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# Download ac voltage ratio measurement

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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, . MEASUREMENT C f w H for Cydie C a p a c h ~mothod; n Is 4-.CtrcIe 8Z on Reader Servtce Card 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. Page 111