Download ac voltage ratio measurement

AC VOLTAGE RATIO
MEASUREMENT
HENRY P, HALL,
w
H E 3 RESISTANCE, mass, length, etc., are
measured in term of standards kept by national
Iaboratories, voltage ratio, being dimensionless, has no
national, legal standard. Thus anyone may make ratio
measurements and may claim my accuracy he feels he
can justify, even if it exceeds that claimed by a national
laboratory.
At reasonable frequencies and voltages (e.g., 1
kTJq 100 v) , avaihble ratio-measuring systems have
sensitivities on the order of one part-per-Won (ppb)
of input; comparisons on voltage dividers can be re
peated to this accuracy on successive measurements,
With two dividers (one reversed with mpect to the
other), the comclion for the 0.5 point cctn ,be re
peatedly determined to within a few ppb.
General Radio Company
3), and a straddling method based on the common reversing technique.
Cyelie Capacitor Method
In this technique, a decade transformer is com-
pared with several capacitive dividers (each capacitor
is used in both halves of the divider and the average
of all measurements is taken). The beauty of the method
lies in its mathematics. For the 3 :1 divider (Fig. 1),
each capacitor is connected serially to the high input
and tbe others to the low. The average of the three
ratios is given in Eq. 1, For accuracy, the capacitors
must nzahtain their values during the measurtmcnt
cycIe; they must have: low tempeathue and voltage
coefficients and the measurements should be made in.-/- a well controlled room.
One way to evaluate the aocuracy of voltage ratio
measurements is to compare results obtained using
several different techniques. Many methods have been
used for this measurement. Several use precision resistors, but at 100 v and 1 kHz, low value resistor^ dhipate excessive power and therefore cbange, while high
value resistors exhibit excessive phase W.
Thus these
methods were avoided.
' Three alternative methods were selected: the cyclic
capacitor method of Cutkosky and Shields (Ref. I),
the bootstrap method of Sze (Ref. 2) and Hill (Ref.
The circuit for these measurements (Fig. 2 ) , contains threeterminal capacitors that have appreciable
capacitance from each terminal to the case which i8
tied directly to the output of the divider under test. This
connection causes negligible loading e m because the
output impedance is low, the stray capacitances form
a divider of almost the same ratio, and rhe cyclic m
tation of the capacitors also rotates thae strays su&
that this source of error is averaged out.
F16. I. CAPAClTtVE divider, using only
F I ~ 2,
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4-.CtrcIe
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The BooMrap M & d
This method uses a shie.lded 10: 1 transformer (Fig.
3) as a ymhtick Each -tenth
step measuremmt
may be hccurate by an srmount 1 (Eq.2), but the
sam of the step mast be unity. This latter condition
In actual dividers, the mexence between the zero
and full-scale voltages is not equal to the input voltage,
because of the voltage drop in the wiring. The input
voltage must be measured at the hihigh and low tentid s if Eq. 3 is to be valid. The corrections for the 0
and 10 positions cm be determined from the difference
(Eq. 3) parnits all voltages to be determined by solving
between the output at thae settings and the value8 at
to obtain the transformer voltage E,, m in Eq. 4. To
~ t d ~ & p , s a m a l l d ~ h m z e r o , s u r i nthe input terminah.
While the voltage, E,, can be any valuey it is deI3q. 5.
sirable that it be dose to E d l O . The error in E, will
then be small, rn that fractional c h w in this error
will not be important. E, must be constant, independent
of ratio setting; this r e q h no capacitance to either
winding from variable voltages, and mggats a doubly
shielded tmsformer.
A two-stage t r d o f m e r (Ref. 3,4) reduces the
ermr due to voltage drop in the primary by sampfing
the flux and adding additional voltage. The frill input
voltage (Fii 4) is applied to one winding. Because of
the voltage drop due to zb e~ and e8 are low. The dif-
Fl6. 8. CONNECTIOH diagram for bootrfrap mdhod; n
number of tonths of Input
is the
ferenoe between ei. and q is applied to a m n d transformer whose output is added to q as a correction.
Such -age
transformers wifh errm of lw than
20 ppb of input are not difEult to find. With the bootstrap mdhd (Fig. 5 ) , m-mements and calcuIatiom
for all 1/10 s q s a n be made in one hour,
I
#
The Straddling Mefhod
The correction for the 0.5 point can be found by
reversal of one divider with respect to another. Conn
t
i e such division gives % points, 341 points, etc.,
(Ref. 5 ) . Unfortunately, most dividers are decade
rather tban binary, so this subdivision is not suitabIe.
With a known ratio between pairs of adjacent decade
stepst, however, it is p i b l e to calculate the amredon
for m& step. Thm ratios can be determined with a
m u d decade t c a d m e r stmddbg each pair of
1/10 step (Pig. 6 ) The arithmetic required to evaluate each point after
measurement is c 0 1 l v h t l y performed with a computer. The divider must have all 1/10 taps brought out
(Fig.
7). The correction for the straddling divider at
the 0.5 point is determined by lead reversal. The s t d dlhg divider loads the divider under test, but in pmcti%
mulag e m -f
mdWle. The magnitude of the change caused by hading csin be m e a s d
Y' plaoinp a third
in parallel
unit, and the resulting change of setting used as a
correction. The high and low input terminah are wed
for Ulc meamemeat so that the total voltage is unity
30 ppb. Multiple runs, made by the bootstrap meth
all fell within this spread, as did the 0.5 point determined by h p l e reversal.
An NBS calibration, which states lt.200 ppb
curacy, differed by a maximum of 50 ppb from the
measured average. The repeataliility of the r d t s de
scribed here suggests that the average of the measlu
ments is within 20 ppb of true value,
One note of caution for others atkmpting thew
measurements. The dividers must be carefully demagnetized before measurement. Previous o v d d
(removed at peak canmi) caused magnetization that
resulted in changes in calibration of up to 10 ppb. Such
overiods may occur in a comparison circuit if the two
dividers are set to widely di&hg values and the ds
tector circuit ha^ low impedance. Cyclic demaguetizatim restores the original calibration.
&'.
References
R. D. and Shields, J. Q., "The Precision
Measurement of Tra+ormer Ratios,'' IRE Tmihm~
on I ~ h w w n Vol.
~ , 1-9 No. 2, September
245.
C., -An Injection Method for Self-Cdibratlm
of fnductive Vol*ge- Dividsrn" NBS Jm-i
of Re-
1. Cutkoaky,
,,izOId..
#&,
hiection C, danuary-darch 1988
~ mJ., J., u ~ ~ e~
oe
~v
, and ~eanurmento f I.ductive Voltage Dividere, PTOC.IEEE, Vol. 115, No.
5, May 11988, p. 727
L Brook, & B. .nd Holb F. C,,
-Sws.
Qlw
rent Tranltfomrc A I E ~
Tm~~dawtbw,
Vol. 41, June
1022, g ~ 882-895.
.
%
6*
eta
Admittances," IEHE Tramme*
0% I ~ s e t m w t m t a t h
a d M~a.au~$?n#tt,Vol. 1-M-13,
No. 4 December, 1904,
Resulfs
Measured
om made by two runs using each
method &owed a maximum spread of points h than
Cut$sp
R. D., L a A ~ tand
i ~ e Pasaive Direct-Reding
for the Cornpanson of Audio-Frequency
Itst10
by dehition.
243-260.
6.
T. L, "The Calibration of Inductive Volts
~ividen:' I$A T - W W
Vol. 2, No. 3, July 19&
g. 196.
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