Title STUDIES ON NUCLEAR INSTRUMENTATION FOR PULSEDREACTORS

Author(s) 飯田, 敏行

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URL http://hdl.handle.net/11094/1632

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Osaka University Knowledge Archive : OUKAOsaka University Knowledge Archive : OUKA

https://ir.library.osaka-u.ac.jp/repo/ouka/all/

Osaka University

STUDIES ONNTJCT.E.IXR INS[rRUPa.F.NTATION FOR PUI,SED

by

Toshiyuki !XDA

Department of Nuclear Engineering,

Faculty oE Engineeringr

Osaka University

RF.ACTORS

Suita-shir

1978

Osaka

Chapter

Chapter

Chapter

Appendix

r

l-l

1-2

l-3

IT

2--1

2-2

2--3

2-4

2-5

2--6

III

3-!

3-2

3-3

3-5

3--A

Contents

Introduction

Intense P.ulsed Neutron Sources

Pu!sed Reactors in Japan

Reauired Instrumentation for Pulsed Reactors aReferences

Transfer Function of Tonization Chambers

Introduction

[Vransfer Function

Transit Time Measurement

Fluctuation Current

Measuremen`L of Average Charge Caused per

Absorbed Neutron

Conclusion

References

Fast Response Flectrometer

Introduction

S,ta.bxÅ}lty ana Response ,qpeed

Practical Circuit and Experimental Results

Conclusion

Noise Characteristics

References

i

Chapter

Appendix

Chapter

Chapter

IV

4-1

4-2

4-3

4-4

4--5

4-A

v

5-1

5-2

5-3

5-4

5-5

VI

Fast Response Logarithmic Electrometer

!ntroduction

Stability and Response Time

!mprovement of the Response Time

Practical Circuit and Experimental Results

Conclusion

Cornpensation of the Temperature lnfluence

References

Fast Response Log N & Period Meter

Introducti,on

Transient Response

Imp.rovemen`L oE the Response Chara•cterist-;Lcs

Practical Circuit and Experimental Results

Conclusion

References

Summarv

Acknowledgements

List of Publications by the Author

ii

Chapter ! Introduction1--l !ntense Pulsed Neutron Sources

The availabUity of a device for generating either single

or repetitive intense bursts of neutrons is the basic requirement

for a wide variety of experiments for fundarnental and applied

researches in the field of nuclear engineering. The extensive

application of time-of-flight methods in the field of neutron

spectroscopy is the typical example of this. Another exarnple

is found in the study of transient thermai processes in reactor

fuel e!ements, where the requirement for an effective!y

instantaneous heat input of given intensity under the selected

test conditions can be adequately satisfied by an intense

neutron pulse whose width is com.parable to the characteristic

relaxation time o:' the ef-{ect caused by a reactÅ}vity accident.

Methods used for generating such intense bursts of neutrons

include the following ways; 1) the use of neutron beams, which

are supplied by the conventional steady high flux reactor, in

combination with choppers, 2) the use of intense accelerators

such as an electron linear accelerator, with a target

appropria`Le for the (p,n), (d,n), (di,n) or (ec,n) reaction ,

3) the use of pulsed reactors designed either for repetitive

or single pulsing and 4) the use of intense accelerators in

combination with pu!sed reactors.

A survey of intense pulsed neutron sources in operation or

under developsent shows a wide variety of types, designs and

pulsing chayacteristics, which make the classification difficult.

However, it is safe to say that such a device can be operated

-1-

with the pulse width from 100 ms to a few nano seconds and atthe neutron Å}ntensity higher than lo14 neutrons/em2 sec <

pulse peak val, '.'.e).

1-2 Pulsed reactors in Japan In gene-ra-2•, the definition of " a pulsed reactor " is the

followings: a nuclear reactor designed for producing intense

bursts of nent• r• ons for a short interval of time by means of

the insertion or-: positive reactivity exceeding the prompt

critical during a very short time.

In Japan, t' he first one-shot thermal pulsed reactor, l) ( Hitachi Training Reactor - P > served with IOO msHTR-P

pulse width tÅë ex.n.eriments on self--lirniting power excursion

characterist.l.cs of liqht water reactors since 1967. The 2)second one-shot "Lherm.al pulsed reactor, NSRR - (Nuclear SafetyResearych Reactor, ), has heen operating as the highest peak power

pulsed reacto-r in the world since August 1975. This reactor

is an ACPR type reactor and has contxibuted to the investigation

of fuel behaviour under the reactivity initiated accident

conditions witn the pulse width of 5 ms. 3) The z"irst one-shot fast pulsed reactor, the YAYOI--P ,

which wen`L over the prompt critical in 1975r has been operated

with the `Lwo r.alse widths of about 100 jpsec and a few seconds.

Additioina! rn,,e•chanisrns of six different reactivities for pulsing

in various ways make it possible to be used for researches in

reactor kinet-;..'.'s, safety, detector development, radiation effects

etc.. The u:]B ( Japan Linac Booster ), a planning facility

is a repetitive pulsed fast reactor. The JLB is a Linac--driven}

-2-

boosted system and will be used for studies in huclear physics,

solid state physics, neutronics, radiation chernistry, etc.. The

smmaxy of JLB designed characteristic is the followings. Effective thermal neutron f!ux == lxlo16 n/cm2sec

Pulse width o# fast neutron flux = 10 psec Pulse width of thermal neutron flux = IO .-v 30 >asec

Repetition rate =5--. 200 pps Reactivity insertion =-4$ subcritical to l$ supercritical

Average power =2 MW 4 Peak pulsed power to back ground power == 10

The .TLB project was adopted by Science councU of Jal.ran as One

of the m.. ajor university nuclear research programs for future.

The basic researches have been carried out at Osaka Univexsity

and oilner institutes. The major parts of this work are carr-

ied oui as contributions to the researches and developments

for this JLB project. In addition, there is a plan of

developing an intense pulse neutron source hy the use of a proton

synchrotron wÅ}"Lh uranium booster at KEK ( National Laboratory

for High En. ergy Physics ). [Chis neutron source is also expect-

ed to be able to produce about one tenth of a peak power of the

pu!sp"d reaetor JLB.

-3-

1-3 Reguired :,nstrumentation for Puised Reactors.

A rapid response and stabie neutronic power monitor system

with wide measuring ranges has clear!y become the rnost important 'nuclear instrumentation for pulsed reactors. For safe opera-

tions and ver• sae' i]e applieations of intense sources, the accurate

measurernent of pu!sed output shapes is essential. Even for

a conventional s'L-'eady reactor, the rapidness and the stability of

electronic instrurr,ents in a neutronic transient power monitor are

very favourable.

Precise reactor powers are generally determined by instanta-

neous measurement of the intensity of radiation generated from

reactors. There are two fundarnental systemB for measuring

the intensity or- radiation and they have been both used for

nuclear instrumentation of conventional steady reactors.

One is corrLposed of a pulse counter such as a fission counter or

a BF3 proportional counter, pulse ampiifier equipments to shape

current signals from the counter, a scaler and a recorder.

The b!o::'< di•agr• am o."• rl his syst•em,. is s2ow. n in F.ig. I-1. This

system is exceUent in the removal of gamma ray background and

externa! electronic noises. It has been employed at low power

level, where t• he 1•evel of gamma ray background is very high due

to delayed g&rn,!m.a rays generated from fission prnvductva in -Fuels.

But, excessÅ}vely n.S.gh counting rate distorts the linearity oÅí

this system, si•nce this system has inherently a dead time.

The other system is composed of a current-type ionization

chamber, an electrometer to amplify the chamber current and a

-4-

Reactor

Fig. 1-1

Coaxial cable of several tens of,meters

' Charge sensitive type Fission counter or BF3 propertionai counter --- - i' ,pOrreC)litArpeinikgrUiSe tYPe

' '

' puise shaping'-'5m51ifier

or linear arnplifier

Discrimi.nator

Scaler

Recorder

pulse counting system of nuclear instrumentation for reactors

-5-

.

recorder. The block diagram of this system is shown in Fig.

I--2. The output current of the 'ionization chamber is the re-

sult of the pile of many elementary current pulses induced by

detection of radiation, so that the ionization chamber can be

used in the range of very high counting rate. This system has

disadvantage of slow response time in comparison with that of

the pulse counting system. The response time of this systemis main!y determined by that of the electrorneter to amp!iEy the

low output current of the charnber. Table 1--1 gives the rise

times and the available counting rates of the rnain Emiplifiers

of these two systerns. - Now let us consider nuclear instrumentation for pulsed reactors.

In order to observe the precise power shapes of pulsed reactors,

it requires fast responsiveness and sufficiently sta'tistical 5)accuracy based on high counting rate. Ngure l-3 shows the

measured results of• power shapes of the pul.sedreactor YAYOI by

the two systems . Both shapes in Fig. 1-3 are normalized at

the low power level. There is also no time lagbetween both shapes since they were rneasured by the use of the

same trigge.r. signal from t.he pulse operation systern of the reac-

tor. It is evident from the comparison of the two shapes that

statistical inaccuracy at low power level and saturating effect

due to counting loss at high power level are found in the pulse

counting systeim. Even if the fastest and very expensive

pulse amplirr"i-er equipments are introduced into the pulse counting 'system, the avaUable counting rate of this system should be 8limited to IO cps. Hence it is difficult for even this fast

-6-

Coaxial cable of several tens of meters

Reactor Current-typeionization chamber - ---- .--- - - Electrometer

Recorder

FÅ}g. 1-2 Ionization

tation for

Chamber-Electrome`Ler

reactors .

System of Nuclear Instrumen-

-7-

Table l-l 1'he rise times

nuclear instrrunentation for

and avaUable counting rates of the main

reactors.

amplifier of

l

co

l

System Amp1Å}fier Risetirne AvaUablecountingrate

Currentpulseamplifier u5nsec <lo7Pulsecounting

system Chargesensitiveamplifier u30nsec <1-o4

Ionizationchambersystem

'

Electrorneter >O.5psec <co+

?.

$.U

..

g-

se)oaLo

d--,•,

vUNct

1000

100

10

1

e

e

•e

e

ee

ee

e

e

e

e e e eee

e

e

eee

e

ee

e

eee

eeee

ee e e eee ee eee e e ee ee eee ee . ee eee ee Oe ee e eee ePulse Counting System

!onization Chamber-Electrometer Systern

e

Fig

o

. 1-3

5

An example of the

yAyoz.

Time

mea sured

-9-

10

(s)

results of power shapes

15

of the

system to rneasure the precise one-shot power shape of which pulse

width is naLv-vcwer than 1 msec. Thus, the pulse counting system

suffers fr- o'.n= t• ,he statistica! inaccuracy in the measurement of

power s2.iapes oE the one--shot pulse reactors. On the other

hand, an ioni•zation chamber easily permits obtaining a very high l2 cpsr which is eguivalent to an outputcounting ra"v• e of 10

current of a-bont l rrLA. The ionization charnber-electrometer

systern• is m.ung-ln superior to the pulse counting one in point

of counting rate, and hence the former system should be mainly

app!ied to the nuclear instrumentation for the pulsed reactors.

Remarkable improvernents can be expected in reliabUity and

rapidness by incyeasÅ}ng the neutron detection efÅíeciency of

an ionization charnber. For fast lpulsed reactors, the neutron

de-L' ecting eff• iciency oi an ionization chamber with the l/v

type neutrcn energy response i$ improved large!y by introducing

a suita-'ble neu•itron rnoderator layer. The sensitibity. can be

irp,] roved by reducing the incident neutron energy through the

ne u trr o n moC e -T a tc r• , w i t h im f- h e p e rm i s s i b l e b r o a d e n i n g i n t h e

6)observed r.u]se width of the reactor power. Figure 1-4

gives the c.).xperimental result of the detection efficiency and

the pulse wia"th versus the moderator thickness in the case of IOa hydrogenett•s moderator with B coated detector.

Ths pur• pese of this paper is to clarify factors in the

determirtat-'-lon oL= the response time of the ionization chamber-

electroiin.et' er• system and)moreoverSo design a fast response

nuclear instrumentation for p. ulsed reactors. FÅ}rst, the

transfer function of an ionization chamber is discussed in

- IO -

Ao'Eii

8

2NSiit

eza1:OL

•,=-"

,2il

8g2g-

(ill.

1OO

40

20

10

4•

2

Incldent Fast Neutron Put)"e Width: lys

,-e--•-m---

b/ b/ A/e/

o-`Xe

/

3 4

•-•-•- )b

120 ps10

80

6

4

20

5cmPol•y-ett;'N,yl?ne Th;ickness(Hydrogen Content Ratio 1.25 xH,O)

zoÅ}.-

e.

ciZ

e-i

s,igs

\ScS2

'q'

Fig•

and

l-4

pulse

An ex&me]e •ani

wi dth hro =. ding

increase

with a

of neutron detectien efficiency 'moderator layer ( poly-ethylene )

-ll-

Chapter II and the relation between the transfer function and

the transit times of positive ions and electrons is c!arified

from the res;;•:, t• s obtained by the use of a linear accelerator.

This wili be useful for the development of a fast response

ionizatÅ}on ch,p..mber for pulsed ]reactors. Chapter rlT

deseribes the response speed of a linear electrometer to

amplÅ}fy a chatm•tber current. The relations between the response

speed and measuring conditions, that is, the length of a

detector cable, current sensitivity and so on , are obtained

from the equivalent circuit analysis. Moreoveri a fast

response linear electrometer circuit with a new technique

for reducing a cable capacitance is illustrated and it has

been successr-ully applied to the rneasurements of power shapes of

the YAYOI. Cb-apter !V shows that the response time of a

logar• i.LLhmic e!ectrometn.-r i`s severely limited due tO the strong

curremb dependency of the resistance of a logarithmic

element. A new technigue of using a current-dependent

imp,edance element for the phase compensation of a logarithmic

electrometer is discussed to cope with this problem, and a newly

desi{,ned loga-rithnic electrometer has b.een also successfully

apnlrlied to the measurements of power shapes of the YAYOT.

I' n+. chapter V, the instantaneous measurement of a reactor period

which is closely related to the reactivity inserted to a pulsed

reac-uor is described. A fast response log N & period metercircuit which has been developed in order to rneasure a time•-

dependent rewn.ctor period is shown. Some examples of the

rneasured results of the instantaneous prompt periods of the NSRR

and the YAYOZ are illustrated.

- l2 -

!n the

lt is also

with above

tation for

necessary

thai of the

last Nn"hapter, the whole of this work is summarized.

shown `Lhat the newly designed power monitering system

techp,iques has been adopted as the nuclear instrurnen--

the NSRR and the YAYOI, and that it is moreover

to develope a fast response ionization shamber for

JLB.

1)

2)

3)

4)

5)

6)

References

rm Imai, et ai., J. Nucl. Sci. Technol. 6 i2], (1969) 69.

S. Saito, et al., J. Nucl. Sci. Technol. 10 I12], (Z973)

739.

H. WakabayashÅ}, et al., Proc. US/Japan Seminar on Fast Pulse

Reactors !-2 (l976).

uT. Wakabayashi, ibid., I-3 (1976).

T. Iida, N. TNakayama and K. Sumita, Proc. for Syrnp. on

Int.D.nse Pulsed Neutron Sources in Japan, Py-5 (1975).

K, SumÅ}ta, T, rlida, et al., Proc. US/Japan Seminar on Fast

Pulse Reactors III-1 (l976).

- 13 -

1) Chapter II Transfer Function of ZonizatÅ}on Chamhers

2 - l. Introduct;• en

Many experin,`eni s have been made for the investigation of reactor 2) safety at thepu]sed reactors of the NSRR , the YAYOr and others.

:n order to obtain preeise data in those transient experirnents,

measuring systems ior radiation reguire fast responsiveness and

sufficiently stat:'sticaZ aecuracy based on high counting rate.

There are two typi•cal systems for measuring Yhe intensity of

radiation. One is composed of a current-type ionization chamber and an electrometer 'Lo arnplify the chamber current, and the othei

composed of a pulse eounter such as a Åíission counter or a propor.

tional counter, pulse ainpZifier eguipments to shape current pulses

frorn the counter and a scaler. The forrner systern permits obtaining

very high counting ra"i e but the latter one has inherenstly a dead

time resulting in counting loss. Therefore, ionization chairnber

systems have been used preferably for' rneasuring narrow pulse of intense ' radiatÅ}o rL .

The response of the ionization chamber is distorted by the effect

of the posit:'ve ien transit time, which is the ti!ne taken for positive

ions fvo move the interval between the electrodes, in the case that

pulse width o.`-• radiation is smaUer than several hundreds of Tnicro-

seconds. Hence i+v has become importa;it in recent puisedreactor ' experiments to dete.r.mine the precise response time oi the ionization

charnber . ' - Wiih respeet "L'o the deterirtinat•ion gf the transfer function of the ionization chanber, R. subramaniarn and R. vedarrt 3) measured the

4) freguency response by beam modulation and also S. Gotoh obtained

that by utilizing uncorrelated reactor noise. These rrteasurements

-l4-

can con"Lribute to obtaining general freguency characteristics Zike

break frequency ci the ionization charnber, but those methods are not

sufficient to d..'.' .-A.rmine the precise transfer function in very

high freguency r• egÅ}on. Those measurernents in Åíreguency domain

cannot give efiective data on the transit times which are expected

to be ciosely re]ated to the transfer function. The precise data 'on these transii "i irnes shouZd be obtained by measurenient in time

domain rather than in :"requency one. This chapter ana!yzes the

impulse response of• the ionization chambeF measured using intense

gama ray pulses produced by a iinear acceZerator and clarifies

the relation between the traxisfer function and the transit tirnes of

positive ions and electrons. Moreover the fZuctuation current

induced by random detection of radiation. is also discussed based

on the measured transfer function.

2-2. [Pransfer Function

A current pulse of the ionization chamber is formed whenever t a charged partic]e passes thropgh the gap between the eleetrodes

and the resultant• electron-ion pairs are swept to the electredes by an apptied elect"r.ic fieid. FxorR 'the principie oi the conserva•-

tion of ene.v.gy, ihe external current indueed by point electronic

dnaxge Å} Qo meving toward each elgctrodes is given by the following

eguation aSter• A..'H. snen 5). '

Lo = t<Q.ELJL - Q.E ule), (2-1)

- l5 -

where V is the appiied voltage,

E the strength oÅí the electric field,

wi the drift velocity of positive ions and .

we the drift velocity of electrons.

Hence, taking the numbers of positive ions and electrons produced

by a single detection of radiation in a unit volume dtr at a

iocation Sr and time Å} to be rL;(sr,t>dlr and ne<Tr,'e)cln'

respectively, we obtain the following equation for the elementary current

pulse of the ionization chember.t ct) = li IR ( 9>, 7z i (sy, t) E ( sr, t) LUL ( ty ,t) "' {}one ( tr,t) E ("e. t) Ltie ("r. t) l dfr, (2-2)

where R is the total space of the ionization chamber and 6o

the elemen"Lary electronic charge. ronization charr[bers used in

reactor instrumentation are generally cylindrical in shape but the

electrode structure is considered to be a-pproxi;nately of parallel-

plate, since'the interval OC between the electrodes is Tnuch smaller

than the rad# o.F. the electxod.es. Conseguently, the strength

of the eiectrie field between the electrodes becornes

Ote . 'As is weU known, the drift velocities of positive ions and "t . 'electrons are also. given by

' Wi=vÅíA•iS=,Ui pVd , (2-4) - E V' 'U7e =7'Ue p =./Lke pct ) .<2-s')

- l6 -

where P is the p• ressure of the enclosed. gas, ,Lti the mobility of

positive ions an";' .L4e that of electrons. Here it is assumed that

the density distrÅ}butions of positive ions and electrons produced

directly after a singZe detection of radiation are uniform alopg

a track. When Vne ionization charnber is operated under saturated

condition, the eiiects of the recombination and the electron

attaciment are neglSgible. Then taking the tetal cha;ge produced Qby the detection of radiation to be Å} 2. , we obtain a simpZiÅíied

expre$sion as a substitute for Eq.(2-2). i(t) = QT., <s'pt- \;)+ TQ, (t- ",) fov ostsre

= TQi (l'"" \;) '+ot TeStsTi )(2'6)

where T; = ,,e,tiv ,

p ct)

The value of Q varies accordipg to the direction of a track and it

is therefore expected to be stiatistically distributed. rn the case . 'that ÅÄ-T:..e directiop. oi a track is nearly paralZel to the electrodes, //the elerp.enta.ry c'.irrent pulse cannot be. expressed by Eq. (2-6).

However such cases seXdom take place and are therefore ignored in

this chapter• Here ' ri is the transit tirne of positive ions and 're

that of electrons. These times are not zero. so that the response

-17-

of ionization chamber must be evaluated with distortion to the

narrower radiation puises than these transit tirrtes.

Now let us consider the output current of the ionization

chamber set up in a radiation field. The output current is

the resu!t of the pUe of rnany elementary current pulses.

Though all shapes of elementary current pulses are not practically

equal, it is assumed that they are all represented as the expression

(2-6) with {.".. replaced by averaqe charge Q to sirnplify the determination

of the transfer function of the ionization chaxrtber Eor the foUow-

ing reasons and 'experirnentaZ resuZts in next section. Eirst

the transit times of positive ions and electrons are constant except in

the speciaZ case that the direction of a track is neariy paraUel

to the electrodes. Second!y the total electrenic charge is fixed

inde-pendently of the intensity of incident radiation and time. 'Taking radiant flux density at tirne e to be (b(t). we can obtain

the output current of the ionization chamber as follows. t, (b) = J .t E O (z - o '> QQ- Z (t ') d t ' (2-g)

' 'where E is the detection efficiency,t which is delermined by the

total cross section of the reaction materials of the io4ization

ehamber. Then we can take the Laplace tran$Åíorm of both sideswith resPect to Z and the transfer function oE the ionization cha-

mber is given by

' ' G(s) = $C((sS)) = rc 6 ( T,ls,(Ti sLi +Ie"iS) + .rdis,(T.s---i +.eTeS)j ,(2-io)

-- l8 -

.where Ic(S) is the zapiace transform of Lc(t) , Åë<S) that

and S the Lar.:• ace transform variabZe. This eguation

the transfer fuLnct.`.•on of the ionization chaxnber is mainly

by the transit ti-mes of positive ions and eleetrons. , '

oE fp(t)

shows that

expressed

2-3. Transit Tiire Measurernent

rt is evident Åírom Eg.(2-q) that the irtpulse respense of the

ionization champJ)er is expressed by Eq.(2-6). The impulse response

is characterized by the two functions of the first degree with resp--

ect to tirne as shown. in Fig.2-1. 0ne is based on the positive

ion coTn..ponent and the ether based on the electron one. Hence the

m` easurerrLent oÅí the impu!se response of the ionization chaip.ber should

elarify the relation between these transit times and the transfer

function.

Figure2.-2 shows the instrumentatien for measuring the impuXse

response of the ionization chamber. As is well knewn, the drift

velocity of positive ions is much slewer than that of eZectrons and

hence thLAJ impulse response due to the positive ion cornponent was

Åíirst measured. T.he ionization chamber used in this experiment

was a gamma ray compensated type Westinghouse model 8074 and the

compensating electrode was grounded. The specification of the

ionization clna-r•nither are given in Tahle 2-1. Gamma ray pu!ses of 6) about 2 ys"'ec pr• oduced by the linear accelerator KUR-LINAC

were used for Å}n•pv'Lt signals. The pulses were regarded as

irnpulses for the posttive ion component since tbe pulse width

was much narrowe]•r than the positive ion transit time.

- 19 -

I

No1

1Q ('Ti•'

i<t)

+",)

.--.

co"L=U

QT•

o

- . . - . . . -"l

t

t,

t

l

l

1

i(t) Q= "(1-

Q" T• (1-

=o

tTi

Ti

)" 9e(i- e)

)

(OstsTe

( Te st <- Ti

( Ti <"t

)

)

)

o Te

Fig,Z'1 The

Time

elementary current

Ti,

pulse shape

Ll NAC

l

M-t

'cf'ronizationCharaber Oscittoscope

Rf

--.

8O74 H.V.-e

E{ectrome-ter

Trqnsient

Memoryt-

,Flg.2"2 BXock diagram of the equiprnent for measuring the irnpuLse respon6e.

'

Bl

Table 2-1 Specifications of the detector used in this experirnent .

Westing house 7ype 8074

Overatllenth 23'f/-inches

Outerdiameter 3'r6'inchesSensitivelenth 74inchesWeiht 5'#)oundsCoatin Boronenrichedin'OBFiUinggas N,Operatingvoltage 300--SOOVComensatingvoltage -70--80VNeutronsensitivity 4x10-'A/nvNeutrenfluxrange 2,5x702•-25x70'OnvUncompensatedgammaSensitivity3x70-'OAIRIhour

A fast response eZectrometer was manufactured for thisrneasurement7). The time constant of the electrometer containing

a detector cable was about 3 }isec in lo"'6 A range. This was

much smaller than the pesiti,ve ion txansit tirne. so that the time

lag of the eZect=• ometer was negZigible. ' Figure2-3 shows an exainpie of resuZts observed by the use oE

an oscilloscope. The response shape due to the electron component

is too sharp to be visible together with that due to the positive

ion component in `Lhe screen of an oscilloscope. Concerning the

positÅ}ve ion component, the observed pul$e is ap.parently linearly

falMng to zero. This agrees guite welX with Eg,(2-6> and it is

therefore proved that the transfer function of the ionization charrtber

is expressed by Eg.(2-10>. The output voltage oÅí the current

ampiifier was !etG not only to the oscilloscope but aiso to a transi--

ent-rr{emory !watsu model M"4 701, by which the transit tirae of positive

ions was preciseiy measured, varying the appZied voltage as a para-

:rieter . The results orF che positive ion transit time and its

reciprocal versus the ap.p-iied voltage gre shown in Fig.2-4. The

positive ion dr•iÅít velocities indicated by the reciprocais are repre-

sented as reiative vaiues since the precise value of the interval

between the electrodes is not obtained. rt is. however, evident

frorn the xesults shown x'n Fig.2-4 that the drift veioeity of

positive ions is direet!y proportional to the applied voltqge and the 'transit time of v. D• sitive ions inversely porportional to that. These

agree guite well with Egs.(2-4) and(2-7) respectiveZy.

-- 23 -

Fis.2'5 An example of measured inpuLse responsescencerning the positive ion eomponent (the appliedvoltage = 300 V ). HorizontaL seaZe : 100 )Ftseeldiv. -• 6VerticaL scale ; 2XIO AIdiv.

-24-

l

:t

900

800

700ut

iv 600i.;, .,

2 soo

l•:':"':

•w 400'mc-rd300

},i;

cNO2oo

1OO

oo

qtEi--•-

o Wi

e Ti

Q..--

ilSP

600 7oo 800 9oo 1000Voltage (V)veloeity of positive ion8,

'a15 E iil5

v ii;:

•:b •.-"10 s >N ptc

a o N

100 2oo 3oo 4oo 500 Apptied Fig.2-4 Transit time Emd dr!ft

o

Now let us consider the response due to the electron component of

the ionization che;nber. rf a sufficiently. narrow pulsed radiation

source and a current arnplifier of which time constan.t is rnuch smaller

than the electron transit time are avaiZable, the sarne simple

experiment as on the positive ion component might be possible.

However, it is ve=ry difEicult. to obtain sucii a fast response current

aimpZifier so far, so that we have to take account gf the tirne lag of

a current aimplifi•er in anaXysis of the response of the ionization

charnber. Fro:.n. eguivaient circuit analysis the transfer fupction

of the current aAmplifier is approxirnately given by

Gea(S) :'- IR+fzs , (2-ii)

where - U is the tirne constant, which is determined by the product

of a current range resistor RÅ} and a feedback capacitanee Cf.

Here, it is assumed that the transfer function of the ionization

chamber is expressed by Eq.(2-IO). Then, if we rneasure the tiine

Tp from a square pu!se change of input to the ti.me the corret

sponding output arrives to the peak value as shown in Fig.2-5, tthe electron transit tirne is obtained by

Te '= To' eexXp?lltiS.;I)i -- t 'fotc? Te `< T; )(2-J2)

'where To is the puZse width of input. rn the exper-;.r-,ent, garrma r'ay pulses of 100 nsec were applied

to the sarae ionizaeLion chaxrtber. An ,exarnple oE rneasured results is

shown in Fig.2-6. The ti;ne constant 'oÅí the electrorneter was about

-26-

Aut.-b-.

'E

D.;hb

9A"'

dtZ

1•

s:

]F

U

1.0

O.1

O.O 9

o.o g

oo7O.O6

O.O 5

oo4

OD3O.02

O.O1

o .

o

'.

.

InputTo

Tp"ll.

ee -" " tt . : :

:

:

:

'

'

-e

--

et

e-."-

.

:

Pulse

t-

.eb

..

..

-e-

..

t-.

..

..

..

.. .

. . . . . -t e- . Sb e- .

'

. . - -- -- --o 05

Time1.0

(Ns>1.5 2,O

Eg.2-S Response to sgua re pulse ch ange of input.

-27-

Fl.c-2'6 An exampLe of measured responses to gemma

ray p.uLses of 100 nsec. The upper traee is an injeetion current ef the aecelerator and the lower one an output voltage of the eieetrometer. Horizen+.a-iL seale : O.5 jpsee!div. VerticaL scaLe : O.2 A/div. (upper) and 2xlo-4A!div. (lovrer>.

-28-

350 nsec (Rf=10'-n, Cf==35pF ). Since a tran$ient memory with a

sufficiently smaU resolving time in comparison with the eiectron

transit time was not available, we took photographs of the responses

frorn astorageosci!ioscope and magnified them about four tiines to ' measure the tine Tp . Zn FÅ}g2-7 the response caZculated based

on che transfer iunctions of the ionization chamber anq the current . aLmp,lifier is compared with the measured one shown in Fig.2-6. The

calculated response:.is norruaZized by the peak vaiue of the measured One. Both response shapes are in good agreernent although there'are rnany

external noise sources in the accelerator room. Figure2-8 shows the

results of the eiectron tr• ansit time and its reciprocal versus t.he ' applied voitage aiike on the positive ions. The electron drift

velocities are also represented as relative values because of the ,obscuritylof the intervai between the electrodes. Aithough the resuLts '

apparenLLIy differ frorn Egs.(2-5)''t'(2-8), the tendency that the electron / drift ve!ocity increases Zinearly with applied voltBge appears to agree with experimental results reported by L.coni8) and T.E.Brotner9).

2-4. Fluctuation Current :n order to measure precise power shapes ofpulsed reactors .by the

ee- -use of -omzation chambers, it zs necessary not oniy to determine the iresponse tirne of the ionization chamber but also to evaldate the error

due te the fluctua`Lion current induced by randorn detection oE radiation.Frorn Carnpbell's theorYO>the value of the'averpge current and the mean

sguare vaXue of the fluctuation current ef the ionization charriber set

up in a steady raL""tatz'on field are given by

- < eq> == N• :ti •I-:d(o dt f= N 'Q' , (2-is)

- <Ln2> == N '( QQ )}11.. [lll {e<t)}2 oC't , (2'i4)

•- 29 -

l

coo

l

/•wlldittli,lll,,li,i$

;X7sgerr e eq

ut

sil//'ki,Ilii'f

Cat ,t lll' 350ns 520ns)

,,t. ,3,i-'

esY!)qifl

8 ,g,

illSi

tw,,agl/lll,{sy,ilfgeeIee

Wri

tw

8""'

pmptJ

:/'t

i vet

it

gz

'"'`',,,,,,x'.iiYiS ec,$'`•k,/l'{,it`ww,tx,:t,,//•eg,l{k?i,in/L'g\:/•l'llXs•L,iri:,ii

ig!i?l N

gedii'$11t"

,4 ikthtig,,

?li•IEi\lfiesfii•

pt,"L,ts,iNsillwa

.I7,IZgt!r.,4}ftT lll

wa'i,;,1' " ,

V'

S t'y..V,;LS'P

,tt,tit,lxX

eq,gl,.s$}{ue,

pt[ltk/ti.,y,:z,.T

.,"F••,//•i•

iag"•{veekix,,llii

••tw

ij,ge,\iillleei,li,1:ll,31<lsi,

v

,,ee'ee?'9\•r-"ee,fg

1 u.i -.LpMJ1"intaL.,J;v l:tl' di

180

,i,lll,lillllllj,i,i[kl,

v a. dwL"asJ '",, tsx,l•4aSIT•

,,/ix17if,i•lvliilSÅí1,,{g,ag'ii})li•c•l,i

'l',S'k'/si':iiilg,E

vott

e(ps)

Fig. 2-7 Comparison hetween calculated response and measured one.

1

beP

:

Aut

ivNt-

Q8

O.7

Q6

Ns E Q5--

.- .Hpt o.4fiii

,i:

O.3c9

'tl

si O,2ut

O.1

o

t

e

o

o

dcEf----e

o

e

o

(e o

e

Te )

We

e

Exp.

e

,

e

1oo 2oo 3co 400 Apptied

Fi' g,2-8

5oo 6oo Vottage (V)

Transit time and dr'Å}ft

7oo

veloeity

8oo 9oo

of electrons.

g1.5 i

v

iN;

->-'

1.o ' g l;N

-"'u-

a 8o.s B L--,-IN

where N is the average countipg rate oE radiation. rn practical

measurements of the outp.ut current of the ionization charnber, a current

arnplifier systetm aets as a low pass filteF, so that.the mean square

va!ue of the Åíluctuation current is estimated smaller than is expected

frora Eg.(2-J4). Then taking the transfer function of such a low pass

fiZter to be H(s) ,we cain rewrite Eq.(2'-14) as foUows.

<e.2>=N62L:{A(b)S2dt , (2-}s) ewhere 1/(.s)ts theLaplace transform oE b(O and Q.A(e> the inverse

Laplase' transEorm oi !(s)Hcs).

Conseguently, the ratio of the average current to the root mean

square value of the fluctuation eurrent, in othe= words. the ratio of

signal to noise is given by

. '< ea> N = < e n2> 1co. (x (t )}2dt

lt is naturally expected r-rom this that the

< in other words, the average current ) is, of Jl-co,.('iil(t)}2oCt <in other words, the

amplifier systein ) is, the better the ratio.

From Egs.(2-13) and(2"15) the averqge electric

-- <Ln2> l Q == <La> ' I-".{A(")}2ott

'2-5. Measu.rm. ent oi Aver4ge Chayge Caused

This Section describes the rneasurement

by absorption of a neutron in the ioniz.ation

(2-16)

.

Iarger the value of N

or the sm.aller the value

bandwidth of the current

of signai to noise''is .

charege is given by

(2-17)

. per Absorbed Neutron

of the aver.age char.ge caused

charnber . The average

- 32 -

chars7e is one of the important facters that deterrdne the rrtpgnitude

of the fluctuation current of a neutron sensitive ionization charuber. 1!) described the average current and the power C. E. Cohn

spectral density of the iluctuation current oi a neutron sensitive

ionization chamber set up in a reactor as follows.

<daM>= .n2 E.Q- , (2-ls) ' <1e.-(}co)2>=2-jlS-c,Q--i{i+s,•1qR(}tu)i2•(-it211s-Sil-Z" -V )} ,(2-ig)

E.D : Detector effieiency (- lll,g:iill f,r.g,ille.:'gill gf "e.".glgllwhere

reaction in the detector ) in the reactor

rt :.Tota!- neutron in the reactor

.2 :' Ef.Fecbive neutron lifetime

qR"to): "i"ransfer r-unction of the reactor

V> : Number of neutrons generated per fission

Ne>2 : Mean square value of nurnber oE neutrons generated

per fissien

Consequentiy, in the case that ilD is sufficiently smaZl. the

fluctuation current only due to the random detection can be observed

in the neutron :Pield oÅí a reactor since the contribution of reactor

noise ( the second term or' Eg. (2-lq) is negl;gible.

Figure2-9 shows the block diogram of the eguipment for raeasuripg -the average cha:ge Q caused by absorpEion of a neutron in the

'ionization charr[ber. The thermal colum of the swinumipg pool typereaetor KUR w,as utilized as a neutron field and there the sarfie ioni-

-33-

l

was

I

Reac or

utli

Current SourceKeithted -;bM-

261nvl

r"-"- (srf-'-'-

CIC

WL-8074iii-i'illi-'-li

1H.V. 1L-t.--.J

"' illl1l

1

pt - --- ---- --- - --pt M pt

II

.

--. -.- - l I l I I i l i

-

Rf

A

---- ---p -- pt ----e ---

Rt

illIlltf

L

ct ct

-

+

Rt

A

irIE(ectro-

l meterL------ --

=

--.. -- -

IC2

H.P, F.

"pt - --- " -h-- .m-

(T,S)

l Ri R,IlI

"J -- -. pt e-

"

---

A

--- -qa

:Ci'

ltltt1

•-• Rf

(1 + Ts s)2

L,P, F.

-- - ---p

1.-e.,.--d.,,-,.-.,.d,--.h

<1 + T,s)Z

l l l l l 'l i'i-w"

RM.S.YHP 3400A

(1+tS)

1,=Rf•Cf

=23FST,= R,•C,

:O.1ST.= R,•C,

: variable

Fig.2-t? Bioek dtagram of the

eleetronlc charge,

equipment for measurtng the average

zation chatTnber as used in the transit tirne raeasureirtent was set. The

•values oÅí the average current and the root mean sguare values' ofi che

f!uctuation cux' rer;"v• were measured at a reactor power oÅí 5"rw. varying

the time constaint o:' the low pass fiiter as a parameter. The value e,of the average cur• r- ent was nearly constant duripg the measurements( =l.l2x lo-6 A ). A current source Keithley rnedel 26i was empioyed

to cancel the a'ver- age current. Thus the sensitivity to the flUctua-tion current was raised tenfold. The equivaient fiuctuation current

due to the internal noise sourees of the eguipments was also ineasured

for the shut-down reactor. rt was much smaller than the fluc-

tuation current measured at the operating reactor ( power level=

5rvKV ) and therefore ignored. In analysis of data obtained

the transfer function of the rfteasuring eguipment was approximated

by the product of `Lhe .F-ollowing three expressions :

. -R+ The electrometer : '-i-FVtr- Thehighpassfilter : sut,S)2 <l +T,S)i The low pass filter : -r.- L-- . ' (t+T.s)zHere the time censtant 't of the electreineter containing a detectorcable was found to be 23 ysec in lo-7A'rapge from the response simulated

by the use pf a step current source. The time constant 'rl of O.1 sec

was also ÅíixeaS :•-er the.;high pass filter. The transit:,tines'T;

and Te had been :'ound to be 14S psec apd O.35 ysec respectively fromthe experimenta] resu!ts by ultilizipg the !inear acce!erator ( the

applied voltage = 580 V ).

'

- 35 --

Table2-2 shows the values of the average chaxge caluculated Erom

Eq.(2-l6) using "vhe va!"e oE the average current and the rneasured root

rnean sguare val"es of the fluctuation current. These rneasured

valties of the average charge in various T2 cenditions show. good agree-

raent altogether.

rn Fig.2-10 the root mean sguare values caiculated from Eg. (2-16)using the relation - Q = 3.7xlo-Z5 A.sec are cornpared with the measu-

red ones. Both results are in good agreement and aZso show the

effect of the trA".nsit tirne oÅí positive ions.

By the waye ED was aZso found to be about 7.9xlO-iO and sufÅíi--

ciently srrTaU frem Eg.(2-l8) using the relations,- :-= 3.lxzolOx sxlo6x

2.47 /sec, Q= 3.7x lo-15 Aesec and <Lah> = l.l2xio-6A.

2'6. Conclusien ln ordeac to obtain pre'cise power shapes in pulsttdreactor experim-

ents, it is im.oortant to deterrnine the response tine oE not only an

amplifier system but also an ioniza"i ion chamber used for a radiation

detector and moreover to evaluate the statistical error due to the

fluctuation current caused by the random detection oÅí radiation. i With respect to the deterraination of the treuLsfer function oÅí the

ionization c'namber, the impulse response was measured using intense garruna ray puzses produced by a iinear accelbrator since the transit

times of positive ions and electrons. The results obtained made it

elear that the trainsfer function is.mainly expressed by the transit ' times of positive ion$ and electrons and that the positive ion transit

time decreases proportionateZy with increasing applied voltage and the

- 36 -

Table 2-2 Average e1ectronic charge caused per absorbed neutron.

;

w"1

T,(iJS) gi(xid`SA•$ec)

1OOO 3,83OO 3e6

1OO 3,7

30 3e610 3.7

3 3.8'

1

8•l

(A)

-7E10LO.

" ivc.9.as-,

J., VF"'

2g- -96108g2n

-1110

'

lt Te

T

NNNNNNxNNx

WL-8074 Te=O,3yS Ti --' 1-4, 5FS

<ia> =1,12xlO A -IS d =3.7x10 A•Sec

N N N N-. NN

Ti'5ii'

Cat.o e Exp•

1ons 1FS

Tiine constant

100pSof L.P.F.

,

F;g.2'iO Root mean square valueS of fiuetuation current.

.

'

electron one consÅ}stently with that. Fror;r the measurernents of the

fluctuation cu]rre.nt utiizi;ig the neutron iield eE a reactor, the

power spectraZ density of the fluctuation current was found to be not

perfectly white bu't dependent on these transit tiraes. This is

expZained irorn the fact that the elernentary current puise of the •

ionization chamber is not <S -Åíunction but'expressed by Eg.(2'6) ,

-rn the past, current-type ionization chambers have been considered to

be unsuited to the rueasurements of puised radiation because of the

slow responsiveness attributed to the posiLive ion co!nponent. However

the electron component ef the ionization chamber permits measuring a

radiation pulse eÅí which width is consi.derably smaller than the

pesitive ion transit tirne, although the response'is accornpanied

by a little error due to the slow component of positive ions.

As, a successfuZ example o-F this propesal, the observed result of the

sarne ionization chamber to a gamma ray pui$e of about 1 psec is, shown

in Fig.2-ll, This response shape i$ mainly based on the electron

component:-•and the positive ion one is scarcely contributive to it.

This will be exarttined in detaU fior the instrumentation of a faslpulsedreactor like the JLB12}.

-39-

Fig.2-llMeasured response to gaumn racyr pulseof about l ysee. [iifh-e upper trace is aninjectien eurrent of the aceelerater and theZorwer• one Em output voltage o.P• 'uhe electrome`ver.HorizontaL sca7Le : l >isec/div. Vertica-trL scale :

--O.2 A/d!v. (upper) and 2Å~10 A!div. (lcwer).

-40-

l)

2)

3)

4)

5)

6)

7)

8)

9)

IO)

ll)

l2)

References

T. Iida and K. SutTnita, To be submitted in N. ucl. Instr. M.-eth.

H. WakabayashÅ}, et al., Proc. US!Japan Seminar on Fast Puise

Reactors r-2 (Z976). .R. Subrarr,ar,ia=, et al., Nuci. Sci. Epg. 13 (1962) 271. .S GOtOh, J• N'-'C-i-e SCi• TeChnOl. 3 [91 (1966) 359e

A. H. sneil, " Nuciear rnstruments and their Uses "e New Yorks

John Wiley & Sons (l962)

Y. Fujitai et al., Proc. SyTnp. On rntense Pulsed Neutron Sources

in J-' ap an !:Z -p -2 (197 5) .

T. Xida, et al., Te be publÅ}shed in Nucl. Znstr. Meth.

L. Co!li, et al., Rev. Sci. rnstr. 23 (Z952) 39.

T. E. Bortner, ee al., Rev. Sci. !nsir. 28 (l957) 103.

A. Van der Ziel, "Noise", ChaprTian & Hall (1955).

C. E. Cohn, Nucl. Sci. Eng. 7 (l960) 472.

J. Wakabayashi, Proc. US/Japan Seninar on Fast ?ulse Reactors

Z--3 (l976).

-- 41 -

!) Chapter I:,I Fast Response E.lectrorneter

3-1. !ntroduction ' ' Pulse reactor• experiments, which contribute 'to the investi-

gation of reacter safety, always require 'a stable and fast response ' . electrometer with a long det'ector cable. rn praetical experi-

ments,.howeveri stability and response speed of an electrorneter ' ' are oÅíten degra•eed by the lopg debectgr cablet in other wordst by

tt . .t .t t a large inp, ut capacitance.. A Åíast' response el'ectremet'eti fer ., puise reactor experimentsJ theref'orer should he designed in

' c6nsideration o.F. the effect of such large input capacitance.

With respect tc the inprovement of the' respon.ge speed of

elec`L.y-ometers, PelchoT"nitch and Zaalhe;g Van Zelt , Dever and .' 2) 3) Sickle and Broo].shier suggest the method of reducing a Åíeed-

back stray capacitance w'hich 1'irnits the response speed in smaU

current ranges. However, this method is not appiicable in'

large current ranges, since the stability condition of the

electrometer usually requires a larger feedback capacitance than ' the feedback stray capacitance in thi's region. On the other hand, pres!ey4) describes a guard technique whi'ch prevents the

' input cable capacitance from reducipg the response speed. This technÅ}gue rnust be useful for pulse reactor ekperiments but

there is a phase shift prob!em for hSgh frequency signals in

large current .ranges.

We obtained a good result Å}n improvement of response time

of the electrorue`Ler by introducipg a new.guard technigue and usipg

the compensation method of the feedback capacitance. At

-42-

first this chapter• clarifies the relation between stahility and

response speed of an eldctrometer and then shows the new, guard

technigue and- experimental results of a fast response electror

meter to w:n.S"ch th•is technique was applied. '

3-2. Stability and Response Speed .

. With a long detector cable, the res'ponse 'of an electrometer

is often accom.panied by overc's.ho'ot" nnd xipgipg" phetiOmena.

t .- such instabiliri.es of thLe el'ectromet'er' can always be reduced by tt increasing a feedL'ack capacitance, which vi11, however, result

in reduction o:•- 'L-esponse speed. rt is therefore important

to choose at first• an adequate feedback capacitance in design

of a fast response electrometer.

Figur.es-1/ shows the equivalent circuÅ}t oÅí a typical electro--

rneter. Here Cin represents the total capacitance oE the

cable and a deteLn.tor. It can be assumed that the input imr

pedance of an operational amplifier is inÅíinite in this discus-

sion. Then, the transfer function of this circuit is described

as follows :

-Rf <5-l) Gi<s)

where

.'t.o

miO'

fo

Rf

-- :E.Lg(S)-) -

!iCS> 1-th("t7o+Rfcf+RfAC,tn)s+'zroRf(ctn+Cf)s27

ro.i To = Ao - 2 X fo , zs tb.e open loop. gain oE the operational arn.plifier,

t:b.e open ]oop time constant of the operationai arnplifier

the unity-gain-crossover-frequency of the operational

amp1itier,

a feedback resistance,

- 43 --

'

cf

Rf

!ircs) i

r

iT•

i-:.

G'n

.=.

+

AoFl()

To=ReCoI o

+

V7.

1

Ei (sl

s 7

Fig,3-IEquiva='-ent cireuit of a typieal e1ectrometer.

- 44 -

Cf a feedback capacitance and

s the Lar.LZ•ace transforTn variable, respectively.

Then, the stab• .'i!i- ty condition of this circuit, in other

the condition tt:/-n`L the poles of Eq.(3-l) are aZl negative,

expressed by

Cf ->. '2R:Oi - C)ii2 +2 tZoCin -- cf,

For C:- < CEo the eiectrometer jl$

having high .F-reguency

ringing- phenomena. Theavoi, ded in measurements of

darrtping condition is realized

rela"Lion gives the fastest

the stable condÅ}tion. If we

into Eq,(3-1)Jthe time constant

T= -t'o+ 'troRfCiM '

Equation(3-3) shows the lirnit of

oÅí a stable electrometer is

and Cin. FÅër Cf> Cfo the < O the electrometer isFor C foCf may be rednced to zero.

condition can be easily realized

technique5) 6). , Table3-:/ gives the critica!

electrometer and an electrometer

technique was applied.

wordsr

can be

(5-2) Rf -' - underdamped and a pulsed inputr

coTnponen'ts, must cause overshoot- and

underdarnped condition should be tt transie'n.t phenomena. The' critical when Cf is equal to Cfo'.' This

response of the' el'ectrometer within

substitute the relatt'on Ci = Cfo

at critical darnping becomes

=. 'ZTo RfCin. (5-5)

the obtainable response speed

deterrnined not by Cf but 1o r Rf

e!ectrometer is overdarnped.

thereÅíore overdarnped even if

rn this case, the critical damping

by using a negative capacitance

damping condition of a typical

to which the negative capacitance

-45-

l

Aor

l

Table 5'lwith a

Criticalnegative

darnping condition of a typiealcapaeitance.

electrorneter and an electrometer

. e-ee-----

Rangeconditlon' Equivalentcircuit FeedbackcapacitanceCforCp TimGconstantT

va '

l- 1cf!cs

I(s) Rf

o9in•,

t-' Zo'' CeClnRf<-4cAiO.Te Ao

colvr7rrES6S")

r

R--

/--CLil/IiL,+F2RfL'-cs.'Uo+CoRfCin

iCP"t'

Rf>;4:=e.:s.AoT

Cin

i

cs-IF-,1. v

1(s) CinZoCinElectrometer

Withnegatjvecapacitance

,

RfRo •+Cs 'CoRfCin

trT.:in J,'t()

tColrr E(s)eli•.,

,

3-3. !rnprovernent of the Response Speed

The response speed of an electrorrteter with a long detector

cable can be rnarkedly improved by reducing an effective cable

capacitance, which is easiZy expected from Eg.(5'3). The '

effective cable capacitance can be redticed using a, guard arnpli- . . fier to equalize cable-sheath potential to center' conductor

potential of the detector cable. ' Figure5-2shows the block diagraJn of an electrometer with

such a guard atmplifier designed by Piresley. This electrorneter

has good response speed in the low current ranges. Zn large

current ranges, however, the response speed cannot be particularly improved because the guard emitter 'follower with a heavy capaci-

tive load cannot reduce the effective cable capaeitance in high

frequency regions. A-n electrometer of this type rnay also be

aPt tO become unstable because or- the degradation of phase stabilitY

of a feedback circuit

!n orde,r to solve these problems)a new guard technique was

introduced as shown in Fig.3-3. This guard rnethod differs

in the following ways from that used by Presley. Firstr 'a

guard arrLplifier is connected to the input terminal of a current amplifier. This is elrfective in preventing extra phase lag of the

guard arp.plifier from resulting in reduction of the stability of

the eleetromeier. Secondly, the open ioop gain of the guard

amplifier is adjustable in respective current rapges. Thi$

gain adjustment of the guard amp!ifier is very useful for control--

Zing the efr-ective cable capacitance and obtaining a best tran-

sient response without any instability. Thirdly,.a iow capae-

itive coaxial cable is employed apart from the ground to mini-

.H 47 --

TRiEAX!AL

.t t

---p

CABLEi

- d-- -e --- - "-

-tt- --- e- - --

-- - -pt- d-- -.

r

r

!NPUT

CIRCUIT

'IF'

GUARDEMITTER OLLOvVER

+- th

-

ENTIALUFIER

ZEnc AOJUST

"eo

Fig o3-2 B]oek diacrram of the o electrometer designed by Presley U).

-48-

.-,y--F:S99tr'aE"Cpa.p--t."--'6'ts'".2/ig.s...-.t

:ll1sl;1lllL...

rt1Esll:

Cp -rFlj,,

+1

circu;

-- ---- s

ci

--"- - " --- ----- --"- ----} - ---e ----- pt - ---p --e - - w- - ---

-.-- .-- " "-- --- --p - e-- -- --- ----pt --p Cs r----l 'h-;

?

I2<s)

CDCL[

i

!1l!l

,l

s

rliil1lll;1

l

AoÅÄ

Ro

Rf

coz

ÅÄ

1

L -l l s 1 s l 1 l l s 1 I l--M-l

M--"1 l l l l 1 I l !

.--' - - --. ..-.1[L,:Roco-. ":.-. -- - -... nt- "- .- - :- "-J

Lcurrent ampliiier-- N- .. -. -. -.- .-," -" .- : .-- pt .pt ---t--e-" - '-' ---1

+ RiAi

CiZ T!=R;Cl

+ 1

R2

IE2(s) I.,i!i,. I

l l l l 1

Fig•3 -3

ALGuard ' 'EczuivaLent eircuit of

-- pt pt ---- r" -- -" ----- ----- J

ampMier

a nevly aesigned eiectrometer.

-49-

G2(S)- I2(S)' '

where Ci" : CAC,-+t' CID •

Al is the

Tl the open

R2 the output

Cc a cable

CD a detector

CF an

CL the 'rt is evident

effectiveiv . 1 andboth aR"are much smaller

G2(S) becomes

mize the capacitive load of the guard arnplifigr. This is

effective in maintaining phase stability of the guard amplifier

'in the high freguency regions. Furtherrnore the circuit shown ' 'in Fig.5-3 has a feedback-capacitance adjustment circuit, which -•can add an equivalently negatiye or p6sitive capacitance in

para!!el with a feedback resistor Rf.

The transfer function of this circuit can be written as

follows :

'

--:ti- F( EI; Fi+(•t +RfcF+ SRSÅíii<g4:, )s+'toRf(cLn -t-cF)s2,

( 1 -t- Ti S)( 1 -t- R2CLS)

(3-4)

l+( A,+L IS-V[ A,.i Si open loop gain o.F. the guard arnpZiÅíier,

loop time constant of the guard arnplifier,

resistance of the guard arnplifier,

capacitance

capacitance,

equivalent feedback capacitance oÅí the feedback-

capacitance adjustment circuit and

capacitive load of the guard arnplifier, respectively. ' . frora Eg.(5S) that the input capacitance Cc+CD iS CCtCD for the frequency much lower than reduced to A,+ 1 2T(IR2c.• '!f the vaiues of both Ti and R2 cL

than the time constant of .this electrometer,

approximately egual to the expression(5-1) with Cin

Ti + R2( Cc +CD 'lr CL) R2(Cc + CD+CL) T,(5 --5)

- 50 -

rep1acedby-iCts5i-IFX?iÅ}tCID'

electrometer at c-v• itical

Consequentlyr the

damping becomes

time constant

=!IMT- by a factor of

of" this

' T'= to+

The response

beyond the usual

-' o R Cct D

Al

speed can

limit.

tbe

1

improved Jrxl;;i-

(3--6)

'

- 51 --

3-4. Practical Circuit and Experimental Results

A practical electrometer circuit is shown in Fig. 5--4

A model 1430 FET operational arnplifier ( OP. Arrtp. I ) is used

for the current arnplifier. A unity-gain-crossover-freguency

of the operational amplifier is about 100 MHz. The.guard . antplifier is rnade up of a junction FET model 2SK19 ( Qz ) and

a rnodel 1430 operational ampiifier ( OP. Arap. 2 ). The FET

QI has a nominal transconductance oE 6 etN(5 at 200 MHz < VGs== O ).

The open loop gain of the guard arnplifier is given by

Ai" gTn RL) (5-7) where grn i$ the transconductance of Ql and RL is the feedback

resistance of OP. Atmp. 2. The time constant Ti of the guard

arnplifier is mainly determined by the product of feedback

resistance RL and the stray capacitance oÅí the resistor RL.

Hence Tl may be considered to be of the order of 10 neno-

seconds. The output resistance R2 is generally several tens

of ohms and CL may be of the order of several thousands oE pico-

farads in practical experirnents. Then the time constant R2

CL becom.es of the order of IOO nano-seconds. Therefore, it

rnay be considered that R2 CL is much larger than Tl and mainly

detemeines the frequency bandwidth of the guard amplifier.

[[Xvo transistors, rnodel 2SA495 ( Q2 ) and 2SC372 ( Q3 ) are used

for a negative capacitance circuit to give an adequate feedback

capacitance for critical darnping.

Tab!e5-2indecates themieasured results of response speed of

this elec"LrorReter with a signal cable ( RG--59/U )r whose length

was 45 rneters, laid on the flOOr. The feedback resistor R Ti was adjusted in order to obtain a best transient response fOr

-52-

COAXIAL

Cp sp

CABLE

Rp

I-

t1l1lIl

rIlltl

O.ln1K ' d-twf6m =cF-,,{-151K

'I['lgr'i}

i(t) r

-ny

fi IK e

g,/tt.Il,s'1nys.a.;/,

5 loSAefpacho+.

+15V

t

pt

7r2N3058x2

1Il

1l

lllii

L

r

1430

+ IK

1lt

?

100

+15V

3K

1

tr

7

2M495 2K

3d3

r

.1

5K

=10

o.vaXlbe1ooK o-,v5 Ze soKRL "-ve i-o soK

-15V

OUTPUT e<t)

vFD 6A

+1' 5- V 1OKo-`,51-o 1OK

2SC372

2K

2SK19

3K

+15V

-15V

1430

+IK

hi

2K

i2i

-1Sv"'

ISV10K,1

10 '

O.1

=

IK

Fig,5'-4 A T.,ractic al electrometer eircuit.

.

s

,

-53-

Table 3 -2

in Fig. U.N!easured response speed of the

fb = 100MHz ; Cin = cc =eleetrometer3ZOO lpF .

circuit shown

sFeedbaek

(

resistanceohm)

Rf Measured<IO-90 %

risetimeptsec)

CaLcuiated.galn Al

open loop

o .2 IUloS o5

'

23lo6 z 58

lo7 3 6k

log 9 71

-

-54-

each current range. The increment of RL shortened the risetirne, 'e ' ' but for too larg.e RI, the electrometer becarne unstable.

Henee the maxiLT.'L=n value of Rl" was selected considering the

stabUity and ihen an adequate feedback capacitance for critical . Table3'2 also darnping was adjusted by a variable resister R p' ' gives the open !oop gain Al calculated frorn Eqs. <3) and (6) by

using the measu:.Led risetime, and Al shows the degree of improve-

ment of the res-ni onse speed. ' Me.p.sured ntvsise of this electrometer is shown in Table3'5and

a discussion on the noise problem of the electrorneter with a

long detector cable is shown in the Appendix.

Figure5-.: shows an exarnple of observed results of power . 6) with this elec- shapes o-F the one shot pulse reactor "YAYO!

trometer and a current charnber WL-6377.

Figure5"6shows an exarnpZe of measured burst shapes of gamtma .7) rays generated by the linear accelerator " KUR LINAC " with this ' electrometer and a current cha;rtber WL-8074. The response is

noisy because of many intense noise sources in the target room

where the current chamber was set upr but no overshoot- and

ringing- phenorrtena are observable.

3-5. Conc!usion

The limit o-F the obtainable response speed of a stable

electrcm.et• er• wi'-• h a long detector cable is determined by the

Åío!lowing three iactors : Il] The unity--gain-crossover-frequency

of an operationa! ampliÅíier, I2] a feedbaek resistance and [3] ' the detector cable capacitance. In order to obtain fast

response of the electrometerr it is,therefore, necessary to use

-- 55 -

Table 5 -5

in Fig. 4Measured Cin =

noise eharaeteristies of

3100 pF..

the electrometer circuit shown

Feedback resis+.-=.r•:e r•leasured noise voltage(ehn > ( rms mv)

lo4 u

10S 12lo6 35lon 63io8 130

A--..<c

So'iE

:•

c o L L =v

1

O.5

..

l. .. -LLi.

1 -Lp ,l. + i l''l'

4t

.- +l. -.I il ..

I•l r+ -l''

''' -t- '- H'{'"'" I i' Li '

l.l''tt ''

. I,....l•-.

' +1 .L

"i" }"'ir;4'- •- -Li r'

i

.!... ..iti

'i--t-Y• i-- I•i.J'i-.-

'i

l

i'n i '.' r-t" 't

,

l- -• /- ;/

t "It''/,T.l.'::i r/::

-r'`--:ll, l-

1" l I t-L'1 '-' r--lt-. -- -;:

I, -i- i : t.t

l•.

;- 11r

r.Y..-'/1i'i/ll/;.,liL.L.]L'rl'iF--

;/

i;-- iiril•:

1

} trrl-i'

. ;.

]1•, 1.: . .LLE-.:H•

't''--IT.F':•

l.

[ •l: .I;Tl.J,1-

Eiiiii '•- •li.

Ih

,F,-i-L-;-".T;L:-l-:t

i!

.i' i' . r

/J t i•I

/t:'re + r'-. ri 1' '

,.•l , iEi:,rf•?l/f-l"

' /t.;

1 d 1II

--• I t 'l

-" -l 'r.1.

r' i '+

re1I

:t

i3s-{iL{/rr'':.Illl'i'iiIlil':'

''t'

'+- rl-=7t-l':T+tr1'r•

l' I

.iT. J.f

.l- i-

1,.I.ii' r='

i::-;• IL ;-ri,/

'''- r '/'=' tZ' -.i Ll rl-

/lt i

'l''' l

t-t '

ITIi-ii:-r-:.•l'-.i.i•ii

t' I

- r- I Hf.

't

''i'

J. :i lL:

,7•:' I" l•

l t'I l 4Lk. L-L=-I i]=' l

-i;• -I li '. .i' .l/.

't

1 't Mr ;- -t• -t -L--.- - !- lt . tt tti•

.: -r --. -..L-

l

-- "i' ' '- '-'

i '' 't'

s-. I

v- :l•' 'i l" I

-----S- --- -F- t l l . I t. .;-- r---7-7T---tt7=.Tr. ,

ri :.Ll.l

•i-l :-+- i

i11

-l:-,i- 1,. rt,I•ri,l/:ll-;-

.I11 .1•1 ;.ll -L ;•- F-

l

A-.L•I

l'' -i• =

,

--•l.i l-i. I.. t +t

tsI." H L---

il iiIll,.iTL,•.l•

i' il• --

'', -. l::,

-?-- '

t/

'r,- t• i--

i'

tIH'`v

L.F it. IITT•l'Ii!ui`:

/ tt t-tt

i

:: iLil• Il-y- ;,'i' li.i .";I

. . l/ . , .

'rL.'1t-.-t- t

,

i't'

l'

'

..1.-..1

l'x i tt .T i i' l''

i•l•-t", ,- i'i i ' tl ii 1-l -'' :-' J

.;,. .- .. -l .. ...

i"

l'TL' i ! l

t i l 'l

i-r:iill

.Ii,r+ -- i' •I-

"'-' i-:r '/r l.i.

'i' •II

i: 1 l-rl-r

{;i"'- F-' i" ii."-v,;l gii {ii[lflLl -'"L-rt'-J

-i'ilyS,A-Y

'

I.

't.-

.I

;.

iigP u h

- !.-

;lili ':z :-

.I -.it.t-

oTt f----- I

.tttT,ii2i,.,llll;li,tttkTK•ll,ii'-f-'-ii'-i'

l- av,-tL-li- Xlj it"gV NJill

;

'" 1, :- t

..-. ;

o

Fig.3-4 PLn example of observed

O.5 '

T

results

--- 56

1

ime<ms>

of power shapes of the " YAYel tt.

E.,i.

'

E5L;i.,

ie--,.gl -Eil-i•...

F-.-`•

E..i•

eweeeepaeeggeew- eswayggNsesss ggsggxgsggggeesptgr. ggg:sue.g::x:xee

Fig.5-6 An example of measured burst shapes ofgarzrna rays generated by "KUR LINAC". [Vhe upper

trace is an injeetion eurrent of the aeceleratorand the iower one an. output voltage of the electrometer -' U A range. Horizontal scale : l}is/div.in the 10Vertieal scale : 200 mAldiv. (upper) and 2xlOrU

A/div. (lower).

-57-

an operationa! an•plifier with a sufficiently high unity-gain-

crossover-frequavncy or to reduce an effective cable capacitance.

Until such opgrati•onal amplifiers become generally available,

we have to imrv.v.• •Jve the response speed by reducing an effective

cable capacitarsce. For this purposer a new. guard technique

was developed and a fast respense and stable eiectrometer was

made. 'i"he response speed of this electrometer with a

detector cable c:-; 45 m iong was improved about ten times compared 5) 6)with conventio.'•';a:t ones . A feasibility test of thiselect-rom"eter systern• was also carried out using the one shot

pulse reactor "YAYO!" and the linear accelerator "KUR L!NAC"r

and satis-Factory results were obtained in transient measurements

of those devices.

-- 58 -

Appendix 3-A Noise Characteristics

When a lon,g detector cable is cbnnected to an electrometer,

a considerable output noise voltqge is present even under the 'ideal conditio=•i where there are no external noise sources. 'This noise voitage is due to the internai noise sQ'urces of. an

electrometer and its magnitude is related to the' construction

of the electrcx•:.e'L'er circuit. Sources contributipg to the

internal noise cf a typical electrometer circuit are as folXows :

[1] Johnson noise of a feedback resistor.

[2] Eqwivalent input nolse current of an operationaZ

amp1ifier.

!3] Equiva!er.it input noise voltage of the operational

ampZifier.

Jo:nnson noise of a feedback resistor may he represented in Fig.3-

Al as a voltage source enl.. Equivalent input inoise current and

voltage of an operationa! amplifier may be represent as in and

en2. In large cur• rent ranges, the valu.a. of boVn enl and in Rf

are mueh smaller than that of en2. The output noise voltage

is, therefore, mainly deterrnined by equivalent input noise voltage

of an opn-.rational amplifier.

The mean square voltage of the output noise of the electro--

!neter circutt• oi Fig. Al is approxirnate!y given by

<eT2>=--. ST <)v,-(co) Gi8fde)•(lt2bo Rf<cin-c?l2 dw ) (s-Ai)

where (t)ftv•,e(iw) is the power spectral density of the eguivalent

input noi•se voftp"ge of an operational amplifier. At critical

danping, we get g.n.y substituting the relation Cf = Cfo into Eg.(3-Al)

- 59 -

' ' <ecjk> = S[l' (it) Q, zr(co)l c} .tr Jd'. :i ;\N), 2d co . (s-A2)

'where TN =.tt J' ilT tJ'R:f71i3;)2 .i RfCin

'

rf one adopts an approximate condition that Åëvv(co) = k( con-

tstant ), whic:n- is reasonab!e in large current ranges , Eq.(5-A2)

becornes

<e.2>.-.T4EKYBt\il!sCLn (3-A3) 'Equation (A3) shews that the output noise voitoge at critical

damping is determined by the following three factors alike on

the response speed : !1] The unity-gain-crossover•-frequency

of an operational ampli-Fjer, I2] a Eeedback resistance and [3]

an input capacitance. It is also evident from Eqs.(5-5) and

(3-A3) that it is effective in the design of a fast response, low

noise electrometer to reduce an input capacitance.

Figure3-A2 shows the equivalent circuit oÅí the electrometer

of Fig5'4 for'the aid of noise analysis. Equivalent input

noise voltage of the guard amplifier may be represented as en3. 'The Tnean,square voltage of the output noise at critical damping .is similarly gÅ}ven by

<es, 2>ti 5ff #>..(Lo> (ii t, /I Iil;I;"l)2 2dw+Ir (i> .(w) aJ'.coai"T,), 2d co , (3-A4)

. rwhere TN,, k RfCtn ' Al+1 ,

* !t is

istics

t

necessary

in small

to consider the excessive l/f noise character-

current ranges.

- 60 -

cf.

c•pt Iv

en2 N

Ai 1/P.

t-it

F

l

Ao

Ri

Ro

Nenl

col

+

T=

-

1T

ens - -.

Fig.5-Al Noise ee'L::':va Lent eirctitht of a typieal ..1

electremeter.

CF

Ci,n -

'

ng

en'2

7

+Ao

'stV

en3"

Ri

Ro

ql

ÅÄ

A,

'=' T

-

+

1

Rl

c'I

=7

-

.-

1

T.en

&v

Fig•5-A2 Noise eauivalent cireuit af the newiy designed eleetrometer.

-- 61 -

Åëtv(co) is the power spectral density of

noise voltage o!r the guard amplifier.

= k'( constant ), Eq.(5-A4) becomes <eRR> " "z- F"'?'<,;'Cltilll5IllElf C,5" '(Ai+l)-i+ 'i4< k' RfC

'The output noisav voltage dUe tO en2

cable capacitance, but on the other

age due to en3 increases. Assuming

s <eon' 2> :---. <er,2>•( Ai+ 1)T for

This shows that reducing an effective

approximately equjvalent to extending

frequency of an operational amplifier

t,3

decreases

hand the

k= k'

A,

cab1e

the umty-gazn-crossover-

.

the equiva!ent input

!f we assume Åëlv(tu)

in .(Ai+l)l (s-As) .

with an effective

output noise voit-

t we obtain

>>l (5-A6) •

capacitance is

--

- 62 -

1)

2)

3)

4)

5)

6)

7)

References-

T. Zida, Y. Kokubo, K. Sumita, N. Wakayama and H. Yainagishi,

To be publishedin Nucl. rnstr. Meth.

J. A. Dever and L. Sicklesr Proc. Nucl. Epg. and Sci. Conf.

Paper V - l5 (l959). 'W. K. Brookshier, Nucl. rnstr. Meth. 25 (1964) 317.

S. P. PresXey, Rev. Sci !nstr. 37 (l966) 5.

N. Wakayaima and 'i". rida, JAER!•-M 5955 p.p. 127•-130 (l975).

K. Sumita, T•. Zida and N. Wakayarna, Proc. US/Japan Seminar

on Fast Pu!se Reactors !rr - 1 <1967).

Y'. Fujita, Y. Kinura, K-. Takamig S. Yamamoto, T; Kezuka,

S. Hayashi, K. Kobayashi and T. Shibata, Proc. Symp. on

Intense Pulsed Neutron Sources in Japan II! - P -- 2 (1975).

.

-63-

l) Cha.pter IV Fast Response Logarithm.ic Flectrometer

4-1. rntroductÅ}on Many experiments have been carried out Åíor the investiga- .2) tion of reacto=• safety at thepulsedreactors of the " NSRR , the "yAyol"3> aind others. The lpgarithmic electrometer,

which covers a very wide current rapge,is useful for those

pulsedreactor experiments. rts response time has been

generaUy iimitn-d on account of instabUity caused by the input

capacitance oÅí a detector and a cable. Zt requires a large

feedback capacitance to obtain the stability at high current

levels. Therettoret its response time is severely degraded

at low current ievels. In the ease that a smal! feedback

capacitance is selected to obtain a fast responset the response

of the logarithirLic electr•orp.eter is often accompanied by overshoot--

and ringing- phenomena at high current levels. Such contra-

ries between the response time and the stability oÅí a logarithnic

electrometer are caused by `Lh' e rnarked change of the current

dependent resistance of a logarittmic elernent. This has

made i`L- difficu!t to design a fast response logarithnic electro-

meter forpulsed reactor experiments.

In order to solve this problem, we proposed a phase compen-

sation techniquav which was reaZized by inserting a resistor between a detector cable and the input terminal of the circuit4).

This technigue made it possible to improve the response tirne

at low currerit levels. Howeverr at high current levels, the.

Iogarttnmic e]ectrometer with this technique has poor response

time which is determined by the product of the inserted resistor

' and an input ca.pacitance.

-64-

A new phase cornpensation techngque was deve16ped to over-

come this problem and the marked improvement of the response

time of the !ogarittmic electremeter was obtained. At first,

the relation be':'-ween the stability and the response time oE a

logarithmic elavctrometer shall be generally discussed and then

the new phase corrpensation technique and experimentai results

of a fast response logarithnic electrometer shali be intreduced.

-65-

4-2. Stability and Response Time Figure4-l shows the equivalent circuit diagram of a conven-

tiona! logari'L"!hL::•ic eleetrometer. Here Cin represents the

tota! capacitar.-=e of a detector and a cable. An operational

arnpliii'er has srn•ooth 6 dB/octave roll off providipg stabZe

operation at aU values of gain. Se:niconductor diodes or

sUicon p!anaL. ='ransistors have been recently employed for the 5) 6) logar-'thmic e!eme,nt D .. The relation between a current } Ld. , flowing t.t•"'.-ough the p-n junction and a voltage 'UTOC across

it is given by

Lck =Ls •[ ex p(f vd /nkT) -- LS , (4'l>

' wherav Ls is the saturation current and is ternperature depend- •

en#t

X the electronÅ}c charge,

trL a factor which depends on the density of the

recombination centres in the junction region, l? Boitzmann's cOnstant an, d

1- the absolute temperature, respectively. When eot >> t[ s , Eg. (1) is app roximated by

ifct == nigT 9. gL&s , (4--2) which shows good logarithrnic characteriStics.

Figu-re4-:7 sln•ows the rneasured LcL-'Ud characteristi.cs of a

diode-connecta.-a' model 2N3058, which was used for a newiy designed ' . Iogari'thmic eleci -rometer. The result gives the following

va!ues : 'rL = i.o, ts= 6.oxio-i4 A (T = 3ooQK ).

- 66 -

l cf

D

r

orst

T

--S .Atl --he>

/lx Cin

- "' r.,- = d-t

Ao+ To=RoCo

co

]e

+ 1

'

.b- =.e

e+Aq

-

Fig.4'1 Eguivalent

Xogarithmic

circuit diagram of a

electrometer.

conventional

'

orco

:

.

'

.

,

A>vv>

O.7

O.6

O.5

O.4

O.3

O.2

O.1

o

-- L'r'n-""'--ml

is{

:

!

ii

1

lL

v-

/

-"

L l 1T--L' t" 1

+

(

-SLOPE=60F t

i

,

60 mVldecade

1

l'1

-1310

Fig.4'

-t210

2Logarithmic

io"' io"O io-9 io-8 io-i io-6 '

characteristics

. Id (A)

of a diQde-connected 2N 3058 for [r=

-510

'3eo K,

-410 lo-3

G, (s)

where

The transient response of a logarithmic electrometer can

be generally exr.-ressed by a non-linear differential eguationwith respect to iime7i. rt 'is troubiesome to soive the

difEerentiaX egL'a`i ion, so that it is difficuit.to obtain the

simplified relai icn between the response time and the stability

of a logartthtT:Li• ny'v' electrometer. For present purpose, a srnall

signal response analysis was adapted and it makes easy to eval-

uate the reZat• i-on•. between the response tixte and the stability

of a logarith- imic electrometer. rt is evident. from experS.-

mental results T.rhich shall beshown in section4'4that this analysis

applicab!e to our• purpose.

The t.T.ansfer funct-`.ton of the !ogarithrrric electrometer

circuÅ}t shown in Fig.4-lcan be described as foilows :

6}!s (S) --' rD 4ll (S

To ='

rD--

Ae

mi•O

fo

Vp

) i +( YXC.ih + rD Cf +Ce) S + VD (c;htCf)z,s2 )

'r7. N = Ao 21Llo ,npT.! I L )

is the open loop gain of the operational

ampiifierr

the open loop time constant of the operational

ainp li fier ,

the unity-gain-crossover--frequency of the ' ' operational amp!ifier,

the linear resistance of the logarithrnic elemenu

is

(4-3)

(4-4)

(4-5)

- 69 -

Cf- r. A. -V2

For Cf< Cfo the iogaritb;m.ic

a pulsed inputt having high "

overshoot- and r• inging

should be avoid in

critica! darnpimg condition is 'This relation gives the

electrometer within the stable

the relation Cf == Cfo into

critical darnping becomes

. Ti --- Co t Co rD C;n

Which shows the lirnit of the

logarithTv.ic eiectroraeter is

.and Cin . For Cf > Cfo theoverdamped, not to raention of

meter sbould be overdasmped

As showi"i by Eg.(4t:4b")r the

element varies according to a

for the small signal and it increases proportion-

ate!y with decreasing bias current,

Cf a feedback capacitance and

s the Laplace transform variable, respectively.

Then, the stability condition of this circuit, in other words,

the condition that the poles of Eq.(4-5) are ail negative can be

expressed by

> 'Ce- Cin ToCin .-.. rD

electrorneter

!requency

phenomena.

raeasuremen`Ls of

rea!ized

fastest response

condition

Eg•(4'-3) r

==. T.Y,C

obtainable

deterrnined

logarithrnic

stable

for pulsed reactor

resistance

bias

'--' Cn (4-6) to .

is underdaimped and

components, rnust cause

such underdamped condition

transÅ}ent pheno;p.ena. The

when Cf is egua! to Cfo.

of the logarit- hmie

. If we substitute the tirne constant Tl at

in (4-7) )

response time of the

not hy cf but 'C., rD

electrometer is

. A logarithmic electro- experiments. s Yp oE the logarithmic

current flowipg through it.

-70-

Consequent!y the darnping coefficient' of the lpgarithrnic electo-

rrteter dependS'on the level of an input current. Hence, it is

necessary in thmu design of a logarithmic electrometer to ensure

the stability all over the measuring current range.

The criticai damping condition of the lpgarithrnic electro-

meter shown in Fig.4-l was calcuiated varying an input bias cur-

rent. Here input capacitance Cin was esti!nated at 3000pF, which is nearZy equivalent to the total capacitance of a

detector and a cable of about 40 raeters. A BIOS FET opera-

tional amprifier which is easi!y available also has the follow-

ing features : Ao = 10edB, fo= 1 MHz. The feedback capaci-

tance and the tiiin,.e constan"L at critical damptng were caiculated

fro;n Eqs. (4'5) ,(4-6)and(4-7) using above values. The

results are shown. in Fig.4-5. In the design of a linear

electrometer, Å}t i's possib]e to select an adequate feedback

capacitance for each current range, but in the case of the

logarithrT.,tic electrometer such a selection is inpoSsible. Whenmeasurements of the rnaximum current of io-3 A are assigned to

the logarÅ}thrnic electrometer shown in Fig. I, it needs a feed-

back capacitanc.e of 14700 pF ( = Cfl ) Åíor the stability. which 'is shown in Fig.4-3( curve A >. The response time of the

iogari'Lhmic electrometer with that feedback capacitance Cfl is

nearly determined by the product of YD and Cfl , so that it is

inversly proportional to the input bias current. This is'shown in Fig.4-3 ( curve C ). Consequent!y that logarithmic

electrometer suL"--f• ers from the severe degradation of the

response time a`L low current levels. For exarnple, the re- -IOsponse time becomes about 3.8 sec at IO A level (= O.026V

- 71 -

1

"Ml

AtLct

vNv cU

-"bJ.UUQUv

"Y.UrrAvNNL

S10

.10

310

210

10

1

---

.

.

.

<tta"--i

c -•.ti.b)

A

B!-"..)

muN-"-b.""

147OO pF ---•

5tabte

Unstabte

.

.

.

.

io-'O ib-S 'io"8 io-7 io'6 ie`5'' io-4 !nput Bias Current <A)

F'ig, 3 lhe crttical. dEunpSng eondttlon of the iogarSthnic eleetrometer Bhown in Fig. 1

the feedbaclg capaeitanee for crttical damptng, curve B the tlme constant at criticaLeurveC the time constant of a eonventtona.l logaritnde eieetrometer, fo = l.MHz ;, AQu3000-pF ; nkT/g = 26 mv,

, Curve

daniptng

100dB ;

1OOm

1Om

lm

100p

1Oy

10

".nd

Cin

lp

O.51p

-3

shows

=

l.,.,.

ut

v .-., c U .+.., ut c ov,NEF

ÅÄlo-10 A Å~ l47oo pF ). Thus, the conventional logarittmic

eZectrorneter such as shown ' in Fig.4-1 cannot be aPplicable to the

wide range instrumentation ofpulsed reactors of which powers

widely change wdS.th very short reactor period. It is impor-

tant in design of the logarittmic electrorneter forpulsedreactor

experiments to Å}mpxove the response tirne especially at low cur- 'rent levels without any instability.

-- 73 -

4-3. ITnprovement of the Response Tirne

If the feedback capacitance of a logarithmic electrometer

can be regulated along the curve A in Fig.4-5 ,the response

tirne will be rctarkedly improved without any instability. t Such improvement is shown as the change frem curves C to B

in the sanLe r"ig.4•-5. The curve B shows the time constant.of tt the ZogarithrrCic electrometer at critical damping. Such ' eonceptien, usinc. a variable irnpedance element for the phase

compensation should be vaiuable in the improvement ef

the response time of a ipgarithmic electrometer. rt is difii-

cuit to obtain a suttable feedback capacitor corresponding to the

voltage across the logarithirnic e!ement. Thereupon, a new

phase comp.o.nsatien technique was developed in place of the eonven-

tional method, w:nichwas using the feedback capacitance in paral-

lel wtth the iogartthrrnic element. The eguivalent circuit of

a !ogar"Lb-.rp6vny' e!ectrometer with the new technique is shown in'

Fig.4-L'". This technique is based on that a resistance rx

inserted between a detector cable and the input terminal of the

logarithnic elect-roni eter recovers the phase iag caused by the input capacitance 4) 8). Moreover such inserted variabie

resistance rx can be regulated according to the level of input

current and is easily available to adapt this phase compensation . ' technÅ}gue.

The trans:ee-r function of the logarithrnic eiectrometer

circuit shorm Ln Fig.4-4is expressed by

4E. t,tS) --b G2 (S) 6 ;• : (s's)t l -t ( trxCs•n + y. c;A + 'cb) s -}- 'CTo (tb+ icx ) Cin S2

The stabUity condition of this circuit' can be given by

.

(4-8)

-74-.

D

'

"C.J'1

'

eel,.A-IS) rx a)

.

1(t) '

-- "- -

-

AoRo

+

ICo

+

-

v

1

e,"Ae,(t)

-

Fig. 4-4 The

electrometer.

equivalent circuit of a newly d+ esigned logarithmic

'CO VD Yx >' c;n - Ao +2

For rx > ro Th•e logarithrp,ic

for rx < ro it is underdarnped

rx = ro into Eci.(4-8), we

critical damping as foXlows :

T2 = T. + v. r.Cin

which is the sam.e as Eq. (4-7)

the new phase compensatiofi

$tab!e response as well as the

The values oL` i'Å~

obtain the critÅ}cal daimping

electrorLete.'" vt-ith this

If the inseried resistance rx

D in Fig.4Sethe response time

will be Å}deaUy improved.

obtain such an ideai resistor,

$uitable for this'technique

use oE some resistors and a ' 'the response time of the 'technique cairr be markedly

ci. -- ro .

electrometer is overdamped and

. Substitutipg the reiationobtain the time constant T2 at

v.rp (4-q)

"• To XpC;n , - (4'IO)

rt is evident frorn this that

technique is eÅífective in obtaining

conventional rnethod.

depending on input bias curre-nt to

condition of the logarithmic

technique is shown in Fig.4-5 (curves D).

can be regulated along the curves

of the logarithrnic electromeYer

Although it Å}s Å}mpossible to

a cu'rrent variable resistor

can be easily obtained by the

semiconductor diode, and hence

logarithrnic electrometer with this

irnproved.

-76-

I

susl

l,-.--.

qvÅ~

-

100K

`

10K

IK

100

10

A,=1OO dBE

-Xk

Ao= 60 dBD

.

io"O io'9 io-8 io-7 io-6 io:5 . io-" Input Bias Current (A)

Fig.4-5 The critical damping condition of the logarithmic electrometer shownCurves D show the inserted resÅ}st.ance for criticai damping and curve E that ofelectrome'ter''shown in Fig. 6.

in

the

-310

Fig. 4.

1ogarithmic

4-4. A Practical Circuit and Experirnenta! Results

A newly designed logarithrnic electrometer circuit is shown

in Fig.4-6. A model }ipc l52 A MOS FET operational ampiifier

with a unity-gaÅ}n-crossover-frequency oÅí l MHz and a bias current of lo'-!3 A is used for the input stage ( Amp. 1 ).

The open loop gain of the operational amplifier is Eixed at 6o dB by a source feedback technique 9). !Ehis is effective in

suppressing the maxirnum value of the inserted resistance as .

shown in Fig.4-S (curves D). But it will cause a steady-

state off-set positional error to fix the gain too low. A -- 1ly rnodel 2N 3058, having a saturation current of 6Å~10 A,

is used for the logarithrnic element. . The inserted current

variable resÅ}stor is composed of a current variable ele;nent Di

and two resistors Ri , R2. [Phe same diode rftode 2N 3058 is

used for D{ .' The calculated resistance of the inserted

resistor for si.all signal is shown in Fig.4-5 ( curve E >.

A logartthmic output is aimplified by next arnplifier ( Amp. 2 >

b.uilt up with a rnodei 2LA 741A operational am.plifier. [Vhe

gain of l6.7 magnification.g. <= IV ÅÄ 60 mV ) was adjusted

by a variable resistpr R3 and hence the gain per decade for

this logarittuntc electrometer was chosen as IV/decade ef

input cu-i rent. ' !n order to iix an output voltage to O V at an input cut-vent of lo"10 A, a bias voltage of 22o rnv

was applied 'to the A:np. 2. The zero adjustrRent was made

by,a variabZe resistor R4.. The temperature infiuence for

the IQgaritbJntc elanent is also compensated by two therrnistors

RAr RB used in this arnplifier stage. The fundamental

principles are shown in reference 10).

The input current signal for testing 'was prepared frorn

-78-

t

Ne:

rx(i)

10k

---

5k

-"r-

RI 60k

.

I (t) 4

2N3058

tr

Dl

Cin(3000p)

R2500

.=-

"5V

;447 11 -10

2N3058

-- =-

Zero Adj. 20k 2k 20k-15\.wwww>.

R4

D

-p

+PC152A

500k--it-

- :-•

500

+15VPii

O.1E[.

-15V

500k

Gain 200

Adj.300

LR3

--15V

500

15V

500p

5.34k

40k

s3oS

2k RA

+

2k

pA 741A

'r

10k

5T-32+15V

EOI:i

e(t)

to

-=.

Out Put.

-15V

2k5T--32

RB

L-isv

.. =-.

.- :-.

'

Fig.lt-g6 A newly designed logarithnic erectrorneter cireuit.

.a bias current Lb and a squaace pulse current with an 'arnplitude of about O.05Lb. As expected from the stqbiiitycondition shcgyTn. in Fig.4--5 the observed output waveforms were

accompanied Py no overshoot- and ringing- phenomena in the wholecurrent range :prc.m lo-IO A to lo'"3 A. The:measured' .resuits 'of the m'se ti,grme, oE this lpgarithmic eiectrometer are shown in

Fig.4-7. The measured data ogree neariy with curve F

calculat• ed Åírom :•a..(4'8) using the curve E in Fig.4-5. A

curve G Å}n Fig.ts7- shows the rise tirne of the conventional

Zogarithtrnic eieetTrometer. It is evident frem these results

tha+L at ]ow curr- ent levels the response time of the iogarithmic

electrometer wi• th this new phase compensation technique has

been improved two decade compared with the comventional

one. ' l?ow-er shapes of theon-e-shot pulsed reactor " YAYOX " we]re

rneasured by the use of this logarithnic elegtrometerr an

ionization chamber Westdnghouse type 6377 and a transient

memory Iwatsu type DM 701. Figures4-8 and4-9show examples

of the cbserv'ed power shapes oE the " YAYOI " in the puise

operation below and above prornpt critical state, respectiveZy.

- 80 -

l

coNt

voeoE

--

o.9cr

1oom

10m

lm

100P

10P

IP

.

10-io

Fig•4-7

"h,

K N N N N

F

NX

NN .G

Å~x

NN

NN

o

""

o

Calcutated

Experlmentat

Conventiona(

NN

NN

N N N N

NNNO

xN

NN

NN

NN

NN

10-9

Rise times

lo"'8 lo-7 lo-6 lo-5

Input Bias Current

of the logarithmic electrometer shown in Fig. 6

(A)

and

10-4 la3

the conventional one

t

coN

l

v<

9Iiiiii

ee-' s

ag-.,

=

163

lo'4

10lt5

lo-6

167

16810"9

16iO

li-' ii"

iop. -e.. L l r-Li

HJ=r

cliL

-- :"

= ,

t

b.:. -..i-+ 1

itT-

'l • T ;

tl J

+T ' ,rtt -

,

t

--ITTt

l

- gf,i,

+-''1

-" r.N-bll

+l

tL 1'I' t++ tT rri +tb

,l,,1

"' lx

,i , lll'r

t-+ vt. i-Ti 4tf,xL lhSdT

tl:/lI'i-r

rtll

-r,rIIrl

-:'ti

1-A. + , - -l

-l i

-•;-kb,T l

""t' tlt+;Ii+i ++hll "1rt i.:'.yt

/

-:t

y-"t'li;

JI'lt

ltu,!

1

ii

Il tT

+Tt+

-f:

L

lz

pt It

-l'i'

ltir

-tt 1

,

1

' li'

"lr IT

' y+

IT:

rlli

TIFHt

,

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Hl

li,

T;:,pf

I"•

1

L7 t

--Tr'IJtT

-"1-

vl

1+,+'1

," 1

t-lv1-,

rt;t

."1Vl

•1,i

l.i

[11

:'i

kk'

lb

!r-yl

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1, i-' dL .---.F -

t'i !

..-L" L

l

:-

lt

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;ft

,ÅÄ1

,l,

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llr

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iv +iril'

:r,

r-1

tifl

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l:, ;t'

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Str' L

l•l

tll'il'iTi'i

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[j

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ll,i

-- T-.J ;

t

lb

Liiit[

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I:t-tttl:

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Lit,

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'117,ljtt

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d IL

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t"1

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rlit

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-tllilii

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llu

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ll

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l`It

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il,

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ll

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r7,

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l -t

'rl,-l

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t

1'

o.o. 1.0 20 3.0

T

4.0

.Ime

:rwO

(sec)6D 70 eo 9eO 10.0

FÅ}g.4-8

below

An example ofprompt eritieaL

the observed powerst ate.

shapes of the " YAYOr" in the pu Lse operation

1

cobe

l

A<vvco L L JUv=ae=o

10'2

10"3.

10'4

loes

-

.

,

/t. i +..

i tt. ;.t 1 'l peak

------ .---- -L

Power' 1,

tt-t .fi 4 tT 1 'i 1 -11:76 KW i

Base Power:

' .-E-...,.- il

tT ttittt t-t

IFiil

' i''f-T'

3.2 KW

'i

.l

ll

t

...H.. . + ".

i' • i•

r

:

ii

2ttt-t. tt t-t-vt ..t-.t .L.. . -.,. t[ '-.-"..----...J -- i.--.. l.-

llr

l

o.o Q5Time

1.0

(msec)1.5

Fig.4-q An

the pulse

example

operation

of the above

observed

prompt powercritical

sh apes of

state,

the " YAYOI ft' ln

4-5. Conclusion !t has bee-n- difficult to obtain a stable and fast response

logarithrrLic electrometer with large input capacitance of a

detector and a cable. At high current levels the stability . of the logaritr"Taic electrometer requires a iarge feedback

capacitance, by which its response time is severely degraded

at low current levels. This is due to the marked change of

the current-dependent resistance of the logarithinic elernent.

In order to cope with this problem, a new phase compensation

technique was developed and a stable and fast response loga-

rithrp.Å}c electrometer was rnade. For example, the response

tirne of this logarit}Mmic electrometer with input capacitance

of 3eeOpF was inproved about twodecaa"escompared with the conven-

tional one at low current levels. This logarithrnid electro-

meter ci.r-cutt z's based on clear transient analysis and reguires

no skilful adjustment. A feasihility test of this logaritlLmic

electrort.eter system was also carried out by the one-shot pulsed

tieactor " YAYOI " and sa"-isfactory results were obtained.

- 84 -- '

Appendix 4-A Compensation of the Trmperature Influence

The logarithrnic characteristics shown in Eq.(4-2) can be

rewritten as

'Urek == A(T) 2.Cd --B(-r) , (4-Ai)

where A(T)= n sRT and B(T) == nRIT 2bCs ./

.The saturation current Ls is temperature dependent and is

given by

Ls == t. eXp (' ?), (4-A2)

where io is a constant and B is l2000 for Si. It is

evident frorn Eq.(L'Ll-Al) that the temperature sensitive 'Vrtk can

be compensated by- balancing the A(T) and theB(-[-)with an ampiiSier

having a gain artd a bias vo!tage which are dependent on temper-ature9). The sim.plified diagrartt is shown in Fig. 4-Al.

Here, R(T) is a temperature dependent resistor and Eb (T) the

temperature dependent bias voltage. The terp.p, erature depend-

ent gain .( (-r) of the ampiifier built up with an Op. Amp. 2 is

given by

R(rl-) • d(T)=- R. . (4-A5)

!f we ignore temperature drifts of, the Op.. AMp. 1 and the Op.

Arnp. 2 , the terr,perature dependent output voltage Eb(T) of the

logarithrnic electrometer shown in Fig.,4-Al can be expressed by

E.(T)' =(n;' 2. i.f -• E,(-r)}&cT) . (4'A4)

- 85 -

ilX

id

1

ooor

l

.

I

.- =••. -M :b.

-

S:)FL-mD

Op.Am+

.

Rc

R(T)

OP, Amp,2):>---

+

![!-. Eb(T)

-=r'

----- *Eo(T)

" :-d-

Fig.4-Al Principle of compensating the temperature sensitive diode.

DiÅíferentiating Eq.(4-A4) with respect te T, we obtain the

temperature coefÅíicient of Eo(T) as follows:

2ETo = udi(# .gT\U)- (Eb.t,d. t gEx.b•s •-- n\Bld > . (4-As)

The first term and the second term of the right hand of Eq.

(4-A5) should be zero for exact temperature cornpensation.

From the first term, the temperature ceefficient of d becornes

El 'eO-Cf'L '---\ =. -- o.ooBB /OK art BooOk. (4'A6)

Frorn the second term and Eq.(4-A6), the temperature coefficient

of Eb becomes

-ilB•DoEliP == "- s'nTk'?EBb =-o.oi? /oK n-v- )oook. (4-A7)

Zn the circuit of the nevLTIy designed logarithmic electrometer,

these temner• a`Lure coefficient were realized bv the use of sorne

resistors and two thermisters RA, Rb , which had a nornina!tempereature coefficient of -O.042 /OK at 3000K. Thus,

variation of less than O.l decade was obtained in the rangefrom !o"!O A to lo'"4 A ior the ambÅ}'ent tetrrtperature variation

oof 20 C.

- 87 -

!)

2)

3)

4)

5)

6)

7>

8)

.

9)

10)

References

T. Iida and K. Sumita et al., To be submitted in the IEEE

[Pransac`Lions on Instrurnentation and Measurement• 'N. Wakayama, H. Yarnagishi, T. :ida, N. Ohnishi and S. Ohtorno

JAERI-M-6710 pp.ll5-l18 (1976>.

H. Wakabayashi, A. Furuhashir S. An and T. Tarnurar Proc. US

/Japan Ser•nttinar on Fast Reactors r-2 (l976).

N. Wakayaima, T. rida and K. Surnita, Preprint 1974 FallMeeting At. Energy Soc. Japan, (in J' apanease), C21 (1974).

rv!. Y. El--rbiary, rEEE Trans. Nuc!. Sci. NS-IOr 21-31 (l963)

W. L. Patterson, Rev. Sci. Instr. 34, l31i--l316 (l963).

L. S. Horn and B. Z. Khasanov, Nucl. Instr. Meth. 40, 267

-271 (1966).

K. Sumita, T,'. Iida and N. Wakayarna, Proc. US/Japan Seminar

on Fast Pulse Reactors IIr-1 (1976).

NEC E]ectron Device Data Book '72, 818 (l972).

T. Furukawa and N. VVakayama, Nuclear Electronics !-1ll]Ar

l41-i55 (l965).

r

-- 88 -

Chaptesc V. Fast Response Lpg N & P, eriod Meter

5-l lntroduction Various applications of this s-ystem can he expected in

transient neutronic measurernents in reactor operations. 'One of the typical examples is the instantaneous measurement t.of the time dependent reactivity. Such the measurement

is needed urgently for determination of pulse shape control

of apulsedreactor. Other application is to obtain the

safety scram signal in rapid transient situation of a steady

reactor.

In kinetic studies on pulsed reactors)it is often useful

to characterize dynamic behavior hy instantaneous reciprocalpe riod or z' nstantaneous O(. (t) (E th C-t>/n (t)) . Major

'response characteristics can be determined if ct(-t) is elearly

known. Excess prornpt reactivity in apulsedreactor isevaluated by measuring the value of ct(t} with power excur- , !) 2) . As the simplified treatment, the excess promptsion

reactjvity is obtained from one groupr one point reactor

kinetic eguation with delayed neutron neglection as follows.

p(t) - p = Z• ct (t) = e d--dt { -e,nn(t)] ,

.where P(t)is the reacbivity at time t.

There is the proportional relationship between the inst--

antaneous e:cess prompt reactivity and the value of Oe(t) ,

that is, the !nverse of the prompt period. Then the time

dependent exeess promp`L reactivity can be observed directly

as the output of a fast response log N & period meter.

-- 89 -

.

Of course, the integral tjJne constant of the lpg N & period

meter should be much less than the xeactor period itselE; .tthe time constant in a reactor power increasingr and the

effect of the icn transit time of the ionization chamber

should be neglected by the suitable correction rnethod. 3) pointed out that the lpg N & period meter T. Furukawa

for steady reactors was liable to ttip spurious!y due to inverse

period overshoot o-F the period meter output, resulting from

exponentially increasing reactor power from beyond the rangeof the log N channel. He also obtained data sheets4) which

'were effective in designing the optimum time constant of the log N

& p, a"riod meter for steady reactors. Howeverr his data

sheets are not applicable to the design of the log N & period

rneter for pulsed reactors, since the log N & period meter for

pulsed -reactors requires very fast responsiveness and there-

fore a new circuir design which is different from one for

steady reactors.

A fast response log N & period meter was developed forpuise reactor operation.5) A new phase compensation technique6)

was applied to the logarithmic electrorneter circuit in the

log N & period rneter, and the response time and the overshoot

error of the log N & period meter were markedly reduced.

At first, the tTransient response of a !og N & period ineter

sha!! be dÅ}:cussed in this chapter and then the new phase

compensation techniqup- and experiTnental results of the fast

response lo- .i N & period meter shall be shown.

-90-

.

G,(s) E,(S>

where RdCd isThe fastest

Cfd is equaldiscussed in

i n t o .F. q . (5 -- 2 ) , t h e

becornes

TD = 'g'-z+

rt is irn`Dori ant in

differentia+vtor `:•-.o

small. Suchand a fast response

Hence it is assumed

ponse time of the

5-2 Transient Response

' The inst.A.i":taneous prompt ct(t>, i. e. the' inverse of the

prompt reactor -period, is giVen by ct(t)= zf\n(t)/n(t) = -dd-t (2n n(vj . cs"'!)

The value of ot(t) can be, therQfo]re, observed as the output

of an ideal log N' & period !neter, which has no time lag.

However, a real !og N & period meter, whose equivalent circuit

diagrarn is s:norMn. ]ig. 5--1, causes an inevitable error due to

the following trmo effects in the rneasurement of ct(t) value.

One Å}s due to the lag of the response time of an analog

differentiator which is built up with an operational amplifier.

The transfer function of the difEerentiator shown in Fig. 5-1

is given by

- Eo (S)- -Rd CdS (5-2) l + (z, + Rd cfd + Å}RSSSIL2d)s + •c, Rd (cd+ cfd) s2 ,

the gain oÅí the differentiator.

response of the differentiator is realized when to Cf, (= iia- CAd, +2 ft2d ) iike as

section 3--2. rf we substitute that relation

integral time constant of the differentiator

tCiRdCd (5-3) .

the desigen of a fast response analog

make this time eonstant TD sufficiently

design of the time constant is not so difficult

differentiator can be easily ohtained.

that the error due to the lag of the res-

differentiator is negZigible in further

- 91 -

l

OMt

•-!g(!]t.t)

4 Zci."r

-' Ao+

i>

.

Ro

cf

-

D--

To=

Xco-

+

-

-

1

RoCo

Cfd

CdTcHe,(t)

Al

ww

Rl

Rd--b------

+

-- =--

-

rci.

+

-ny

1

eo(t)

th .=-•.

Tl=RlClLogarithmie electrometer

Differentiator

Fig.5--l Equiva!ent circuit diagram of a fundamental log N period meter.

eo(Å})- t<L) cf

whe]re 3(t)=-irRTi#!-?N-Tcf

and Cr is anH e r e , t h e f, o l l o 'w+i n g

ana17sis on the

Lct) = fo exp(

.where Lo is an ''

constant 'tion is ef• fect• i•ve in

istics of a log N &

mately appli•eable to

power of a pulsed

of the ideal ]og N &

easily given by

eo(u= %

which shows that the

inverse of the

output voltage of

some time constants

discussions. The other is due to the Zag ofi thAe

time of a loaartthnic el'ectrometer. This rnakes Jcult to observe the precise ct(t)value.

From circuit analysist the transient response

log N & period meter circuit shown in Fig. 5-1 can

ly expressed by

.RdCd•` nkTRdCd exP{S(t)l

xesponseit diffi--

oÅí the

be general-

(5 -4) % S,t expi6(t)ldt+nh-rgCfCr ,

ji(t>dt ,

integral constant.

a s s u m p t i' o n is i n t r o d u c e d t o s ii,n.p l i f y t h e

transient resp• onse o f the circuit .

mitial input current and Tp is a time

corresp, ondmg to a reactor period. This assurnp-

est.i.matirig the general response character-

period meter circuit and is also approxi-

the real situation of a transient reactor

reactor. rn this assumption, the response period meter circuit with no time lag is

nk-rRdCd..}p (= constanÅ}), (5-6)

output voltage is proportional to the

reactor period. On the other hand, the

the real log N & period meter circuit with

gradually the constant value shown in

-93-

Eq. C5-K6).

Figure 5-2 illustrates profiles of th.e transient response of the lag N & period rueter circuit shovm in Fig'.' 5-•1.

These were calculated from Eq. C5-4), varying the initial cur- rent to as apararneter and using the fonowing vaiues; nET=26mv,

Ct:14700PF, The former two values' have heen descrihed in. Tp=lms. .. section 4-2. It is evident from the profiles that the . sraaller the initial current Lo is, the larger the overshoot

error of the reciprocal period is. The response cha]racter-

istics which are accompanied by such overshoot error disturb the

precise rneasurement of a.C(t)value. A fast response log N & pe-

riod mQter circuit for pulsed reactors should be designed not to ' cause such overshoot error.

- 94 -

40

30

20

10

o

-7l.= 50xlO`

Io= ID x1O7

55.0xlO

Fig. 5-2 Profiles of

periotl meter circuit

34 Time (msec)

the transient

shown in Fig.

-95-

5

response

5-l.

6

of the log N &

5 - 3 Inprovernent of the response characteristics

As describe•Rv.• in previous section, the overshoot error of

the log N & perio• d meter is governed by. the lag of the response

time of the logarÅ}thmie electrometer. Therefore, the error

can be reducea7 by improving the response time of the logarithrnie

electrometer, especially at low current !evels.

Figure 5-3 shows the equivalent circuit diagram of a new 6)type logariihniv'" electrometer designed by N. Wakayama etc .

This circuit m.aintains the stability based on that a resistance

Rin inserted between a detector cable and the input terminal of the

eircuit recovers the phase lag caused by the input capacitance

at high current levels and moreover a feedbacl capacitance Cf

does that at low cuxrent levels.

The transfer function of this circuit for small input

signal is gÅ}xren by

GD(s}: 2lil8((sS))=-rD[i+(-!r:9fg!rLC, +cf +Rinctn+ti o)s -t- [Rinctn rDcf

-1 -b "co( rDCin +RinCin +rD Cf)] S2 +RinCtnCÅ} rD 'uoS31 . (S -- 7)

Thei , the stability condition of this circuit, in other words,

the conditi,on tha`L the poles of F,q. (5--7) are all negative, can

be gxDressed bv L -L b2 -3ac 2 o (5-8) a2 bZ+2sabc -4a3c -- 4b3 -27c2 2 O '

-- 96 --

1

o<I

e-lo.Al(t)

-------- ).Rin

-

AoRo

cf

.1(t) ' ICin

- e

.

-

D

Ico-

+

'

-' r

1

ww

e,.Ae(t)

-

Fig. 5.--3 F•quivalent;

logarithmi-c

crtrcuit diaqram of a

electrometer for the

newlv

log

designed

N period meter,

where .. rD Ctna- A, +rDcf -t-Rinci.+-u, ,

b = Rin rD CIn Cf + "C o( rD C tn + RinCtn + rD Cf) ,

C= R ln rD CtnCf1 o .

!t is troublescm•ne `Lo obtain the exact relation between R. and mCf at cri`LicaX datmping from above equations. Thereupon, a

simplified method is here proposed to estimate roughly the

relation. The sumumary of this method is shown in Fig. 5-4.

A curve A shows the time constant of the logarithrnic electrometer

at critical daimping. In the case that a small feedback ca--

pacitance Cf' is selected, a conventional logarithmic electTo-

meter, whose eguivalent eircuit diagram is shown in Fig. 4-1,

becornes unstable at the current levels above J:x in Fig. 5-4,

which is easily from the discussion in section 4-2. Conse-

quently, it becomes necessary that a resistance is inserted

between a detector cable and the input terminal of the arnp!ifier

to suppress too fast response at such high current levels.

Hence, the resistance Rin can be approximately determined by the

following relaticns. ' . nkT ro - zo

The

as

of

)m>

time conb"tan•.t of

a curve C in Fig.

the conventional

ClsCtn!x - Cf'2 .

this tYpe logarithmic electrometer

5-4. A curve B shows the tirne

logarithmic electrometer. It is

-- 98 --

(5-9)

is shown

constant

evident

from ,the coi,ntp, arison of the two eurves B and C that the response

time of the new type logarithmiÅë electrometer is markedly

improved a'L-' lcwt current levels. Needless to say, the time

eonstant of i.-J lh.e new type logarithmic electrometer is reduced to

Rin Cin at high current levels and it sheuld be sufficiently

small than the r.a.aetor period.

Figure 5-5 shows the profiles of the transient response of

the log N & pe-'•'iod meter with the new type logarithmic electro-

meter. "i"hose were approxirnately calculated from Eg. (5-4)

using the following equation

i(t)= :LoeXP(' RL,tci.)+ Tp j'llOii!itP,ci, eXP(':T\ -)p [1 - eXP[l'"(=llp + Rinlcin)t])

(5-ll) sand the following values ; Rin = 6.6 Kst ; Cf' = 30 pF ; Tp =

l ms. It is evident from the comparison of the profiles in

Figs. (5-2) and (5-5) that the overshoot error of `Lhe new type

log N & pen'od meter is markedly reduced at low current levels.

Figure 5-6 shows the relation between the reactor period

Tp and the minÅ}rnum initial current io when the overshoot error

becones less than l per cent. A curve D shows the minirrtuam

initiai cur• rent• of the new type log N & period meter and a curve

Edoes that of, the conventional one. It is evident frorn the

comLparison oL` the two curves D and E that the new type log N & .period met• er can cover the current range much rnore widely than

the conven•stiona] one. '

- 99 -

I

Fool

v(1.,

U)

v•v,-•,'

ut

covoE

i'i'i'-i

102

103

104

105

106

107

lt-L"-tu-k-maNt- • "--i

(.-- rD Ci

b""--t -t---Nlit"--"dtPM

Stable

ww "-M--M-bptMh--

<---lbCf

RnCin c

Unstable

'

iRlxlx1Å~1llli

lI

I:llIiI,

<'`To"Å~Å~

xx XN xx

rDCin

Nxx

xxx

..."-Lul-.

:e,

N

A

B

10

Fig. 5--4

condition

9

A

of

lo-8 !Å~ lo7 `lo6 165 164 !nput Bias Current (A)

simplified method to obtain roughly the stabxlity

the logarithmic electrometer circuit shown in Fig. 5-3

10

.

3

40

30

RdCdx

r

IoM= 1.o xlo'9

(

Io=1.0 x1o'8

,Tp

A•'c"- 20?R

t• U

ce.

c-(2,o,

10 E

l!l

Io=1.0xlO-7

ystij

,i

,

.

Fig

log

o O1. 5-5 Profiles of

N & Deriod meter L

2 3 4 Time (msec)

the transient response of

circuit.

- 101 -

5

a newly

6

designed

:

-410

v."N<v o- "me

.---.

c N L L =v'iiii

IEÅí

10

I,F

1d6

1o-7

1O-8

!o

L

,l

D

E

.Z(pi

'J>-:)`

. Q

eobb

e6x.6

bei

Evlll 100p lm 10m Reactor Period Tp(s)

Fig. 5-6 The relation between the reacter period T p and the

minimurn iniiia! current io when the overshoot error becornes

less tl an 1 per cent.

- 102 -

5-4 A Practical Circuit and Experimental Results -

A practÅ}cal logarithmic electrometer circuit with the t.tnew p, hase com.pensation technique is shown in Fig. 5--7. !ewo

model l430 F.T operational arnplifiexs with a unty-gain-crossover-

freguenLny of• a-bout IOO MHz are used in the circuit. A silicon

planar transÅ}stor model 2N3058, having a saturation current of6x!o-l4 A, is used for a logarithrnic element. A detaued

design on tempeyature compensation, zero ad5ustment and so on

is desc-ribed ir chapter IV. The inserted resistance Rin and

the feedback capacitance Cf' should be adjusted according to

measi-'-ring conditions, that is, a cable capacitance and a reactor

period. A practical period rneter circuit is shown in Fig. 5-8.

A rnodel l430 FET, operational amplifier is used for the analog

differentiator. The gain Rd Cd of the differentiator is

fixed to the magnitude of a period range of 2.30 rnagnifications.

Consequently, the reactor period Tp is given by

-l-p=mT!il}l}:-P, - (5"-IO)whe-re Tp R is the period range and eo the output voltage of the

log N & period meter ( volt. ).

ic'igure 5-9 shows some examples from the observed results

in the pulse or.eration of the NSRR with this log N & period

meter• . In 'L'hÅ}s experiment, the inserted resistance of 5 kSX

and the L`eefiuba•.n.k capacitance of 40 pF were selected based on the

principle described in previous section. The measured results

are appare-ntly accompanied by no overshoot phenornena shown in

section 5-2.

-- I03 -

t

Hopt

l

,

.I (t)

10k

Rin

-

4

-

Cin

5k .1 5V

X478-

=-.

cf

Zero Adj-15v 20k 2k <'wwwwr-

10

2N3058

,

D

" 143O+

.15V

e&l

R4

lk

Gain Adj .

200 300

R3

.autf-,i`,,..15v

50p

5.34k

-15V

Fig.

new

5--7

phase

b15V

A practical

compensation

40k

2k RA

logaritlrmic

technique.

2k

-1430

830

electrometet

+

5T-32.15V

. Ik2k5T-32

RB

' with a

EOti

?I901

. :-

-15V

e(t)

Output

.- =.-.

,clrcuxt

R5R."

!npui i

+35V

10k

8p

15p

G1

25p

40p

70

)

130pCf

240

IM

300k

1OOk

30k

10k

3k

Rf lk

+15V

.- :-,

2300p

Zero Adj

"1

.1d-

5k

10k

+

1430

-15V

Fig. 5-8

300

l

tr 1OO

lk

Output

A Dractlcal

1

tr -•:•,

-15V

period meter

•• :.

CIYCUIt.

-- I05 --

.

Fig. 5-9

operatlon

Some

of che

eÅ~amples

" NSRR

from

" with

the

our

- I06

observed

systems.

; i -1

resUiil S' in the pulse

Figure 5-10 shows an example Åíro.rn the observed results in

'the pulse ope-rai ion of the YAYOI. !n this experiment,

very fast res:,"onsiveness was required for m.easuring systems and

an inserted resistor of 350R and a feedback capacitor of

25pF were selected in the new iogarithrnic electrometer

circuit. T:n.-u•s, the tirne constant of the logarithrnic electro--

meter was reduced to about l psec at the current levels above -7IO A. Ther- efore, the measured result is hardly accornpanied

by such an overshoot error as described in section 5-2.

- 107 -

,ti

, t3-3.6ig'f-;;.

(A)l :" i.: 121xlony6 s lti-e----p 1- --7--- --p47o xld • •. -e- .

'alsec) . --- o --••"

p(o/o) esl .::" '•.

'O.7

O.6 ------

.

.

-t

I-

.... Logarithr)nic Pewer -"-t" --- --N "ti--- "---- -- ----------

Period

t-

.

.

"-

e- e-e -v---- -- - -- - -e -e e- -- -e- -- ------

• Reactivity-}-

---- --"- e- --- ------------6-

Fig. 5--IO

'oDeratlon

O 100

An ey.amDle l Lof the " YPYOI

200 300 400 seO Time(g sec )

rom the ohserved results in

" with our systems.

- 108 -

the pulse

5--5 Conclusion

It has been difficult to design and manufacture a stable 'and East response log N & period meter' for pulsed reactors.

At low current levelsr it often produces an overshoot error,. 'which is caused by the Zag of the response time of the lpgarith--

mic electromefver. rn order to overcome this probiem, a phasecompensation technique reported by N. wakayama etcE)was appiied

to the logarit'nmic electrometer circuit and a stable and Åíast

response log N & period meter was made. The range which

could be covered by thSs new ty-pe log N & period meter was

extended about twodecades as wide as the commercially supplied,

conventi'onai one. This log N & period meter circuit is based

on clear transient analysis and reguires.' no skUful adjustment.

A feasibility test of this log N & period rneter was also carried

out by utilizing the one shot pulse reactors "NSRR" and

"YAYO!". Satisfactory results were obtained in the instant- .aneous Ot(t) meausrements and the precise values of reactivÅ}ty

inserted into the reactorc. were deterrnined.

- 109 -

l)

2)

3)

4)

5)

6)

References

H. Wakabayashi, etc., J. of the Fuc. of Eng., the

u. or' Tokyo (B) vol. xxxrv, No.1 (1977).

N. TA7ak4ayarna, H. Yamagishi, T. Iida, etc., JAER! -

M-6710 pp. l15-ll8 (l976). , •T. Furukawa, J. of the At. Energy Soc. Japanr

Vol. !2, No. 2 62 (1970). 'T. F' uxukawa, J. of the At. E.nergy Soc. Japan,

'Vol. Il, No. 6 347 (1969).

K. Sumita, T. Iida and N. Wakayarna, Proc. US/Japan

Seminar on Fast Pulse Rp-actors XI! -- i (i9.76).

N. Wakayama, T. Iida and K. Sumita, Preprint l974

Ann. MeenLming At. .F,nergy Soc. Japanr (in Japanese)r

C -- 21 (1 9. 74).

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Chapter Vr Summary ' Tn chapter r, requirements #or the nuclear instrumentation of 'puised reac"Lors have been discussed. 'The ionization charp.ber--electrometer system is rnuch superior to the

puZse counting one in the view point of statistical accuracyr and it

is eviden-t that the former system shou!d be applied to a power 'shape rnonitor for pulsed reactors. The response time of the ' 'former system must be z'mproved to be successfully applied to a power

shape monitor fo-r pulsed reactors.

In chapter rZ, the transfer function of ionization chambers has

been investigated. The impulse response of an ionization cham.ber

was measured using intense gamma ray pulses produced by a linear 'accelerator, by varying the applied voltage as a parameter. The

results obtained clarified the following points. First the

transfer r-uncticn of the ionization chamber is mainly expressed

by the txansit times of positive ions and electrons. Secondly

the positive ion transit time decreases proportionately with

increasing applied voltage and the electron transit time does

consi$tently with that. The fluctuation current of the ioni-

zation chairtber, set up in the thermal column of a reactor, was 'also ;ineasured by varying the time constant of a current amplifier 'systern as a paecarneter. The results show that the power spectral 'density oL= the fluctuation current is not perfectiy white but 'dependent on these transit times in the very high frequency region. ' ' 4Theseexperiments should be useful to select detectors for pulsed

reactors and to develope newly a new fast response one.

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In chapter IrX, a fast response electrorneter for pulsed

reactors has been developed. The response speed of an electre- ' 'raeter with a long detector cable was markedly improved by reducing

the effective cable capacitance. rn the cireuit of the electro-

meterr a new guard technique was used to reduce an effective eable

capacitance and a negative capacitance technique to obtain the 'critical damping conditjon. Stability of this electrometer is

ensured by adjustment of the open Zoop gain of the guard amplifier 'and the feedback eapacitance. This stable and fast response

electrometer was successfu!ly applied to transient power raeasure-

ments of the one shot pulse reactor " YAYOI ". ' In chapter IVr a fast res-ponse logarithmic electrometer has

been developed. The response tiip,e of a logarithtnic electrorn.eter

was improved by introducing a new phase compensatz'on technique.

rt is based on that a current variable resistanee inser`Led

between a detectox eable and the input terminal of the logarithmic

eleetrometer recovers the phase lag caused by the input capacitance.

This stable and fast response logarithrnic electrometer was suc-

cessful!y applied to transient power measurements of the one shot

pulse reactor "YAYOX ".

In chapter V, a fast response log N & Period Tneter has been

examined. The covexing range of a iog N & period meter was

markedly extended by improving the response time of the logarithmic 'electrorneter. The logarithmic electrometer maintains thestability based on the fact that a current variahle resistance inserte-d

cable and the input terminal of the circuit recoveys the phase Zag

caused by the input' capaeitance at high current levels and

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moreover a feedback capacitance does'that at low current leveis. 'These xesistance and capacitance are adjusted according to ' 'measuring conditions in a cable capacitance and a reactor

period. This fast response log N & period meter was successfully

used to determine the precise values of reactivity inserted into 'the pulsed reactors "NSRR" and "YAYOI't.

The fast response arnplifier system shown in this paper has

been used for the nuclear instrumentation of t' he "NSRR" and the '"YAYOI" and should be also useful for that of the JLB. 'consideration for the response time of an ionization chambbr

should be also useful to develope a fast response one as a detector

'for the JLB.

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Acknowledgment

The authcr would like to express his greatest appreciation ttto P-roL=. Ken#- Sutnita whO has guided the author to the -- 'present study and has been giving the continuous encouragement

and criticisms. Many thanks should go to Prof. Tamotsu

Sekiya, PxoÅí. Masaharu Kawanishi and Prof. Toshihiko Namekawa

of Osaka UniveLvsity for their critical reading the manuscript 'and instructive advices'.

Most works contained in this thesis had been carried

out at the nuc!ear instrumentation laboratory of the 'Department of Nuclear Engineering, Faculty of E4gineering,

Osaka University. The' author wishes to show the sincere 'grabitade to Mr. S. Makino (Osaka University, now NAIG), 'Mr. Y. Kokubo, D4r. H. Kamimuxa and Mr. Y. Maekawa (Osaka

University) fox their kind suggestions and discussions

in the experiments and analyses. tt The author is great thankful to Mr. N. Wakaya;na and 'Mr. H. Yamagishi (.JAERr) for their vexy useful suggestions

and discussions in designing the arnplifter circuits and

carxying ouaL- `Lhe experiments at the "NSRR". The author

is also grea`L thankful to Dr. H. Wakabayashi Cthe University

t. t tt ttof Miokyo), Dsc.Y.. FuVta and Dr. K. Kanda CXyoto'Vniversity)

foac LLhei-r he]piul suggestions and discussions in carrying tt 'out th-ay. expexiraen`Ls at the "YAYOI",.. irhe "KUR•-LINAC" and the

"KUR") re$pee-i ively. The author wishes to thank the Japan

'Atomic Energy Research !nstitute,' the University of Tokyo and

Kyoto Vniversity for their kind permissions to refer the

experirnental resuits. This work was partially supported by the '

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Grant-in-Aid for tha..

of Education.

Scientih'c Research Promotion of the Ministry

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l.

2.

3.

4.

5.

List of Publications by the Author ' 'T. Iida, N. Wakayarna and K. Sumita : Proceedings Eor the

Symposium on Xntense Pulsed Neutron Sources in Japan (Tokai)

'(l975)p. 205-223 (1975). ." Rapid Neutxon Flux Monitering System for Pulsed Reactor ". 'K. sumita, T. :ida, et al. : Proceedings of US/lrapan Semina x,

on Fast Pulse Reactors, (!Vokai) (lg76), p. 183--204 (l976).

" Rapid Response and Wide Range Neutronic Power Measuring

Systems for Fast Pulsed Reactors "., 'T. Iida, Y. Kokubo, K. Sumita, et a!. : [ro be published

in Nuclear rnstruments and Methods.

" A Fast Response Electrometer for Pulse Reactor Experiments ".

T. Iida and K. Sumita : To be subraitted in Nuclear

Instruments and Methods.

" Transfer FunctÅ}on Measurernent of !onization Chambers " `T. Xida and K. Sumita, et al. : To be submitted in the

IEEE Transactions on Instrumentation and Measurement.

" A Fast -Response Logarithmic Electrometer for Pulse

Reactor Experirnents ".

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