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IEEE T R A N S A C T I O S S O S AUDIO
VOL.
XU13,N O . 5
SEPTEMBER/OCTOBER
Voltage Controlled Attenuators Using Field Effect Transistors GOSLING AbstractA FET operated so that channel pinchoff is avoided behaves like a voltage controlled variable resistor. This paper considers a “voltagedivider’’ attenuator using the devicein this way. Attenuation (in decibels) varies almost linearly with control voltage over a range. Distortion may be less than 0.01 percent, temperature effects are usually negligible, and the network can operate satisfactorily up to a few megahertz. Circuits of this kind demand a FET having special characteristics.
w
I
OF’;
+“PINCH
REGION.
IXTRODLCTION
H E N USED as a n amplifierthe
fieldeffect transistor is normallyoperated Tvith the conductingchannelpinched off. Inthis way a high value of drain impedance, and hence of amplification factor, is attained. The device ma) also be used, however, as a voltage controlled variable resistance, in which case the draintogate voltage is restricted sufficiently to avoid pinching off the conducting channel. Typical drain characteristics of a field effect transistor (Type C.82) are shown in Fig. 1, and an enlarged plot of the region near the origin where the channel is not pinched off is showninFig. 2. This is sometimesreferred to as the triode region of the device characteristics,although as nill beseen it bearsverylittle resemblancetothecharacteristics of thermionic a triode.Therelationshipbetweendraincurrentand voltageisalmostlinear,providedthatthegatetochannel junction remains reversebiased, and also that the channel pinchoff conditions are not too closely approached. There is no voltage offset; that is to say, the draintosource voltage is zero when the drain current is zero. Thus, over a limited range of voltage and current,the field effecttransistor is equivalenttoan ohmic resistor betneen drain and source terminals, the magnitude of which is determined by the potential difference between gate and source. Used in this 11ay as a voltage controlled resistor, the device has no exact parallel in any other circuit element and thus leads to a whole familyof new circuit applicationssome of whichhavebeenreviewedbyGosling [ l ] . The purpose of this paper is to describe the prsperties and design of one circuit of this class, namely, a voltage controlled attenuator. Such an attenuator can OUTPUT be realized in many forms, including a bridge network with the field effect transistor as one branch or ernbodying the device in the feedback network of an amplifier, but the simplest is t h a t in which the transistor forms one arm of a resistive potential divider (Fig. 3), and i t is this form which will be considered here. The field effect
Fig. 2.
Draincharacteristics near the origill.
INPUT
b

b
+
CONTROL VOLTAGE.
&/lanuscript received May 27, 1965. The author is with University College of Swansea, S.E.ilales.
Fig. 3 . 112
“I’oltage divider” attenuator, using a FRT.
1965
CVG OOO XA LSTTLRA TIO N E GW LG N ELI:UT EAH DT O R S
FET'S
113
> 0.7 (at which value the drainsource resistance has transistor cannot be regarded simply as a pure resistance, increased only by a factorof slightly over six, relative to sinceacapacitancealsoshuntsthedraintosource terminals; however, the effectof this capacitor is usually its value a t zero gatesource voltage) the relationship of (1) diverges sharply from the exponential approximaappreciableonly a t t h e higheraudiofrequenciesand initially. Therefore, i t will be convenient to ignore it, tion. For the present application i t would be desirable for postponing consideration of highfrequency effects until the sharp rise in resistance as l i ~ S / W otends to unity, theotherproperties of thenetworkhavebeeninwhich is duetothepinching off of theconducting vestigated. channel, to be less marked, thus extending the range of All attenuators degrade the signaltonoise ratio someuseableresistancevariation.Transistors of thistype what, due to thermal noisegenerated in the resistors making up the network. Thiseffect is also present in the may be produced by adopting a modified device geomfield effect transistor, used as a variable resistor. Hom etry; one such structure, based on an alloyed junction. 5. Transistors of this type are comever, there is a further source of noise in the transistor, is showninFig. mercially available, and other structures, utilizing difnamely, a component which has a power spectral density function which obeys a 1/f law. This noise source, which ferent fabrication techniques, which would yield comparable properties, are also possible. is probablyassociatedwithsurfaceeffects,typically Thevariation of RDs withgatesourcevoltageobbecomes of significant magnitude, relative to Johnson served experimentally for a number of different comnoise,belowabout 200 Hzand will thereforebeimportant in many audio applications. As will be shown, mercial units is shown in Fig. 6. All the units are etched attenuators using field effect transistors can operate a t alloyjunctionnchanneltypes,andallhavesimilar pinchoff voltages.(The pinchoff voltageisusually quite high signal voltage levels and, consequently, can defined,inthecase of deviceshavingarelatively yield satisfactory signaltonoise ratios despite the will excess noise generated. The importance of l/f noise de gradual pinchoff, as the gatesource voltage that reduce the drain current to 0.01 of its zero bias value, pends very much on the value of the lower cutoff frethedrainbeingmaintained a t apositivepotential quency of the system and on the particular transistor used.Insulatedgate (IhIOST) transistors a t present larger than the magnitudeof the pinchoff voltage.) I t is available have markedly inferior characteristics in this apparent that the lam of dependence of RDs upon gatesource voltage may be reasonably wellrepresented by respect. an expression of the form DEPENDENCE OF ATTEKUATIOK ON CONTROL VOLTAGE RDS= ROexp (XVGS) (2) In order to determine the lawof variation of attenuation with control voltage, it is necessary to consider the where R o , X are constants. Transistors of thesamenominal pinchoff voltage relationship of gatesource voltage to drainsource rehave approximately the same value of X b u t will vary sistance for the transistor. Such a relationship can be markedlyin Ro. Even with the modified geometry of deduced from the theory of the field effecttransistor thistype of transistora pinchoffeffect is observed, proposed by Shockley [2]. According to this approach, which assumes that the a n d a t large gatesource voltages, a more rapid than exponentialvariation of drainsourceresistanceisobtransistor is constructed in the form of a rectangular served.However, (2) remainsa good approximation prismoidalconductingchannelbetweenplaneparallel formorethanadecaderesistancechange,andeven gateelectrodes,thedrainsourceresistance(assuming negligibledrainsourcevoltage) follows the law beyond the resistance, deviates much more gently from theexponentialapproximationthaninthecase of a Ro transistor obeying (1). A resistance plot for a typical RDS= (1) transistor having a gradual pinchoff, of etchedalloyed {l  ($)li2) type described, is shown in Fig. 7 over a wider range than in Fig. 6. The results shown in both these figures were obtained using an ac bridge to measure the resiswhere Ro, LVO are constants. tance(atafrequency w = lo4 rad/s)takingcareto Devices having a geometry similar to that assumed can be manufactured by a variety of processesfor ex keep the ac voltage between source and drain less than ample,double diffusionand showarelationship be 0.3 volt rms. Since the sourcedrain channel is not pertween R D Sand V G S in approximate agreement with (1). fectly ohmic, the applied voltage is kept small so t h a t They are not, however, very useful in variable resistance the true slope resistancea t t h e origin may be measured. applications, since as V G Sapproaches Wo, the rate of T h e consequences of the nonohmic nature of the conductingchannelareinvestigatedfurtherlater in this variation of RDs withcontrolvoltagebecomesvery rapid. Thus, the usefulrange of RDs islimited to no paper. Thedependence of RDs on VGs is stillbetterrepmore than about a 10: 1 ratio. The effect can be seen resented by an expression of the form clearly if thedrainsourceresistance is plottedona logarithmicscaleagainstgatesourcevoltage(Fig.4). RDS= Ro exp (XIVGS A Z V G S ~ (31 The broken line on the same graph represents an exponential relationship. I t will be seen that for I/Q~/WO where Ro,XI, X2 are constants.
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IEEE TRASSACTIONS O N AUDIO
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Fig, 1. The relationship of Ru.3 to m T i, as predicted by Shockley's model. (The broken line represents an exponential relationship.)
AXIS
OF SYMMETRY I
IC
2
4
6
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ALUMINIUM
Fig. 6.
Experi~nentallyobserved Ro.y/T'os dependence for commercial etchedalloyed FETs.
NTYPESILICON
TRANSISTOR TYPE C 82.
ETCHED ANNULUS
Fig. 5.
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Etchedalloyed FET structure.
Theincreasedcomplexity of therelationship, hen.ever,resultsinlessconvenientexpressionsforthe properties of attenuator netxvorks and is scarcely justified in vie\\ of the good agreement bekeen predictions of attenuator performance based on (2) and experirnentalllobservedresults. LAs anexample,consider the simple attenuator of Fig. 3. The attenuation is given by Eout __  , I =
p. 'I,,
Ro exp (XVGS)
R'
+ exp ( X V G S )
(4)
or
V~~(VOLTS)
Fig. 7. Comparison of R D , dependence ~ on V G S for an etched alloyed transistor with the exponential approximatioll.
where
expressed in decibels as
This relationship is plotted in Fig. 8 for the case where If the attenuator is precededand followed by amRoiRl is chosen so t h a t L =  20 d B nhen VGs = 0, and plifiers of zero outputimpedanceandinfiniteinput impedance, respectively, the attenuation of the output also taking  X = 0.135, in accordance with the best linear signal due to the insertion of the netnork may then be approximation to the curve of Fig. 7 . Experimentally
GOSLIPZG: V O LCTOANGTER O L L E D
1965 0
I TRANSISTOR TYPE
C 82.
ATTENUATORS WITH FET'S
115
ent valuesof attenuation atzero gate bias, are compared in Fig. 9. For lower values of series resistor the convex upwards curvature is morenoticeable,while at intermediate values the curvatureis to some extentoffset by thefasterthanexponentialincrease in thetransistor resistance, resulting in a relatively linear scale. Where the series resistor has a still larger value, resulting in evenhigherinitialattenuation,thecurvatureisconcaveupwards;since, in thiscase,theeffect of more rapidvariation of drainresistancedominates.The utility of a voltagecontrolledattenuator,such as thosehavingalineardecibelattenuationtocontrol voltage characteristic, would be particularly marked in audiofrequency equipment where it mill yield a linear subjective loudness to control voltage relationship over substantial range. I t should also proveof value in carrier amplifiers designed to have a logarithmic response. krTENUATORCHARACTERISTICS
vGs (VOLTS) Fig. 8. Comparison of measured ( x ) and calculated attenuation for thenetwork of Fig. 3, thelatterassuminganexponentialdependence of RDSon VGS.
A n important characteristic of a variable attenuator is therange of maximumtominimumattenuation which maybeachieved.Gosling [ 3 ] hasrelatedthis ratiotothemaximumtominimumresistanceratio availablefromthevariableelement,the field effect transistor. If the numerically largest available voltage attenuation [defined as in (4) ] is 24,,., and the least is A m i n , then A,,,,
ATTENUATION
m
__ =

~
Amin
1
(m  1)Arnin
+
_
_
_
( 7 )_
where m is the ratio of maximum to minimum drainsource resistance which may be employed. Clearly, if
(dB.?
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