Pulse analyzing system for a gridded ionization chamber

NUCLEAR

INSTRUMENTS

AND METHODS

14 (1961) 241--251; N O R T H - H O L L A N D

PUBLISHING

CO.

PULSE ANALYZING SYSTEM FOR A GRIDDED IONIZATION CHAMBER MASAHIRO T S U K U D A

Department o/Physics, Rikkyo University, Tokyo Received 12 October 1961

A design method to obtain low noise amplifiers for collector pulses is described. The effect of various pulse shaping networks on minimum attainable noise charge and collection time dependence is investigated. Amplifiers having one differentiating time constant T 1 and one or two integrating networks of the same time constant T 2 seem to be the best ones when T t is equal to T~. Computed minimum noise charge of a 6R-R8 input tube is 340 ion pairs on input capacitance of 30 pF. Discussion is also given for designing a resistance-capacitancecoupled low noise amplifier for grid pulses. Equating the differentiating time constant with integrating time constant

gives the condition for minimum attainable noise charge as well as the condition of fairly good linearity between input and output wave forms. Optimum integrating time constants for various grid pulses lie between (0.55 ~ 1.1) × (collection time of grid pulses). Finally a special linear gate and pulse shape converter for the grid pulses are described. This system converts v e r y slow grid pulses into narrow rectangular wave forms of the same amplitude, thus enabling them to be analyzed by a commercially available biased-discriminator-type t w e n t y channel pulse height analyzer.

1. Introduction The design, construction, and characteristics of a gridded ionization chamber have been previously reported1'2). Careful adjustment of electronic circuit is required to obtain the m i n i m u m spread of the spectrum line for a monoenergetic incident particle to the chamber. The methods of designing low noise amplifiers for step input wave forms such as collector pulses have been discussed by several authors 3- s). But the effect of changing one of the time constants on minimum attainable noise charge and the collection time dependence of various pulse shaping networks have not been given. Six pulse shaping networks have been irtvestigated for a step input voltage and for a trapezoidal wave form of collection time T o. Pulses from grid electrodes have special triangular wave forms. Analysis on these

wave forms after amplification through resistance capacitance networks is made and the conditions for minimum attainable noise charge are obtained theoretically. By numerical computations, these conditions prove to be also the ones for fairly good linearity as a special case of linearity conditions deduced by Ogawag). Finally a linear gate of special design which converts slow grid pulses into narrow square pulses of a fixed duration is described

2. The Design Method of Low Noise Amplifiers for Collector Pulses It is well known that the noise voltage from electronic tubes can be expressed in the following form :~' 6, v) b

1) T. Doke, I. Ogawa and M. Tsukuda, J. A. P. J a p a n 29 (1960) 573 (in Japanese). 2) I. Ogawa, T. Doke and M. Tsukuda, Nucl. Instr. and Methods 13 (1961) 164. s) W. C. Elmore, Nucleonics 2, No. 3 (1948) 16. 4) R. Wilson, Phil. Mag. 41 (1950) 66. s) A. B. Gillespie, Signal, Noise and Resolution in Nuclear Counter Amplifiers (Pergamon Press, London, 1953). 6) E. Baldinger and W. Franzen, Advance in Electronics and Electron Physics 8 (1956) 255. 7) G. C. Hanna, Experimental Nuclear Physics, Ed. Segrb, 3 0959) 198. s) E. Fairsteiu, Trans. I.R.EI NS-8 I (1961) 129. JANUARY 1962

per unit frequency interval V 2 : mean square noise voltage i n volts ; Ci, : total input capacitance of the input tube in farads a: shot noise term -~ 4kT, R,qC~.; k: Boltzmann constant = 1.37 × 10 .23 joule/°K 9) I. Ogawa, Nuovo Cimento, Supplemento, to be published. xo) M. Tsukuda, to be punished in J.I.E.E. Japan (in Japanese). 241

MASAHIRO TSUKUDA

242

T.: equivalent absolute temperature = 290°K; R,q: equivalent noise resistance of the tube - 2.5/gin for space charge limited conditions: g= is the mutual conductance of the tube in mhos. b: grid current and thermal noise term = 2eI, +

4k T/R ; e: electronic charge = 1.59 x 10- t9 coulomb. I , : arithmetic sum of the electronic and ionic grid current in amperes. T: absolute temperature R: input resistance of the tube in ohms. Usually R is chosen to be so large as to satisfy the condition

4kT ~ - ~. 2elg, so that

b ~- 2el,.

to: angular frequency; c: flicker noise term = I 0 - t 3 x C~, (experimental constant valid between 0-50 kc/s). In all the arrangements to be considered here, the r.m.s, flicker noise charge can be expressed as equal to (2.7-6.3) x 1012 C~, ion pairs 1°) and is small compared with the other two noise terms. In the following discussions the term noise excludes flicker noise and thus all results obtained should be increased by the quadrature addition of this small contribution.

The problem is to minimize q. by suitable choices of pulse shaping network which defines f(¢o) and F(0) and of time constants of the network. The effect of six pulse shaping network on the r.m.s, noise charge has been calculated for a step input voltage and the results are summarized in the following and shown graphically in fig. 2-7. Details of the calculations will be given elsewherel°). These figures show, as a function of the ratio 2 of the differentiating time constant to the integrating time constant, (l) optimum integrating time constant T 2 in unit of ~ / ~ (2) minimum attainable noise charge Q, in unit of A / ~ when the two constants are chosen so as to be optimum, (3) r.m.s. noise charge Q' when the integrating time constant is not chosen so as to be optimum, (4) r,m.s, noise charge ~Y"when the differentiating time constant is not chosen so as to be optimum. When the input pulse wave form has a finite collection time T o instead of a step function, the maximum output pulse amplitude will be F(To) (fig. 1). Thus, the fractional decrease of the maxim u m pulse amplitude A is defined by

F(To) = F(0) (1 - A).

(2.2)

These A values are also shown in the figures.

2.1. E F F E C T O F P U L S E S H A P I N G N E T W O R K

A pulse amplifier m a y be considered to be consisting of an amplifier having a gain Go at all frequencies and a pulse shaping network whose response to a sine wave of frequency co/2n is f(o~) and which gives a pulse of m a x i m u m amplitude F(0) from a unit step function input. Thus the mean square noise voltage at the amplifier output will be 2 ~- Go2 I Vnout

vin=!=l tin

Fig. 1. I n p u t pulse wave form of collection t i m e T 0.

o0

V~2f2(co)dcol2n

d 0

2.1.1. RC-RC Amplifier

and the m a x i m u m pulse amplitude from the collection of a charge q is (q/Cin) (GoF(0)). The root mean square noise charge will therefore be q" = '* Fz(0) 30 k

~o2/

2~n"

(2.1)

An amplifier with one differentiating element of time constant T t and one integrating element of time constant T 2: t°2T2 l'f2(°)) ~ (1 + co2T~)(1 + o)2T22) "

(2.3)

PULSE

ANALYZING

2 v.2.o,=4~f. ~

SYSTEM

FOR A GRIDDED

(2.4) ~22 + 2bT2

T2 "

3. F(0) = 21/(1-'0 .

(2.5)

4. Minimum noise conditions T 2 .= ~

~,

5. qnmin = 1.355 ~ ion pairs T2 o,t. = a/aTb see

(23)

flicker noise charge qv..~. = 3.8 x C~, 1012 ion pairs. T 1 (e r°lT' _ 1)r,l(r,-r2) 6. F(To) = -~o (e r°lr~ 1) r~l(r'-r=)

(2.8)

1. f2(m) --

~. (emz -- 1)a/(a-x) P (e u - - 1)1t(z-l)

t°2T2

(1 + m2T~)(1 + o92T2) 2"

~(

2. V,2oo,= 8 ~ 2 \ ~ 3. F(0) =

:. ]y (\T--2 a + (22 +

22

I , : ampere

T2

~ / 2 2 1- + ~

Jb

)

, 2 = 1.06.

5. q,=i, = 1.215ffab,

.

(2.11)

(2.13)

T z optimum = 0 . 5 7 ~ seconds ion pairs

(2.14)

qv.,. ~ 3.7 x Cin x 10 t2 ion pairs.

g=

(2.9)

(2)2{e'--1 ~

~

e

• e-a:'/(a- O -- [ ~ - ~ 1

gin: mho.

II ~ \

1)bT 2

[e ~/la 1) _ (1 + x) e -z~/(a-O] t2.12) where x satisfies the condition e~ = 2x + 1. 4. Minimum noise conditions:

6. F ( T o ) =

Ci.: farads

(2.10)

i--Z-'i-

where/t ~ T o / T 2 .

= 2.12× 10'×

243

An amplifier with one differentiating element of t i m e constant T t and two i n t e g r a t i n g elements of the same time constant T2:

2 = 1. (2.6)

=

CHAMBER

2.1.2. R C - ( R C ) 2 A m p l i f i e r

~ + bT,

-- 4C 2, ~

IONIZATION

-e"(1-

112

I (f1.1)

_x/,z_,)e'--

-

-

1

(2 _ I )

1 ) ] e-a~/(z-') }

(2.15)

where x satisfies the condition 2.0

~

~

tt

ex _

o. o::; 16

',:',,, \\ x

0/ /

0.

_ e u_- 1 x + e ~[1 - p + p l 3 . ] (eu / x - I) (ev i a - 1)

1

L,/, 2.1.3. (RC) 2 - R C A m p l i f i e r t 1)

An amplifier with two differentiating elements of the same time constant T 1 and one i n t e g r a t i n g element of time constant T2: 1. f2(a~) = Fig. 2. M i n i m u m a t t a i n a b l e noise charge, o p t i m u m t i m e c o n s t a n t a n d collection t i m e dependence of a n R C - R C a m plifier as a f u n c t i o n of 2.

004T4 (1 + ¢o2T~) 2 (1 + o~2T~) "

(2.16)

11) A. A. V o r o b b e v a n d B. A. Koreleb, Izv. Akad. N a u k SSSR, Ser. Fiz. 23 (1958) 94.

244

MASAH1RO ,

,

,

22

,

, , , , ,

,

,

,

,

TSUKUDA

, , , , ,

,

T2

1,2

~/~-+~Ji

2=1.38.

(2.19)

k q

~.o

',

18

!,o

5. qnmin = 1.406ff~ ion pairs

i de'u=1)

Z%

~t

[

,

T2opt ~ 1.4~/aTbsec

qFmi. = 4.3 x Ci.

x

1012

ion pairs. Calculations s h o w t h a t q, for 2 = 0.1 is smaller t h a n that for 2 > 1 but at the same time T2op,. for

1.4

Q,

~\

q~

Ta

4

Q.

\\ \x

12

\\

2 2.2

t 1.0

Ol

Q2 03 I 04I t 0.608 I r Ill1 "A

2

3 456

810

,0

Fig. 3- M i n i m u m a t t a i n a b l e noise charge, o p t i m u m t i m e c o n s t a n t a n d collection t i m e d e p e n d e n c e of a n R e - - ( R C ) = a m p l i f i e r as a f u n c t i o n of *l.

. . . . .

' ' 'i'

'

'

,

~ , , . . . . . .

Q.

,

18

t

\

I

i2 \.\\

,~

to . . . o . . ~

an,0~

\

1 n

'

\\

I

a

,I o'~ o!so!~'o~o~,

2

Go2 [

3. F(0)

(?~)2

2

\z/22+

~

i a

{ [ 1 + 2]

T2

.(2.17)

eX/O'-l)--eaxl(a-1)} (2d8)

where x satisfies the condition 4. Minimum noise conditions :

/~2

~6'a~:o°

Fig. 5. M i n i m u m a t t a i n a b l e noise charge, o p t i m u m c o n s t a n t a n d collection t i m e d e p e n e n c e of a D L - - R C plifier as a f u n c t i o n of ~,.

time am-

12

2C

) t-2bT 2

~

22

~ ; ~;'",o

2

~o,~'

f

2

r~

Fig. 4. M i n i m u m a t t a i n a b l e noise c h a r g e , o p t i m u m t i m e c o n s t a n t a n d collection t i m e d e p e n d e n c e of a n (Re) = - RC a m p l i f i e r as a f u n c t i o n of it.

2. V.... = ~ # 4 7 1 )

, , .,,,i

~8

'i d ( f l . 1)

'%,

A 12

,

,~(y 05)! (/j 1)

' ' ' '''

i

22

,

0

e~ = x + 22 - 1.

18

~,< h-~-" -""@=11

10 0~1

02 03 0.4 Q• 08 1 ~ a

2

0 4 5 (~ 8 11()

F i g . 6. M i n i m u m a t t a i n a b l e noise c h a r g e , o p t i m u m c o n s t a n t a n d collection t i m e d e p e n d e n c e of a D L a m p l i f i e r a s a f u n c t i o n of 2.

time (Re) =

PULSE ANALYZING SYSTEM FOR A GRIDDED IONIZATION CHAMBER 2 = 0.1 is v e r y m u c h larger t h a n t h a t for 2 > 1, m a k i n g s u c h cases u n p r a c t i c a l . (2)2{e'/a(l+/~-/z/2)-le,/tz-l) 6. e(To) = ~ #

e==

-

ev / z - 1 -

2 ( e " - - 1)

1-e-a e-Z+2_l

2=1.036.

',~,

IA(Y.o-~)

r,

I

I

~

,

T2°vt = 1.29

sec

qv=,. = 4.3 x Ci. x 1015 ion pairs.

/

I

~o

8

1...

I

16

Q" 1.4

4

1.2 ~

\ O2

x

x

2 TzI/

, 0 ,4o , 0,6 ,,,'J O~ 0 8 !I

(2.22)

"-

1)]}.

(2.27)

DL-(RC) 2 Amplifier

A n amplifier w i t h one d i f f e r e n t i a t i n g e l e m e n t of a s h o r t e d d e l a y line of l e n g t h LD a n d t w o i n t e g r a t i n g e l e m e n t s of t h e s a m e t i m e c o n s t a n t T2:

DL-RC Amplifier

A n amplifier w i t h one d i f f e r e n t i a t i n g e l e m e n t of a s h o r t e d d e l a y line of l e n g t h LD a n d one i n t e g r a t i n g e l e m e n t of t i m e c o n s t a n t T2 :

(2.26)

W i l s o n 4) g a v e t h e r e s u l t for a special case of T2 = ~ and obtained the minimum condition of 2 = 1.2. Gillespie 5) discussed t h e s a m e p r o b l e m b u t n e g l e c t e d t h e g r i d c u r r e n t noise a n d t h u s l a c k e d t h e generality. V o r o b b e v 15)treated t h e s a m e p r o b l e m b u t it seems t h a t his results are b a s e d o n t h e a s s u m p t i o n t h a t t h e pulse m a x i m u m F(To) a l w a y s occurs a t t i m e 2 T D w h i c h is n o t t h e case. 2.1.5.

Fig. 7. Minimum attainable noise charge, optimum time constant and collection time dependence of a (DL)~- RC amplifier as a function of ~.

sin 2 wTD

(2.25)

ion pairs

6. F(To)--l{l--~log.[l+e-a(e

18

1. f2(o9)

J~

(2.21)

2 ( e " - - 1)

zo

2.1.4.

4. Minimum noise conditions:

5. q, mi. = 1 . 0 9 8 ~

2.2

tc

(2.24)

(2.20)

e"/Z(2+/t-/z2)-2

x +

3. F(0) = ½ (1 - e-Z).

T2=#

#,lZ _ 1 x . e : , / ( z _ l ) e~ -- 1 eZX/(z_l) } + /t ----7-where x satisfies the condition

245

sin 2 coTD (1 + o)2T2) 2

1. f~(o~) 2

(2.28)

Co~ I

a

2. V . . . . = ~ [ [ 1 - ( 2 + 1) e -z]T-~16C~.

(2.29)

(1 + o~2T~) + [22-3

where T D = one way t r a n s i t time of the delay line

+ (2 + 3) e - a ] b T

3. F(0) = ½ (e z - 1) e -z*"/('*-l) • (2.23) where 2 = 2TD T2 t Dr. G. C. Hanna of the Atomic Energy of Canada kindly informed me of one of the results he had obtained on numerical calculations of equation (2.30), (2.32).

2}.

(2.30)

4. Minimum noise conditions; r2=

#i

1--(2+l)

22--3+

(2+

e-Z

3) e -z

#i

2=2.623. (2.31)

x2)A.. A. Vorobbevand B. A. Koreleb, Izv. Akad. Nauk. SSSR, Ser. Fiz. 24 (1960) 1086.

246

MASAHIRO TSUKUDA

5. qnmin = 1.107~db ion pairs T2opt =

(2.32)

qr=i. = 2.7 x Ci. x l0 ts ion pairs. 6. F(To) = - ~1 [ 1 + -1 -~. 2 . p it

x. /t

J

(3 -- e -a) (1 - e -a)

a

2-+ 0. (2.36)

5. q.mi. (for 2 = 1) = 1.368 ~ / ~ ion pairs.

.l e - .x ( e .~ + e ~ #

1)]

1 ) x - lea(X- 1) + e U ( p - 1 ) - 1 ] = e ~

and2
T2opt =

2.2~/a/b see

qrmln ~---6.3 X Ci, X 1012

where x satisfies the conditions (ex + e " -

T2 =

0 . 5 3 ~ / ~ sec

(2.37)

Theoretically, as 2 tends to zero, qn becomes infinitesimally smaller, but at the same time T2opt becomes infinitely larger, making such cases unpractical.

(2.33) 6. F ( T o ) = 1 { 1 - ~loge [1 + ½e-a(eU- 1)] }.

(2.38)

where x satisfies the conditions x=

[ 2ea + I t e u - e x - 1 eu - 1

and2+it

2.2. T H E RESULTS OF T H E E X P E R I M E N T S

1]

The foregoing calculations show that R C - R C , R C - ( R C ) 2, and D L - ( R C ) 2 amplifiers are suitable


2.1.6. ( D L ) 2 - B C A m p l i f i e r An amplifier with two differentiating elements of a shorted delay lille of the same length Lv and one integrating element of time constant T 2 :

for low noise performance and small collection time dependencies. Amplifiers of R C - R C and R C - ( R C ) 2 type have been chosen because they are easy to construct and their actual performance has been measured, using 6 R - R 8 as an input tube. The results are as follows:

Cin = 30 pF

Computed noise charge -2-2 V q n min + qF Measured noise charge

1. fl(o,)

-

2. V.2. . .

-

]

RC - - (RC) ~

240

i I

260

380

400

370

]

400

570

600

sin 4 coTD (1 +

(2.34)

~oZT2,)

Goz l 2t '(332Ci,

e -z)(1 - e -a)

Cin = 60 p F

RC - - RC

RC - - (RC) 2 I

a

+ ~22 - (3 - e -a) (l - e-a)]bT2 } .

(2.35)

3. F(0) = ¼ (1 - e-a). 4. Minimum noise conditions: 13) G. A. Korolev and G. E. Kocharov, Izv. Akad. N a u k SSSR, Ser. Fiz. 24 (1961) 357.

RC - - RC

Since the measured noise level is always higher than the computed noise level, the constants a, b, and c used in the above calculations seem to be considerably optimistic. Fig. 8 shows an example of actual alpha ray spectrum.

3. Design Method of Low Noise Amplifiers for Grid Pulses The wave form of grid pulses has been discussed by Ogawa 9) and Korolev et al. 1a). As an approximation grid wave forms of m a x i m u m amplitude Vin having collection time T o and decay time T~ have been assumed throughout (fig. 9). The approxi-

247

P U L S E A N A L Y Z I N G SYSTEIV~ F O R A G R I D D E D I O N I Z A T I O N CHAMBER

m a t e d w a v e forms after passing through the R C - R C amplifier of the time constants T ~ a n d T 2 gave been analyzed and the following equations are derived: Maximum pulse amplitude Volt: V°ut =

Vin

T t [(1 + To~T;)e r ° l T ' ~ o [(1 + To~T;)e r°lr2

--

3.1. CONDITIONS FOR MINIMUM NOISE

In R C - R C amplifiers the shot noise component will be proportional to [T1/T2(T1 + T2)] * and the grid current noise component to [T~/(T 1 + T2)] ~ as i

1] rlllrl-r2)

lo . . . . . . . . . . . . . . . . . . . . . . .

1] T21ITI-T2)

TI

t •

(3.1)

T; /

oe

r~_

In one extreme of T~) -+ 0

2

Tt Vo~t = Vi. To(T~ - T2 ) { TI(I - e-ro/T~) -

-

T 2 (1 -- e -r°/r2) }.

(3.2)

In another extreme of T~ ~ oo (e T°lr' __ 1)Td(r, -T:L) Vou t = Vtn To (eT°IT2 I)T21(Tt_T2) T t

,

,

(3.3)

..:-.

150

'~

II

I$

i t

To

II I I

• TIME

7o ~ To

II I i

II I

Fig. 9. Approximate wave form of grid pulses introduced for calculating the minimum noise conditions and non-linearity of the amplifier.

given in (2.4). Therefore, the shot and grid current noise charges v a r y with Tt and T2 as follows:

1 qnsho, OC [TtT2] t [Tt + T2]½

loc

• { L(l_+ To~T;) e rolr~__ i J r , / l r , - r , ) To I(1 + / o / T ; ) C °/r= - 11r'/
I }-'(3.4) T;

1 qngrid current GC

20

,30

40 • CHANNEL NUMBER

[

50

r o [(1 + To~T;) e T°/r~ - 1] T2/(T'-r2)

which coincides with the equation (2.8) as can be expected. When T t = T 2, (3.1) takes the following form:

--{~-~ [(lq-f~-Z)e r o l r 2 -

1]

exp [ - (T°/T2) (l + To~T;) e r°/r2]

[(1 + To~T;)e r°/r' - 1] T'/(Tt-TD

o

Fig. 8. Actual alpha ray spectrum of Po al0 obtained by the chamber.

Vou t

[Tt + T2] ½

T2

1

7";

3.5)

F r o m an inspection of the right-hand side of eq. (3.4) and (3.5), they are unaltered if T 1 and T 2 are interchanged. Hence if T 1 and T 2 are allowed to v a r y in accordance with the condition T , T z = constant, which is not affected by interchanging of T , and T2, then any bandwidth having a ratio T i l T 2 = 2 will give rise to the same noise charge as corresponding bandwidth having a ratio TI/T2 -1/2. Consequently if the right-hand side of (3.4) and

248

MASAHIRO

(3.5) are computed and plotted for T ~ / T 2 -- 2 as variables, the resulting curves should be symmetrical about the point 2 = 1. Since the condition T I T 2 = constant is equivalent to 2T~ = constant which is the condition for minimum noise charge for an R C - R C amplifier as shown in (2.6), an envelope to the various curves of q~ will show minimum at 2 = 1, if the m i n i m u m attainable noise charge is calculated and plotted for T t / T 2 = 2 as variables and T o / T 2 = / l as parameters. Fig. 10, l l and 12 show the typical qn curves for T o / T o = oo, 2 and 0.1. The following table gives the calculated m i n i m u m noise charge and the optimum time constant for various values of T o / T o.

TSUKUDA

between output and input waves have been carried out for T o / T 2 = 6.66 and To~T2 = 1.33. The

\

. . . . . .

To

i

,u=l

5

,//=4

0.1

To~T" o

M i n i m u m n o i s e c h a r g e qa i n u n i t s of 4141414141414141414~a/b Optimum

time constant

1.68 ]

TolT 2

1.8

~/;24

Q '2 0 3. . . . .0. .5 07

1'

2. . . . .3 4 5 -~'"10

_T,

2'0 . . .4.0.

8o

F i g . 1 1. M i n i m u m a t t a i n a b l e n o i s e c h a r g e for a t r i a n g u l a r w a v e f o r m of To~T" o = 2.

, : , 1:2

1

1.59

-@@]

pulse amplitudes is T 1 > T O > T v The condition means that the b a n d w i d t h of the amplifier is wide enough to allow the faithful reproduction of the input waves and consequently will show a good linearity; but this leads to a fairly large noise charge. The numerical calculations of the linearity

, , , ,,,

~=o.2/

,

3.2. CONDITIONS FOR GOOD LINEARITY Ogawa 9) has shown t h a t the condition for preserving linearity between input and output

' '''"

~=~

1.5

r°2' l.~v ~

--,.JJ-

I

13

]

1.46

I

l.I

0.9

=tO

10

Q J-

,u=O2

5

~ -

~L

O.1

/a=l

,U=2

]

t

[

I

] P I ~1

0 2 0.3 0 5 0 7 1

1

2

i

]

[

i I ] l[

3 4 5 7

10

[

20

I

~

40

1 [1

, Z= r_, r2

F i g . 12. M i n i m u m a t t a i n a b l e n o i s e c h a r g e for a t r i a n g u l a r w a v e f o r m of T o , ' T ' o = 0 . l .

01

02 03

Q5 07

1

2

3 4 5 7 10

20

40

, ~_ r_, -r 2 F i g . 10. M i n i m u m a t t a i n a b l e n o i s e c h a r g e for a t r i a n g u l a r w a v e f o r l n of T 0 / ] " 0 2~.

results are shown in fig. 13 and 14. Although the coudition of keeping T 1 > T O >_ T 2 is quite adequate for the case of T o / T 2 -- 6.66. it is noteworthy that making T 1 _~ T 2 will result in a fairly good linearity for the case of T o / T 2 1.33. Thus

PULSE

ANALYZING

SYSTEM

FOR A GRIDDED

it can be said that the condition for good linearity will be automatically satisfied by the condition for minimum noise. This condition for preserving linearity has been checked experimentally, using a specially designed triangular wave form generator.

IONIZATION

CHAMBER

249

shape of slow rise and are not suited to be analyzed by a commercially available "biased discriminator type twenty channel pulse height analyzer'" which requires a flat topped input wave form of a few microsecond duration. 10

TT"~'== 6 " 6 e

~.= -~, = 1 0 0

O.g

0.8 0.7

IO

To

r~- = 133

0.7 06

0.5

~
0.4

~o 20 '

04

0.3

4

2

02

12

O1

"08 -0.4 02 10

0

r, ,t=~-4o

(11 Q2 0.3 Q4

05

(16 0 7

08

Og

02

04

01

02 Ot 0.1 0 2

• INPUT AMPLITUDE.

OS

04

O.S 0 6 0 7 0 8 Og 10 INPUT AMPLITUDE

Fig. 13. L i n e a r i t y c u r v e s for T o / T 2 = 6.66, t a k i n g T 1 / T = = ~. as a p a r a m e t e r .

Fig, I4. L i n e a r i t y c u r v e s for T o / T 2 1.33, t a k i n g T 1 / T 2 = X as a p a r a m e t e r .

4. Linear Gate Circuit for Measuring the Pulse Height Distribution of the Grid Pulses Fig. 15 gives the block diagram of a typical circuit used with the chamber for measuring the pulse height distribution of the grid pulses. Since it is inevitable that the grid pulses should be selected by the corresponding collector pulse of the specified amplitude which appears at the collector electrode

A linear gate circuit has been constructed in which the amplified grid pulse of the maximum amplitude Vout is lengthened to some 60 psec trapezoidal wave form of the same amplitude and sent to one arm of the diode bridge linear gate. Pulses from the collector electrode are selected by a single channel analyzer and then trigger a univibrator which generates a constant amplitude

GRID PULSE

=

NIVIB.qATOR

DIFFERENCE'

OUTPUT

gou

Fig, 15. Block d i a g r a m of linear g a t e s y s t e m for grid pulses.

after

the grid pulse reaches its maximum, there must be some means of delaying the grid signal to coincide with the collector signal. In addition, the wave forms of the grid pulses have a triangular

(-~ 100V) rectangular pulse of 4~sec duration. This triggered pulse is also sent to another arm of diode bridge linear gate. Since the diode bridge responds to the lower value of either arm, the

IPULSEJ G=,ol ->

5

8,o

6AH6

,j,,~"

BAH6

0.,=

-

(-15o)

i[LiS,

I

,2,~g-

Ef

5667

Fig. 16. Complete circuit diagram of the linear gate.

~5.,

l

,,~ r ° ° ~ -"

2

12AT7

,0

6CL6

:o

12AT7

,80

+300

tO

0

P U L S E A N A L Y Z I N G SYSTEM FOR A G R I D D E D I O N I Z A T I O N C H A M B E R

resultant output wave form is a narrow rectangular pulse of Vo, t volts and 4 #sec duration as long as Vout < 100. This is shown schematically in the figure. Fig. 16 shows the complete circuit diagram. Pulses from grid electrodes are fed into the pulse stretcher (V t ~ V6) and into the trigger circuit 90

~ 8°I O

7° ~

8o 5c 4c

251

square wave of the constant amplitude in coincidence with the collector pulse are sent to the diode bridge (D 1 ~ D6) via a cathode follower 1/'1, or Vls. VI7 and Vls comprise a time delaying circuit to internally furnish a trigger signal to the univibrator (Vt2, Via ) when this system is used as a pulse shape converter between very slow pulses and narrow rectangular output pulses of the same amplitude. Fig. 17 is art overall linearity of the system. This system has been successfully used in the experiment for obtaining pulse height distribution of grid pulses due to alpha particles from ThC' (fig. 18).

ac 2c 1C

,

10

20 - -

3O 4 0 5 0 e~O 7 0 8O 9 0 tOO INPUT PULSE HEIGHT (VOLTS)

Fig. 17. Art overall linearity curve of the linear gate.

(VT, Vs) which again triggers a gate circuit (V 9, Vto ) for the stretcher. The pulse stretcher is of the same design as originally described by A. W. Schardt 14) using a secondary emission amplifier tube (V6) as a charging element. The duration of the positive gate to prevent the discharge of a stretching condenser C is 75/~sec. Pulses from

:= 0

• °.%°°*°•°° "°°o°°O°°'°°°°-,°°°-

0

J 10

-

I 20

30 40 • CHANNEL NUMBER

I 50

(50

Fig. 18. Actual pulse height distribution of grid pulses resulting from alpha particles from ThC'.

collector electrodes are fed into the trigger circuits ( V l l ~ V13) which generates a square wave of 4 microseconds duration and 100 V amplitude. The stretched grid pulse of Vout volts and the narrow 14) A. W. Schardt, BNL-237 (1954).

5. Conclusions The effect of six pulse shaping networks on m i n i m u m attainable noise charge and on collection time dependence is described. The amplifiers having one differentiating element of time constant T 1 and one or two integrating elements of time constant T2 have been shown to be suitable for low noise and small collection time dependencies. The computed and measured noise charge for input capacitances of 30 p F are {a) 260 and 400 ion pairs for RC-RC amplifier (b) 240 and 370 ion pairs for RC-(RC) 2 amplifier. The pulses from the grid electrode have been approximated by a triangular wave form of collection time T o and decay time T~ and the condition for m i n i m u m noise charge for an RC-RC amplifier is found to be T t = T:. The condition also assures good linearity betweeninput and output amplitudes of the pulse. The optimum ilttegrating time constants for various triangular wave forms are between (0.55 ~ 1.1) x To. Finally a speciallinear gate circuit has been designed for the grid pulses and successfully used in the experiment. Acknowledgement The author would like to express his sincere gratitude to Professor E. Tajima for his advice and encouragement throughout this study. He is also grateful to Assistant Professor I. Ogawa and T. Doke for stimulating discussions and kind help in doing experiments. Finally he wishes to thank Miss Y. Ishibe for her aids in numerical computations.