High-speed instrument for measuring small currents
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UDC 621.317.732:681.121.815
In many areas of science and technology it is necessary to determine the frequency and transient characteristics of objects having a very high internal resistance for currents of approximately 10-xx-10 - ~ A. This requires electrometer apparatus of comparatively high speed of response (the electrometer must have a time constant of approximately 0.i-i0 msec). At the present time no such instruments are manufactured either in this country or abroad. Below we describe the circuit of a high-speed instrument for measuring small currents based on the method of integration [i]. Up to now integrator-differentiators have not obtained wide application because of the high level of inherent noise and the cyclical nature of their operation. As shown in [2, 3], the level of natural noise in integrator-differentiators is mainly determined by the noise of the dc amplifier of the differentiator. Figure 1 shows the circuit of an integrator--differentiator which, unlike existing circuits, contains only one electrometer amplifier. The current to be measured im is applied to the input of the electrometer amplifier with gain K, input resistance Rin, and input capacitance Cin. The negative feedback circuit of the electrometer amplifier contains the load resistance Rl, a differentiating capacitor C2, and an integrating capacitor CI with an insulation resistance RI. The output quantity of the integrator-differentiator is the voltage Uou t taken from the load resistance R I. As calculations show, the transfer function of the electrometer has the form Kt TIp W(p) = T Z p ~ +T3p+l 2
(i)
'
w h e r e Kt=RZ; TI=RIC2;
T~=Rx (Cin+Cl)RlC~. T3=R1C1. K E x p r e s s i o n (1) was d e r i v e d on t h e a s s u m p t i o n t h a t t h e e l e c t r o m e t e r a m p l i f i e r i s a d e layless section, i,e., K ( p ) = K. We w i l l r e p r e s e n t (l) in the form of the product of the t r a n s f e r f u n c t i o n s o f two s e c t i o n s c o n n e c t e d i n s e r i e s , n a m e l y , an i d e a l d i f f e r e n t i a t i n g sect i o n and a s e c o n d - o r d e r a p e r i o d i c s e c t i o n , i.e.,
w(p)
Wl(p)'Wdp),
(2)
Kt T~p2@ Tap @1
w h e r e WKp)=TIp; We(p) = C o n s i d e r W2(p). necessary to satisfy
=
As i s w e l l known [ 4 ] , f o r a s e c o n d - d e s r e e a p e r i o d i c s e c t i o n t h e c o n d i t i o n T3 ~ 2Ta, o r RxCx ~ 2 / I R a ( C a + C i n ) R I C 2 ] / K .
U s u a l l y , when m e a s u r i n g t h e same o r d e r o f m a g n i t u d e . Ca = Cin. We then obtain
(3)
El
_
~
T:IiI
u
t
I
-- +c2
Fig. i
~//
I
I
I Fig. 2
Translated from Izmeritel'naya Tekhnika, No. 5, pp. 54-56, May, 1978.
674
is
c u r r e n t s o f 1 0 - x 2 - 1 0 -x~ A t h e c a p a c i t a n c e s Cx and Cin a r e o f H e n c e , to s i m p l i f y t h e s u b s e q u e n t c a l c u l a t i o n s we c a n a s s u m e
KR1C1 ~ 8RtC~.
~in_~
it
0543-1972/78/2105-0674507.50
9 1978 Plenum Publishing Corporation
TABLE I Load
Time constant r, msec
/resis-
f2
[ 0 -In
10 - ~
Rt
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