144 IRE TRANSACTIONS ON INSTRUMENTATION June

A New HigL Stability Miciomicroammeter*JULIUS PRAGLINt

NSTRUMENTATION for the measuremenit of cur- placed oii a general anlalysis of the tranlsienit responiserents from 10-8 to 10-1' amperes is ani ever present problem inivolved in this type of feedback amnplifier.problem in nuclear, high vacuum, and semicon- This is necessary since the design problem inivolves pro-

ductor fields. Beside this current sensitivity, zero sta- visionl of good speed of response by means of very largebility of the order of one per cenit per day and a speed of feedback factors; and therefore, careful design is nec-response of about one second are required for most ap- essary to avoid instability anid poor transient response.plications. Instrumenitation for mass spectrometry in Fig. 1 (opposite) shows the circuit in block form. V,general requires faster speed of response than the above and RI represent a current generator where R1 ideally isand will not be considered here. an infinitely large resistance and VI is a voltage geniera-Three methods by which these currents may be meas- tor of infiniite output. Practical current sources approxi-

ured are, 1) the vibrating reed electrometer, 2) the mate this condition well enough. Neglectinig, for the mo-chopper or magnietic amplifier, and 3) the vacuum tube menit C1 and C2, the current i(t) flows to the input termi-electrometer amplifier. nal X of amplifier A anid through shunt resistor R. SinceThe vibrating reed electrometer is probably the most A is an amplifier of gaini k and the feedback is negative,

satisfactory of these methods. Several excellenit uniitsare available with current senisitivities of greater than Ein -Eout/k (1)10-12 amp full scale, and a dc stability of better than 1per cent in 24 hours. The main disadavantage of thistype of inistrumenit is its extremely high cost. -Eout + Eout/k

Currenits down to about 10-1o amp full scale may be X(t) = (2)measured by high sensitivity magnetic and choppermodulated dc voltmeters. These instruments do 'lot Now if k, the loop gain is large, current flowing into thedrift and are less expenisive thani vibrating reed electrom - input is approximately E0ut/R and the current may beeters, but are limited to about 10-I° amp full scale. read from a properly calibrated panel meter at the out-Measurement of very small currents by means of a put. E input drop of the ammeter, is also given by (1).

simple vacuum tube electrometer is by all criteria the The inp)ut resistanlce of the ammeter, Rj,l is givenl bymost econlomical andep straightforward method of all. E11xi(t) from (1) anfd(2) anedequalsHowever, electrometer tube amplifiers have tradition-ally earned the reputationl of havinlg instalbility and Rrelatively slow response. The purpose ofsthis papfer is to = + (correct this impression as regards the instruments to bediscussed and to describe two vacuum tube micro- Thus from consideration of dc quantities, we see thatmicroammeters, onle of which combines a maximum full the inlput drop (3) canl easily be held to 5 millivolts withscale sensitivity of 3 X 10-13 amp and drift of less than 2 an output voltage of 5 volts if the loop gain is 1000.per cent in 24 hours (iodel 410)anad another which Similarl the input resistance is decreased by a factorcombines a maximum sensitivity of 1 X t-il amp and a k+ 1 over wha3tit would be if the current were measureddrift of less than 2 per cent per week (Model 411). Botha2cross Rbyt a standard voltmeter. As will be shown in amicromicroammeters exhibit speeds of responlse fcaster subsequenlt sectionl, the speed of responlse is increasedthan one secon4d uder most cond1tions and are priced very nearly by a factor k over the response time obtainedcobsiderably below isnstruments which exceed their by readig the same current as a voltage drop acrossspecifications little ifait tll.k. the same R in a voltm eter circuit.

In general, thetyn2pe of dc amplifier circuit used in Fig. 2 shows a simplified schematic of the micro-these instrumentss well kiowni aid has been described microammeter circuit. The amplifier consists of bal-by several authors.1 Wmhile a brief desription of the anced5886qelectrometer tubes, Vi and V2,cononected asspecific circuitry will follovw, the mainl emphasis will be penltodes followed by two 6CB6 tubes in a differential

amplifier circuit. Local feedback from the 6CB6 cath-* Manuscript received by the PGI, December 6,1956. Presented odes to the 5886 screens stabilizes the operating point

at the Second IRE Instrumentation Conference, Atlanta, Ga., Ve-of tea5886 tues. Balncng is accolishedrby arycember 5-7, 1956. o h 86tbs aallg1 eoplhdb ayn

t Keithley Instruments, Inc., Cleveland, Ohio. the bias of V2 the "dummyr" electrometer tube. VS is1 E. J. \Vade and R. S. Stone, "An improved dc amplifier for re- m

actor control" Nucleonics, vol. 13, pp. 28-30; April, 1955. the eathode-follower output tube. The output is suffi-

1957 Prayclitt: A New High Shtbility Microrificro(trnmteer 145

,4lco Ew _ .| __Ilh*| CFAFT,_

C,~~C

*t- Fig. 3- -Completed micromicroarmmeter in cabinet.

Fig. I -Basic dliagram of micromicroamnieter circuit.

I 5886 IM lO4K712.5K V5

250 6CM6

ZERO 0 0.ae40 0 V46CB6

12.5K 12.

5886 IM60K OM M Fig. 4 -Range switch.

and 411, whiichi is pictured in Fig. 4. '1 efloni inisulaitioni isR ~~~~~~~used throughout alnd p)articular care NNas taken to

-125 niliiniize effects of hUmlil(litV, spurious (chairges, anlld

Fig. 2 -Simplified schemat ic diagrami of micro- transients due to range switchi nig.iicroaiiiimieter circuit. M\aintenance is simplifie(l by means of a plug-inl hous-

inig for the electrometer t ubes. Thlis eliminates a sol(der-cient to (Irive a 5-ma recor(ling inistrumeint. Ie loo1) ing operation by the user in chaiginig tubes. Further,gain is about 2500 at midband. TIhe power supply is a replacement inl)ut housinigs can be supp)lieCd with fac-conventional rectifier-filter systeimi supl)lied from a tory-matched and teste(1 electrometcr tubes, so thaltSola regulating tranisforimier. TIhis arrangement provides factory performance canl be (duplicated in the fiel(l.stable, line-trainsicit-free dc amplification wvith great The powver dissipation of the 410 is less than 25 wattseconomr of meanls. Not onli (loes this dlesigi)permit so that multiple installations present no cooling prob-low price but inherently low maintenance since the lems.numl)er of vacuumii tubes is kept to a minimiium, and no ITwo arrangements of feedback voltage and shuit re-mechanical modulator is use(l. sistance are usedl. In the Keithlcy Mlodel 410, from 10-1

Fig. 3 shows the mo(lel 410( micromilicroalimimleter. TIhe to 3X-10- amp full scale, the output voltage is 5 voltscal)inet (limciisiolis are 19 inches wi(le and 54 inlices on all ranges. Alternating 1X and( 3X scales over thishigh and(l 9-3 inches (eelP. 'I'lhe inlstrumllenlt is (lesignle(I for ranige are supplied accor(ling to (2) I)- choosilig theeither rack mounting or with cii(l frames for bench use. prol)er R. From 1 X 10-1 to 1 X 10-12 amp full scale, theAs canl be seen the (lesigii stresses simplicity. 'I'he panel output voltage is atteniuatte(l and oIIe volt is fe(d backcomprises essentially a ranige switch, zero knol), and oni the 1 X scales and three volts on the 3 X scales.panel meter. In addition, a great deall of effort was taken Alonig with this the shunit resistor is changed onice ev-to make the instrumilenit particularly dependable sinice ery deca(le. Oni 3X10-13 amp full scale a 1012 ohm re-many alpl)lications involve conitiniue( operation over ex- sistor is useti with 0.3 volts feedback. This arrangementten(led periods. The basic siml)licity of the electrical de- is the most economilicial, since one hi-meg resistor is usedlsign has already beeni stresse(l as an important factor in per decadle, and( the current senisitivity apl)roaches thereliability. All p)arts are of premium quality. limit for electrometer tubes. I'he (Irift on alny range is

W'here necessary, component parts of the instrumeit less than 2 per cenit in 24 hours with the exceptioll of thewere made when no commercial source existed. An 3X IO-' range wlhere it is about 4 per cenit in 24 hours.examiple is the range switch dlevelopedl for the Model 410 'I'he Keithley MTodel 411 achieves a maximumil senisitiv-

146 IRE TRANSACTIONS ON INSTRUMENTATION June

ity of 10-1k amp full scale. In this instrument the feed- without affectiing the response time to aniy great extent.back voltage is always 10 volts and the appropriate On the other hand RC2, the time constant caused by theshunt resistor is used on each range to secure 1 X and capacity that appears across R, is not affected by the3X ranges from 10-3 to 10-1i amp full scale. Since in loop gain, and thus determines the minimum time con-this instrument the voltage swing across R is always stant possible with a giveni resistor. Therefore with a10 volts, drift is considerably less than 2 per cent in 240 1012 ohm resistor and a C2 irreducible to below 1 micro-hours. This stability is probably as good as available microfarad, the maximum speed of response is about onewith any commercial micromicroammeter. second even if k were infinite. On ranges below 10-12The above considerations show the potential utility to 10-8 amp, C2 is an actual capacitor placed in parallel

of the feedback micromicroammeter and, indeed, this with each resistor. This is done both to correct transienttype of circuit finds wide use either with a dc electrom- response and to limit the bandwidth of the amplifiereter tube amplifier or with vibrating reed instruments. to its maximum usable response. From 10-8 to 10-12The main problem is the transient response and deter- amperes a time constant of 0.5 seconds is usually ade-mination of the maximum response speed available. This quate.study was probably the most important phase of the In the above treatment it was supposed that amplifierdesign and is of general applicability. A (Fig. 1) had no phase shift at any frequency. InTo analyze the transient problem, the input capacity actuality, the amplifier will have a relatively low upper

C1, and the capacity of C2 across the feedback resis- frequency limit since the first stage electrometer tubestor R must now be considered. (See Fig. 1.) Ci is the have large plate load resistors. In addition to this, ansum of the amplifier input capacity and the output obvious requirement of the design is that regardless ofcapacity of the current generator and its connecting how much capacity is placed across the input on anycable. C2 is the capacity appearing across R. This will position of the range switch, the system be stable. Sinceconsist of resistor capacity, switch capacity, and any RC1 which forms the input time constant is not speci-lumped capacity added for damping purposes. Amplifier fied for the designer, but may be anything from nearlyA is of the nature described above. Its gain k is a com- zero to several hundred seconds, it is necessary that theplex number over the bandwidth of interest, as will be amplifier proper contain one RC network giving suffi-shown, but for the present we will assume that k is con- cient attenuation to prevent oscillation when RC1 isstant and real. zero, but having a maximum of 900 phase shift, so thatNow if we equate the currents at N anid let p = d/dt when RC1 is large, the total phase shift canniot exceed

i(t) = einPC1 + (ei, - e.ut)(1/R + pC2). (4) 180°. Loop phase shift less than 1800 is the mathemat-ical condition for nonoscillation but is hardlyJ a satis-

This becomes the following wheni it is combined with (2) factory sitiuationl especially when R is between 109 and

+PC/ 1012 ohms since, in this case, the amplifier will ring ati(t) = -ke.t-- + (1 + /k)(IIR + PC2). (5) perhaps 1 cycle or lower in response to a step function,

L k often with small damping constant. Ringing at this fre-

To find the response to a unit step of current, i(t) is I quency makes the panel meter difficult to read, showsmax multiplied by U(t), the Heavyside funlctionl, and up badly on recorders, and often leads to a condition(5) is transformed by the L.aplace method to give where the amplifier, although "stable," will ring at low

amplitude in response to any spurious backgroundEout(s) = lmax (6) activity.

s[s{Ci/k + C2(1 + l/k) } + 1/R(1 + 1/k)] The solution to the stability problem is to placeenough capacity (C2) across R to cancel the lag formed

where s iS the Laplace operator. The solution of (6) i by R and Cl. However, too much capacity will slowterms of e0t(t), the output voltage for a current step is down the response unduly (8) and too little will allow

F -t 1 ringing. Therefore a criterion for aperiodic response ise _ImaxR I 1_ lRC, RC2j needed.

1 + lI/k L e () To develop this, an expression for K, the true complexgain of amplifier A must be developed. lTo do this we

Therefore, the time constant of the instrument (T1) will assume that a capacitor C8 is placed in the amplifierequals from a vacuum tube plate to ground and that this

RC1 capacitor is chosen to stabilize the amplifier with ade-Tl= + RC2. (8) quate safety factor when RC1 is zero. In this case it will

k + 1 be safe to assume that all other shunt capacities inl the

The main point of the analysis is that any capacity amplifier are negligible. In such a case, the expressionappearing across the input is decreased by a factor for K, the complex gain, is1/(k+ 1). Therefore if the loop gain of the amplifier isreasonably high, large capacities, usually in the form of K =long coaxial cables, can be placed across the input 1 + pT2

1957 Praglin: A New High Stability Micromicroammeter 147

w^here ohms. This coniditioni is remedied bvy mlakinig C2 large

k = (ic gain, eniough to neutralize the phase lag introduced by anyinput capacity u) to 5000 mmf. The capacity (C2)

K = complex gain, needed on e<ach ranige may be calculated from (12).

p-d/dt, Finially, if it is desired to endure some ringing for theRpRLC sake of fast response, (15) will predict the duration ofRp+ RL (9) the riniging.RP + RL Let us iioNo re-examine (8). In view of our develop-

RP= plate resistance of tube, ment of the complete expression for the tranisient re-sponise of the system, we may ask how valid is the as-RL = load resistance of tube,#R =oarsitaceoftue,sumptioni iniherent in (8) that k is a constant real num-

C8 = stabilizing capacitor. ber? To answer this, againi replace k by the actual valueof gain giveni by K in (9). In this case we take the

1 hen to take amplifier phase shift into accounlt we Laplace tranisform of (9), multiply (9) by U(t) so thatsubstitute the Laplace transformed expression of (9) iInto find the variation in K for a step i-put and solve for(5): that is, we replace k with K(s). K(t) the complete expressioni for gaini as a function of

It is not necessary to solve the expressioni since ain time. TFhis isexamination of the poles of (10) will give the needed in-formation. Transforming (9) and substituting in (6) we K(t) =k(1-e112) (16)obtain: T2

E01=__O)[t1 (10)s I [CjT2 + C2T2] sR(Cl + C2 C2k) + T2] 1 [k + 1]

The poles of (1 0) are s =0

-R(Cl +- C2 + C2k) + T2 _r 1 R(Cl + C2 + C2k) + T22 k+1 ] l/2 (11)2T2R(C1 + C2) L4 RT2(C1 + C2) RT2(C1 + C2)

If no riniging is to occur, all l)oles must be real; that is, If we substitute this expression in (8); that is, if we re-the discrimincaiit of (11) must be positive or zero. If the place k with K(t), we obtain:discriminant is negative, two complex poles are present RC,and a damped oscilation will occur. Therefore, the con=- T = + RC2. (17)dition for aperiodic responise is 1+k(1

(RIC1+ C2(k + 1)4 + T2)2° T2_____________+_Co) >k + 1. (12) lThus for the application of a unit step to the input, at4RT2(C1+ C2) >

ver- short times the exponential in the denominator ofThe conditionl for criticall dalmping is satisfied when (17) may be considered equal to one. Thus (17) reduces

the left term in (12) equals the right term. If, oni the to RC1+RC2. SO with an amplifier which does not haveother hand, the discriminant is negative, the circuit will infinite high-frequency responise there is no gain at zerorespond to a current step with a damped oscillatioll. time. If t becomes very long and if we consider kiT2Now since (11) is of the form lalrge comparedl with 1, (17) reduces to

s d + j(w2 -d2))l2 (13) T2RC1+ RC2.

where w = 2rf and ,d is the dlamp)ing factor. the fre- kquency of ringing is given byI Therefore if K is to have effect at short times, T2 must

1 k + 1 1 -/ be as smll als possible compared to T1.

27r LRT2(C1 + C2)] 1)CNLsO

and d, the dlamping factor is givenl by It has beenl pointed out that micromaicroammeters of

R(Cl + C2 [k + 1 ]) + T2 high stability, good speed of response, and high sensitiv-d = ________________ (15) ity can be realized with vacuum tube amplifiers, un-

2RT2(C1+C2) ~~assisted by modulating devices. General expressions for

Eq. (14) predicts ringinlg frequencies as low as 0.1 cps performance have been derived and conclusions drawnunder some conditions with R between 109 and 1012 which serve as guides to the design engineer.