L. v. Medredev, A. A. Feldbaum, and L. N . F itsner , "Single-Input Nonlinear C onverters, Automa.tion and Rem ote Control, 18, Oct . 1957, 945. 2 C . J . Nisson, "An Analog T riode-Diode F unction Generat or," U n­ published Master 's thesis, U niversity of Maryland, 1963. Fig. I - Diagram of an operational amplifier.

J uly - A Ilgusl 1963 15 loop gain (the ratio ofy to x, the output and input One of the major disadvantages of this function signals, respectively) is equal to the negative ratio generator is that to generate a steep slope or a large of Rf to R in . In gain-switching function generators, change in slope, input resistors must be made the effective ratio of Rf to R in is changed as a small. However, because there is a minimum value function of the input voltage amplitude by the allowable as a result of the limited current capa­ operation of voltage-controlled switches. This has bilities of the amplifiers, there will be a limit on the effect of changing the slope of the input-output maximum slope and slope change. For most com­ curve each time a switch is operated. In the diode mercial diode function generators the limit on function generator, the effective value of R in is slope change is between 5 and 20 volts per volt. usually changed (some functions can be generated by changing Rf). In the triode function generator, Triode Function Generator Rf is varied, whereas the triode-diode function Consistent with the function generators of its generator combines both techniques. class, the triode function generator produces a piecewise linear output by changing abruptly the Diode Function Generator gain of an operational amplifier as a function of the input voltage. In this case, triode switches are The general-purpose diode function generator used to change the feedback resistor. uses an operational amplifier as a summing device Operation of the triode switch is quite different to add several voltages in order to approximate from that of the diode switch. The triode switch some desired curve. These voltages may consist of a is a simple triode amplifier driven from beyond constant voltage, a linear voltage, and several cutoff to saturation. It approximates a single-pole, piecewise linear voltages as a function of the input three-position, voltage-controlled switch because signal x. The piecewise linear terms result from the (1) its plate voltage is at ground when the tube is operation of biased diode switches that either cut off, (2) it varies linearly with the input when connect or disconnect input resistors to voltage it is conducting, and (3) it is clamped at -100 v as sources whose values are sums or differences of it approaches and after it reaches saturation. Vi and x. The Vi terms are constant voltages, or A diagram of the triode function generator is biases, of either polarity, which are added to make shown in Fig. 3. In this diagram, Al is a high-gain­ the diode switches operate at desired values of chopper, stabilized, DC amplifier whose third x; The slope of the output in any piecewise linear stage is one of the switching triodes T i in the second region may be defined by the ratio of ~y to ~x. In position. In this circuit, the plate of the switching terms of Fig. 2, this slope is equal to the negative triode acts as the output of the gain-controlled ratio of Rf to Rin, where R in = R 1R2/(R2 - R 1 ); amplifier. Its voltage is equal to - (Rfi/ R 1) (x + Vi), RI and R2 are the effective parallel combinations where Vi is equal to RI multiplied by the sum of input resistors from and - respectively. x x, of all currents flowing into the summing node of At each value of x, at which a diode switch con­ Al from fixed sources; i.e., Xo/ Ro - 100/ Rfl - ... nects or disconnects an input resistor Ri (one of 100/ Rf i- 2 - 100/ Rfi- l . several resistors in RI or R 2), the slope of the output The switching triodes are controlled by the changes by the amount . The direction of Rtf R i tapped divider Rd so that they operate sequentially. the change in slope depends on the polarity of When x has its minimum value (Xmin), the plates the connections of the diode in question and on of all switching triodes are at ground potential. the polarity of its biased source. A combined When x is increased slightly, the triode TI whose biased diode and input resistor is necessary for grid has the most positive bias will start to conduct, each change in slope desired. and its plate will operate as the output of the gain­ controlled amplifier. When x is increased, this + 100 voltage will decrease linearly until it is clamped at -100 v. As x is increased infinitesimally beyond this point, the second triode switch will start to conduct and have its turn as the output stage. This R procedure will continue as x increases until all triode switches have reached - 100 v. The output voltage y will be the sum of the voltages from the switches after they have been multiplied by the associated Ki factors. When x has its minimum value, y will equal 100 Ko. As x Fig. 2- Diagrarn of a diode function generator. increases, y will vary with piecewise constant slopes

16 APL Technical Digest -100 V This function generator has the advantage that very steep slopes can be generated by making K i unity and RJ i large. By disconnecting RJi' the slope of the i tk segment will approach infinity, making it possible to generate discontinuous functions. This type of generator is also more convenient to adjust because the slope of each segment is in­ dependent of other segments. Some of the dis­ advantages are added complexity and the need for a special amplifier Ai.

-1 00 V Triode-Diode Function Genera tor T -100 V "7 By combining the techniques used in the diode ~- eo! I and triode function generators, additional slope --r---potentiometers and closing toggle switches. Given determine the length of the ith linear segment of a set of desired breakpoints and slopes, a 20-seg­ the output voltage. ment output function can be set up and checked with a digital voltmeter in 15 minutes. The potentialities of the triode and the triode­ y diode function generators are good because of their ability to generate steep slopes and the rela­ tive ease with which they may be adjusted. Errors due to drift, noise, and reduced bandwidth are generally slightly greater than for the diode func­ tion generator, depending somewhat on the func­ tion being generated. The principle of changing the feedback resistor, as used in the triode function generator, might easily be extended to equipment using transistor operational amplifiers. Here, the triodes could be replaced with common emitter amplifiers. In fact, both PNP and NPN transistors might be used Fig.4-Triode-function-generator output versus with plus and minus reference voltages, making input. bipolar feedback possible.

.July - August 1963 17