EFFECT

OF T R A N S M I S S I O N - L I N E

ON T H E

READINGS

RESISTANCE

OF E L E C T R O N I C

VARIATIONS

AUTOMATIC

BALANCED

BRIDGES

(UDC 621.317.733.088.24) A.

A. K o l ' t s o v

and

D.

N. K a r a b a n o v

Translated from I z m e r i t e I ' n a y a Tekhnika, No. 1, pp. 78-78, January, 1966

In some of the current literature (see, for instance [1, 2]) an assertion is still m a d e which does not correspond to facts that the use of a three-conductor line to the measuring circuit of electronic automatic balanced bridges e l i m i n a t e s the temperature effect on the resistance of the line. Other authors [3-5] correctly note that a t h r e e conductor transmission line e l i m i n a t e s the temperature error only at one scale point of the bridge, which corresponds to its symmetry. However, in [3-5] no data are provided for evaluating the above additional temperature error Yt at any point of the scale. The basic error component )'R which is due to an inaccurate trimming of the line conductor resistances isnot dealt with at all in literature, to the best of our knowledge. A tendency has appeared rece~ntly to develop narrowrange bridges required for low-resistance thermometers [6]. In this connection great importance is acquired by the rational selection of transmission line parameters. It is impossible to do it without taking into account errors 7R and 7t, which determine the precision characteristics of bridges. Let us refer to error ?'R of the principal measuring circuits used in bridges of Soviet manufacture, For the circuit shown in Fig. 1 (used in bridges type ~MP-209) and a similar circuit without resistor R1 (used in bridges type I~MD-202) we have

Xs

A 1711 R

~R=

1 -9

X A Rlz ARI~_-- ARlz R + Rm

__

--

-

a

A Rlz ARm + Xs-R R

9I00%,

(1)

-

where R is the characteristic bridge resistance in a [7] consisting of the total resistance of bridge arms adjacent to the measuring diagonal for a m i m i m u m value of the tested resistance; ARm is the m a x i m u m increment ARt of the tested resistance Rt (instrument's m a x i m u m reading); X is the relative increment of the tested resistance(0 < X_< 1) X = ARt/ARm; X s is the value of X for which the bridge circuit in Fig. 1 or Fig. 2 becomes s y m m e t r i c a l and, hence, insensitive to equal variations in the line conductor resistances (usually X s is assumed to be 0.5 for ARI1= ARlz = 0); ARlt and AR12 are the absolute errors in 2 of trimming the resistances respectively of the first (upper) and second (lower) conductors of the transmission line. The application of coefficient X serves to e l i m i n a t e the use of specific increments to the tested resistance, thus simplifying the calculations of errors and the comparison of properties in similar circuits which differ onIy by their measuring ranges. For the circuit in Fig, 2 (used in bridges type ~MD-207) and a similar circuit which differs from the first by the fact that resistor R3 is inserted in the bridge arm with the tested resistor Rt we find that (LARll

ARt2

ARh--AR12/ ( / '

R 'P, = - -

(

ARX=

l+--D---

, xARnz~(I+X '

R /~

ARm)

+-VARm] ( 1 + AR,. -Ts


9 100%.

(2)

)

111

II~llllllll

By assuming in Fig. 1 that resistor R4 is connected to the supply diagonal of the bridge through resistor Rs,we obtain a circuit with a two-conductor transmission line for which 7R

=:

2 AR----L 9 100%, ARm

(3)

where 2AR1 is the absolute error in trimming resistances of a twoconductor transmission line.

i

The curves given in Fig. 3 serve to compare the values of )'R for the circuits in Figs. 1 and 2.

Fig. 1

I,

,,l

Bridge circuit with contaetless slide wires [8, 9] are also of interest. They include the circuit shown in Fig. 4 which, however, uses a two-conductor and nor a three-conductor transmission line [10]. If we assume that X = 0 and the circuit is balanced, error TR can be calculated from the formula

....

/A, I

i~,

R1

~

$o ,s

~,

APl(I+

\

~ r - - ~ ' - - - " 0 ~-

/

TR = 2

R

(

\

9 100%.

ARm]

ARI

(4)

ARm)

1+2~-+x

-

R The presence of term R/ARm in the numerator of (4) shows that error )'R of this circuit is particularly large for small values of ARm .

Fig. 2

By assuming that AR1 = 0.01 f~, R = 500 fl, ARm = 0.396 (resistance thermometer with a calibration of 20" and a range of 0-10~ and X = 0, we find that )'R ~ 5%. Let us note that the above change AR1 in R1 = 2.5 f~ occurs for a transmission line temperature deviation of 1~ from the normal. A considerably smaller error ~'R is obtained if the circuit in Fig. 4 is provided with a three-conductor line. Assuming that such a circuit is balanced for k = 0 we obtain

ARli--AR1t

.IR=_

l+t

+k

ARlt

ARm

R

R

R

1+

R

1 § XA/?m/(I-*

1 ~-).

' ,

1~-

R /\

R

•

4-

1

~--. 100% ARm

- R ~] A-~12 l ' 4-i

R

R ,/

9

(5)

For ARh and ARh with different signs and AR1 of the order of ~ 0.01 9 it is possible to evaluate ~R for the circuits in Figs. 1, 2, and 4 with a sufficient precision from the approximate formula TR A R l i - - AR12 9 100%. ARm

(6)

For instance, if ARm = 9.01 f~ ( m i n i m u m value specified by GOST 7164-58 for resistance thermometer with calibration 11 a and a range of 0-50~ and ARli = -- &R12 = 0.01 fL we find that )'R ~ 0.22%. Thus, a further lowering of the bridge measurement range will produce a rise in ?'R since it is hardly possible to raise the precision in trimming the line conductor resistances. For bridges with measuring ranges of the order of 1 f~ or lower it is necessary to use the circuits described in [11-13]. The advantage of circuit [11] consists in the fact that in can be used both with alternating and direct currents.

112

~'5t?o I

A rise of ARm in (6) l e a d s to a r e d u c t i o n of }'R and for ARm of the order o f s e v e r a l tens of o h m s the error b e c o m e s u n e s s e n t i a l .

I R= 5OO a

0..3

It should b e n o t e d t h a t 7R is not e q u a l to z e r o e v e n if t h e a b s o l u t e errors ARh and AR12 c o i n c i d e b o t h in m a g n i t u d e and size, w h i c h m e a n s t h a t it is n e c essary to h a v e a s u f f i c i e n t l y a c c u r a t e t r i m m i n g of R1.

at

\\

O.Og

!" 9

O.OO

]

,

\b.< t

IX ! '~, ~

Let us e x a m i n e t h e e f f e c t of t e m p e r a t u r e v a r i a t i o n s on the t r a n s m i s s i o n l i n e r e s i s t a n c e . In t r i m m i n g the t r a n s m i s s i o n l i n e r e s i s t a n c e R1 a d i f f e r e n t r e l a t i o n s h i p is o b t a i n e d for its c o p p e r wire R1 Cu and its m a n g a n i n wire R1 Mn segments. It c a n b e a s s u m e d t h a t t h e l i n e c o n d u c t o r s h a v e d i f f e r e n t t e m p e r a t u r e c o e f f i c i e n t s of r e s i s t a n c e , and t h a t for the first (upper) c o n d u c t o r we o b t a i n

'" 0

70

+0

~0

80 ~ R m , a

~=~

Fig. 3

Rlcul R1

('7)

a n d for t h e s e c o n d (lower) c o n d u c t o r we h a v e

RI c,.,2

(8)

I,,'i m o r e o v e r R1 = R1Cu + R1Mn" V a r i a t i o n s A t of t h e l i n e t e m p e r a t u r e w i t h r e s p e c t to its n o m i n a l v a l u e l e a d to u n e q u a l c h a n g e s in t h e c o n d u c t o r resistances. Expressions for error 7 t due to v a r i a t i o n s in the l i n e r e s i s t a n c e c a n b e e a s i l y o b t a i n e d from e x p r e s sions (1-5) by s u b s t i t u t i n g for RLli its v a l u e o b t a i n e d from e q u a l i t y R~N~A

ARli = : ~ i A t R 1

L

R1

w h e r e cq is t h e e q u i v a l e n t t e m p e r a t u r e c o e f f i c i e n t of r e s i s t a n c e in 1/~ corresponding transmission line conductor.

I~1

i

~#

\\,4,

The maximum permissible transmission line conductor resistances can

f-~

~fgl=Sg

b e e v a l u a t e d ( p r o v i d e d t h a t t h e v a l u e s of }'t' ARm' R, ct, ct 1, and c%are k n o w n as w e l l as t h e v a l u e of A t under o p e r a t i n g c o n d i t i o n s ) from t h e f o l l o w i n g f o r m u l a s : for t h e c i r c u i t in Fig. 1 7: I- R

a 1 =A~., *1=2~t? tll

7010

?0

of t h e

For a t w o - c o n d u c t o r c i r c u i t w i t h a c o n t a c t slide wire t h e d e t e r m i n i n g f a c t o r consists of the a d d i t i o n a l t e m p e r a t u r e error 7 t w h i c h a t t a i n s i m p e r m i s sibly l a r g e v a l u e s . This e x p l a i n s the use of a t h r e e - c o n d u c t o r l i n e s i n a u t o m a t i c b a l a n c e d bridges. T h e v a l u e s of t e m p e r a t u r e errors Xtz for a t w o - c o n d u c t o r l i n e and k t a for a t h r e e - c o n d u c t o r l i n e of the c i r c u i t s shown in Fig. I c a n b e j u d g e d from t h e c u r v e s in Fig. 5 p l o t t e d for R = 500 ~, k = 0, k s = 0.5, a = 4.3'10-a(1/~ At = 10~ Act = 1.10-5(1/~ The value ofthetemp e r a t u r e error of t h e c i r c u i t in Fig. 4 h a s b e e n d e t e r m i n e d a b o v e .

Fig. 4

0,

(Sa)

,

~ Fig. 5

]

7 7 / - 7 ~ m + Xs I

R 100[~I 7,~--a2>." (~, --, ,) ~.,~.~1 --X: ~t

,

(9)

bO NaRl,a a n d for t h e c i r c u i t in Fig. 2

113

ARm's2 "~t

R~

l+x-Z) 77

(

APm'~ (lO)

(

For equal temperature coefficients cq and ~2 expressions (9) and (10) beeovne a little simpler. In balanced electronic bridges with a three-conductor line and a measuring range above 9 fa it is advisable to use wires of reduced cross section by making, for instance, each wire resistance R10 = 7.5 fa. In fact assuming that ARm = 9.01 fa, R = 200 g}, ks = 0.5, At = 50~ )'t = 0.5%, ~1 ~ c% = 4 . 3 10"s(1/~ zXr = 2" 10-s(1/~ we find from (9) that the line resistance can attain the value of R10 = 8.4 fa, which is more than three times higher than the line resistance of up-to-date bridges (R1 = 2.5 fa). For larger values of ARm the value of )'t is smaller than in the above example. If we assume that ARm= 183.8 ~ (resistance thermometer with calibration 22 and a range of 0-500~ R = 1200 a, k s = 0.5, At = 50~ oc1 -~ c~2 = 4.3" 10-3(1/~ Act = 2 ' 10-s(1/~ R1 = 8.4 a we find from (1) that }'t = 0.07%. The recommended raising of the line conductor resistance will reduce the expenditure of copper by weight in the ratio R10/R1 (for the same lengths of line), i. e., it will reduce it by a factor of three, since R1 = 2.5 a. A considerable economy in copper can be obtained in the installation of lines for each bridge point (about 6 kg if the communication line R1 - 2.5 fa uses wires with a cross section of 2.5 mm2). In laying c o m m u n i c a t i o n lines control conductors (minimum cross section 1 m m 2) are used as well as testing and signalling cables (wires with a m i n i m u m cross section of 0.5 m m 2) [14]. Therefore, there is no danger of reducing the m e c h a n i c a l strength of lines by decreasing the cross section of their conductors. Cross sections of 2.5 m m 2 (or 1.5 m m 2) are used at the present time in order to obtain a conductor resistance not exceeding 2,5 fa for a m a x i m u m length of laying of a bunch of conductors in a trough or boxing instead of conduits will facilitate the use of wires with a cross section of 0.5 mm 2. By using a conductor of the same cross section as for R1 = 2.5 fa it becomes possible to increase the working distance between the bridge and the resistance thermometer by the ratio or R10/R1, i . e . , by a factor of three. Let us note that error )'R will not be increased by raising R1 if the values of ARh and ARI~ remainthe same. LITERATURE 1. 2. 3. 4. 5. 6. 7. 8. 9.

CITED

S.S. Denisov, Instruments for the Testing and Automation of Petrochemical Production [in Russian], Gostoptekhizdat [ State Scientific and Technical Press of the Petroleum and Mineral-Fuel Industry] (1960). L.N. Sokolov, Priborostroenie, No. 1 (1965). G.P. Kul'bush, Electrical Pyrometers [in Russian], ONTI (1982). M.V. Kulakov and S. P. Shchepkin, Automatic Testing and Measuring Instruments for Chemical Production [in Russian], Mashgiz (1961). I . V . Burusov, Automatic Testing, Measuring and Control Instruments [in Russian], Gostekhizdat (1963). V . I . Lakh and G. V. Samsonov, Pribory i sredstva avtomatizatsii [Instruments and Means of Automation], No. 9 (J964). A . A . Kol'tsov and D. N. Karabanov, Izv. vuz. Priborostr., 7, 2 (1964). A . A . Kol'tsov and M. F. Zaripov, Authors Certificate No. 135959, Bulletin of Invention, No. 4 (1961). M.F. Zaripov and A. A. Kol'tsov, Contactless Slide Wire for AC Automatic Instruments [in Russian], PNTPO, No. 26-64-860/46, GOSINTI [State Scientific Research Institute of Scientific and Technical Information]

(1964). 10. 11. 12. 13. 14.

114

L.F. Kulikovskii, L. A. Brovkin, 1~. M. Gashnap, and M. F. Zaripov, Pribory i sredstva avtomatizatsii (1963). A . A . Kol'tsov, Authors Certificate No. 152911, Bulletin of Invention, No. 3 (1963). A . A . Kol'tsov and D. N. Karabanov, Symmetrical Electronic Automatic Balanced Bridge [in Russian], GOSINTI, No. 18-64-348/9 (1964). V.A. Kochan, V. I. Lakh, I. F. Palyanytsya, and M. M. Protsevyat, Izmerit. Tekhn., No. 1 (1965). A . K . Adabash'yan, Installation of Testing and Measuring Instruments and Automatic Control Equipment [in Russian], Gostroiizdat [State Press of Literature on Building, Architecture and Building Materials] (1962).