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FIGURE 9ie relatively low current devices, asompared with some Other non-linearesistors.Like the. Thyrite resistor, the for-

iarcoondueting diode is capable ofistorting an a. c. current waveform

ind occasionally is used to accen-tuate harmonic. The requirelnentis that the diode current magnitude

be such as to operate the diode inits most non-linear region. Thus, thsimple series onsection of a diodin the plate or grid lead of an oscillator or amp ifier can aecentuatharmonic content of the current wave.form when this type of operation r.required. .An example, is the distortion of waseform of a standard

TYPE BAGSoo AMPERE

0 10 2,0 30VOLTS

STATIC D.C.CHARACTERISTIC OF MINIATURE FUSE

FIGURE 10

10 0,00 0

1000

100

102

4, VOLTS

STATIC FORWARD RESISTANCE OF GERMANIUMDIODE

FIGURE II

frequency oscillator to produce high -order harmonies for calibration pun

BIBLIOGRAPHYI-THYRITE, A G. D RESISTANCE

MATERIAL. (Booklet). Genet)1 Electric Company. Scheme,

tady, N. Cl.2-CONDUCTORS WHICH DO NOT

OBEY OHM'S LAW. Dunbar.Gettotra! Ea/Tarte Review, Vol. 24,p. 153.

CALCULATION OF' CIRCUITS CONTAINING THYRITE.Brownlee. G,teral Electric Re-

VoI 37 p. 175.4 SILICON CARBIDE NON -0H51 -

IC RESISTORS. Ashworth,Needham, and Sillars. Journalof the Imlitulion of ElectricalEngine en; Vol. 93, No. 69, p.385,

5-APPLICATIONS FOR THYR1TERESISTORS. Rufus P. Turner.Radio mid Television Newslannary 1951. p.

t-THERMISTOTES. (Booklet). Wes-tern Electric Company. New

7-1'ROPERTIES AND USES OFTIIF,RMISTORS - THERMALL)( SENSITIVE RESISTORS. J.

A Becker, C. B Green, and GL Pearson Eleetneal Engle/denno November 194ti

8-THERMISTORS OS COMPONENTS OPEN PRODUCT DE-SIGN HORIZONS K P Dow.ell Electri,cal Mantrfacturitty.August 1948

- CARBOLOY IHERMISTORS(Booklet). Bulletin Nil. TH 5 ofthe Carboloy Department of Gen-eral Electric Company Detroit,Michigan

10 GERMANIUM CRYSTAL DI-ODES. Bulletin EC 36C Syl-vania Electric Products, Inc, New

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WILKORRESISTORS

WILKOR means precision -type resistorsmade with matchless accuracy ;ad in-tended for circuits calling for the stabilityof wire -wound resistors with the markedeconomy of sorban resisters. Widely usedin wet equipment and laboratory instru-

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A EROVOX CORpoRATION1AV

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EROMLA:

H 0100105°IRAN, N Y.

ty al S 42. Si Wass* is. N s CaitiS Ans., Y Is Rs.... AMY,. CANA. CO 4*.

Editors of aseN

sishb proper credit to

VOL 23 NO. OCT. NOV., 1953

oublished by the

to bring to the Radio

seta., for electrical

Non -Linear ResistorsBy the Eng/Redoing Department ekercega, Corporatioe

ANEW electrical devices ate dirstinguished by their non-linear

current -vs -voltage characteristics of amagnithde stRiDently great to Affectperformative Often this phenomenon is a choracteriRic. For example:

r...linearity is observed in Dm platecharucWristie of a vacuum tube un-der certain operating conditions, theextremity of o dibile tube evens,iron -cored inductors operated in theregion of saturation, and in biasedcapacitors havin% special ceramicdielectrics (dielectric amplifiers).These are only a few examples. The

on linearity of certain 2-termina1 deWves such as resistor also may Srbe

employed to modify the operatingterhciics of some circuit, The.

non-linear S iS tors do not obeythe simple relationship = EI ofOhm's Law.

Simple non-linear resistors are usedin oscillators, wave shaping netwOritkvoltage regulators, current regula-tors, constantutput potentiometersand voltage dividers. voltage -selectivecircuits, amplitude limiters. frequencymultipliers, surge suppressors, etc.Their use in electronics i5 increasing

new, requirements for nonlinearcurrent voltage response arise.

This article describes the generalcharacteristics of some common 2terminal non-lMear resistors of sev-eral classes. In some instances, .will be seen. these devices have otherprime uses and their application asnon-linear resistors secondaryTypical applications will be hown

lYyVP trite registers were introduced

by General Electric Company. andwere applieil in the electric powerheld some numlies 01 years before en-tering electronics Thyrite resistorsare made of silken carbide, boUntiwith a filler, then pressed and firedat high tenmerature 'They are fabri-cated in COe form of pigtailed rods( identical to 'radio resistors"), discs.ykshers, and stacks. Small unilssuitable for electronic applicationsore ruPPlied up to 10 watts powerrating (ontinuous)

The nin-linearity of the Thy rite e-sistor is expressed by I - kEY,, whe1 is the instantaneous a terry ling ordirect current (ampere ), E the n-

stantancous applied voltage, k a constanl (amperes at 1 volt), and n anexponent between 3.5 and 7 governedby the manufacturing process, Figure1 shows a set of fypical Thy like cur-rent -voltage curves for several typesof G. E. Thyrite resistors. The curvefora conventional 1-megohm linearresistor is plotted for comparison.From these MYVOS it may be seenthat large current changes result fromsmall applied -voltage changes.

Figure 2 is a plot. of resistance iscurrent for resistor B from Figure1 Note in Figure 2 that a change

10,6011 to 1 in current flowingthrough this resistor changes the re.sista prnce of the latter apt xi atoll375:1.

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AMPERESCURRENT -VOLTAGE CHARACTERISTICS OF THYRITE RESISTORS

FIGURE I

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THYRITE RESISTANCE VS CURRENT LEVEL(RESISTOR 8 FROM FIGURE I.)

FIGURE 2Thyrite resistors have the ad an

age of operating in both a c. and d.. circuits. Any rectification effectsre negligible. (Figure 3 shows a

typical static positive -negative con -tiducon curve). High -frequency a.

. operation of Thyrite is possible,he limiting factor appearing to beapacitance. It should be noted, how-ver, that in a. c. operation the non

linearity of the Thyrite volt-amperecharacteristic causes distortion of the

,

ii t

CURRENT

STATIC THYRITECONDUCTION CHARACTERISTIC

FIGURE 3

uwent waveform. Figure 4 showhe distorted current wave aceomp-flying a sine wave of applied volt-

age. Observe that odd -ordered haour are prevalent. This phenom

non is utilized in simple frequencymultipliers and harmonic amentuaors.

The temperature coefficient of Thyits resistance is negative in sign andare front -0.4 to -0.73 Pareeo

per degree Centigrade in the range0 to 100°C

Figure 5 shows several typical cir-oils 'utilizing the properties of Thy -

rite resistors.

Figure 5(orA) is a simple voltageregulator compressor for smooth-ing variations in supply voltage. Thefluctuating input voltage producesfluctuating current which flowsthrough the Thyrite resistor (T) anda linear limiting resistor (R) inserMs. Fluctuations in the resultingvoltage drop across the Thyrite re-sistor are considerably lower in am-plitude than those in the supply volt-age, due to the non-linear E/I rela-tionship in the Thyrite. It should benoted that a voltage reduction un-avoidably os because of poten-tiometer actionccur between R and T.

In the expander circuit in Figure5(5), the opposite action is secured,Small fluctuations in applied voltageproduce large fluctuations in cur-rent through Thyrite resistor T. Thesecurrent fluctuations in turn producea fluctuating output -voltage dropacross R. Since the resistance of Rmust be small with respect to thatf T, voltage divider action betweenhe Thyrite and linear resistance legsf the circuit produces a drop in volt-

age level. Several TR sections maybe cascaded, as shown in Figure 5(C),o secure additional expander action,

at the expense of course of furthervoltage division in each section.

Current resulting fromsine -wove of Offilliedvoltage

AC.DISTORTION DUE TO THYRREFIGURE 4

Figure 5(D) shows a potentiometeror voltage divider with Thyrite sec-

tions. The non-linear E/I charac-teristic of the Thyrite sections yieldsa nearly constant output voltage ateach tap, althoUgh supply and loadcurrents are variable.

For efficient operation of the cir-cuits shown in Figures 5(A) and (D),the Thyrite current must be highwith respect to the output load cur-rent. In Figures 5(B) and (C), cur-rent in resistor R must be high withrespect to output Mad current.

Figure 0(E) shows how a Thyriteresistor can be connected into a cir-cuit to accentuate harmonics and actas a simple frequency multiplier. Al-ternating current is fed into the cir-cuit and undergoes distortion in pass-ing through the Thyrite. The tunedcircuit, LC. is adjusted to the desiredmultiple frequency. It has beenshown already in Figure 4 that oddharmonies are favored by this typeof operation. The Thyrite frequencymultiplier thus is most practical fortripling, quintupling, etc, The Thy -rite resistor, is a dissipative element,however, and its insertion into a cir-cuit in them anner shown in Figure5(E) results in some power loss. Inapplications where a considerableamount of power is available, the rel-ative simplicity of the Thyrite fre-quency multiplier can offset its un-avoidable power absorption.

ThermistorsThe thermistor, a product of re-

search by Bell Telephone Laborator-ies and manufactuwel by WesternElectric Company, is another inter-esting non-linear resistance device.Its action results from internal heat-ing effects in special materials.

Thermistors basically are thermal-ly -sensitive resistance devices. Theyare manufactured in the shape ofrods, dims, beads, wafers, and flakesand ere made of various mmicondue-lm materials. L1ke Thyrite, the ther-mistor can be used with either a. c.or d. c.

Figures 6 and 7 show two import-[ response curves describing then

mistor action. From Figure 8, it isseen that the voltage drop across thethermistor increases non -linearly andrapidly with current flow up to aPoint beyond which the rate of in-crease falls. Finally, a peak is reach-ed and beyond this latter point thevoltage drop decreases with increas-ing current, displaying negative resistance. An interesting side obser-vation is that this negative -resistanceproperty has been utilized to obtainlow-frequeney tubeless oscillation andamplification with thermistors.

(A) Voltage Regulator;Compressor

AC DCINPUT

(DI Stabilized PolentioVoltage Divider.

In Figure 7, the plot shows how atparticular applied voltage internal

heating causes the magnitude of the,mister current to vary as a functionf time. This property has been util-

ized in various simple time -delay de.ices.Figure 8 shows several simple aim

sits employing thermistors. In allxcept Figure 8(A), a small current

limiting resistor, r, is Indicated, Fig-ure 8(A) is a time -delay d. c. relayaxed upon the action illustrated by

the curve in Figure 7. Some secondsfter the switch, S, is closed, the dr-sit current rises to a value highnough to close the relay. The de -ay interval depends upon thermistorharacteristics and supply voltageevel, and can be adjusted to msaextent by means of linear series reistance.Figure 8(B). he he circuit of a reg-

ulator for supply voltage variationnd issomewhat similar to he Th -

rte voltage regulator. Its operations based upon the non linearity o

the thermistor which results in smal -

MEC

°MILLIAMPERES-mt.

STATIC DC. CHARACTERISTICOF THERMISTOR

FIGURE 6

OUTPUT %P DC

) Ex pa ad er

OMMONer, (E/ Frequency Multiplier, HarmonicTYPICAL THYRITE CIRCUITS Accentootor

FIGURE 5

R3 OUTPUT

(C) Cos cod E x po oder

er variations in thermistor voltagedrop than the fluctuations occurringis suply voltage and current.

Action of the limiter circuit, shownin Figure 8(C), is similar to that ofthe voltage regulator, amplitude ex-cursions in the input signal being re-duced in the output without dippingor dieing action.

Operation of the thermistor ex-pander circuit, Figure 8(D), is theopposite of that of the limiter. Thethermistor and load resistor are in-terchanged in position, output beingtaken across the resistor. A smallsignal -voltage change produces alarge thermistor current change anda large mltage change across the out-put resistor.

A voltage division takes place inthe circuits shown in Figures 3(R),(C), and (D), as the result of poten-tiometer action between the ther-mistor and the linear series resistor.Because of this action, the absolutelevel of the applied voltage is re-duced in the Output.

Figure 8(E) shows a Imkouttypeswitching circuit employing thermist-ors, In each leg of the circuit, r isa load resistor or represents somedevice, such as a relay, which is tobe actuated by current flowingthrough the associated thermistor.The supply voltage and the value oflinear series resistor R are chosensuch that this resistor will supportthe current of only one leg beforeits voltage drop becomes excessive.When one switch may, 51) is closed,the associated thermistor "breaksdown" allowing current to flowthrough and operate the associateddevice, rt This lowers the voltage

at the inside of R, so that no othethermistor cart "fire." Only after Sis opened, can either of the odecircuit legs be operated. Operationof any one thermistor leg thus lockout all of the other legs. An arrangemant of this type would enablenumber of devices having similevolt-ampere characteristics to be con-nected across a single voltage pairbut with only one device operable aa time.

Fitionedary DevicesThe tungsten -filament incandes-

ent lamp is fairly well known as aon -linear resistor in which currentange lags a corresponding change

d applied voltage. Up to the pointt which heating effects begin to evi-

dence, the filament wit -ampere char-cteristic is linear, or very nearly so.

The non-linear region of lamPfila-meet resistance has been utilized in°nage-Stabilization bridges, simpleegulators, and allied devices.In a common application, the lamp -

type resistor is used as an automatic

r° SECONDS-.

TIME -DELAY ACTIONOF THERMISTOR

FIGURE 7

egulator of degeneration voltage inow -distortion, RC -tuned oscillators.

A typical circuit is shown in Figure

In Figure 9, the lamp (Re) is theathode resistor of the first pentode,

V,. Feedback current from the out-put of V. flows through capacitor Co the frequency -selective RC networkn the grid circuit of Vt. A portion

of this current also flows through re-istor R, and the lamp, Re, establish-

ng a negative feedback voltageacross the latter, The lamp resist-nce is low when the feedback cur--ant is small, and is high when this

current is large. Thus; strong °sell-ations result in large amounts ofnverse feedback voltage across Rmel

this degeneration in turn reduceshe amplitudu The opposite also is

true; at weak oscillation amplitudes;here are lesser amounts of Mg..ration, and gain through the two-Libe circuit automatically rises. The

net result is uniform amplitude of os-illation.Thermistors also are used occaa

malty in some Retuned oscillatorcircuits to stabilize oscillation ampli-ude.

Small filamentary, low -currentuses exhibit a type of non -linearity

somewhat similar to that of the tung-sten filament. Figure II shows thestatic d, r. volt-ampere characteristie of a sample Type 8AG 10-milliampere LIttelfuse. In this instance, re-sponse is linear from zero up to the0.8 v 4 ma. point Beyond this, thenon -linearity is apparent.

When d, c. -biased to a point with-in the square -law region of their non -linearity, such fuses often are usedas bolometer-type detectors in micro -

work. This provides an ex-trentely simple and inexpensive de-modulator at frequencies up to manyhundreds of megacycles.

Diode -Type ResistorNon -linearity in the forward can

duetion characteristic of the german-ium diode suits this simple compon-ent to use as a non-linear resistor inapplications within its current capa-bilities. While the reverse-cmduc-tion (bac.current) characteristic ofthe diode also is non-linear, it doesnat in general offer the same possi-bilities of application that are avail-able with the front conduction .

Figare 11 shows a plot of forwardresistance vs applied voltage for ahIgh-conduction-type germanium di-ode. Here, the polarity of the applied

voltage is such that the anode of thediode is positive. Diodes may beconnected in series, parallel, series -parallel, and parallel -series to obtainmany attractive non-linear resistanceeffects.

Various portions of the forwardvolt-ampere characteristic of the ger-manium diode exhibit square law,logarithmic, and finally approximate-ly linear relationships between E andI. By operating the diode in a de-sired one of these regions, the panUvular corresponding portion of thecurve can be utilized to correct ormodify the Ed characteristic of an-other circuit. For example, a linearmicroammeter may be converted in-to a square -law instrument by Mingthe forward resistance of the diodeas the meter series resistance (muttiplier).

Diodes suffer somewhat in comparison with other 3 -terminal nordinearesistors because the diode is a rectifier. This limits application in mmecases to direct -current use only.However, small a. c. signals may besuperimposed upon a U. c. forwardbias current applied to the diode, thetwo currents being so proportionedthat the net diode voltage never becomes zero or negative. Diodes also

IA) Time -Delay Relay

0

AC DC

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(El) Voltage Regulator

OUTPUT

0

(DI Expander

OUTPUT OUTPUT

TI 0Te 0

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TYPICAL THERMISTOR CIRCUITSFIGURE 8