1966 PROCEEDINGS LETTERS 1211

TABLE I

LONGITUDINAL MAGNETOMETRIC DEMAGNETIZATION FACTORS __ ___

FOR EQUILAIZFAL POLYGONAL CYLINDERS

Aspect Ratio Triangle Square Hexagon Octagon Dodecagon Circle

0.01 0.9706 0.9674 0.9656 0.9654 0.9652 0.%50 0.02 0.9449 0.9415 0.9398 0.9393 0.9390 0.9389 0.03 0.9233 0.9192 0.9171 0.9166 0.9163 0.9161 0.04 0.9036 0.8989 0.8966 0.8960 0.8956 0.8954 0.05 0.8853 0.8801 0.8776 0.8769 0.8766 0.8764 0.06 0.8681 0.8626 0.8599 0.8592 0.8588 0.8586 0.07 0.8518 0.8460 0.8432 0.8424 0.8421 0.8419 0.08 0.8363 0.8302 0.8273 0.8266 0.8263 0.8261 0.09 0.8216 0.8153 0.8123 0.8116 0.8112 0.8110 0.10 0.8074 0.8010 0.7979 0.7972 0.7969 0.7967 0.15 0.7443 0.7375 0.7345 0.7337 0.7334 0.7333

0.30 0.6041 0.5981 0.5956 0.5950 0.5948 0.5947 0.40 0.5360 0.5309 0.5288 0.5284 0.5282 0.5281 0.50 0.4811 0.4767 0.4750 0.4747 0.4745 0.4745

mA

BUCKING LOOP 0.20 0.6909 0.6842 0.6813 0.6806 0.6803 0.6802

Fig. 1. Apparatus for measuring liquid conductivity

coupling coe5cient determined by the resistance of the water loop. A second loop in the form of a figure 8 of low resistance wire with a decade resistor box in series was then used to buck out the water-loop coupling. A signal source connected to a 175-turn primary winding on one torroid and a meter connected to a 175-turn secondary winding on the second torroid completed the setup. The resistance of the water loop was then de- termined by varying the resistance of the decade resistor box until a null was obtained on the meter. The value of this resistance was then taken to equal that of the water loop.

BERNARD L. LEWIS Radiation Inc. Palm Bay, Ha.

Tabulation of Magnetometric Demagnetization Factors for Regular Polygonal Cylinders

Longitudinal magnetometric demagnetization factors for several equi- lateral polygonal cylinders have been determined by inductance analogy [ 1 ] from available tables of inductance [2]. These values are listed in Table 1 as a function of the equivalent-area aspect ratio mA:

where I is the length of the polygonal cylinder, d, is the diameter of the circular cylinder of equal cross-sectional area, and A is the cross-sectional area.

Note from Table I that, for aspect ratios above unity, there is less than 1 percent dzerence in demagnetization factors between the 3-sided poly- gonal cylinder and the infinitely sided (circular) cylinder. For aspect ratios greater than 5, all of the shapes have essentially the same demagnetization factor.

The table can be used to determine the Brown-Momsh equivalent ellipsoid [3] for a regular polygonal particle. For these particles, the cross- sectional periodicity requires that the transverse demagnetization factors be equal [4]. Thus, in this case, the equivalent ellipsoid is a spheroid.

As an example, let us find the B-M equivalent ellipsoid for an equi- lateral triangular cylinder of unit volume and aspect ratio mA=0.02 [or shape ratio nA = (mA)- = 50). From Table I, Dl = 0.9449. Therefore, the transverse demagnetization factors are D22=D33=)(1 -0.9449) =0.02755. Interpolating from the tables in [5 J we find that the spheroid shape ratio is n=27.23. Equating the volumes of the two particles gives, for the semipolar axis,

0.60 0.70

0.90 0.80

1 .00 2.00 5.00

10.00 8.00

0.4358 0.3978 0.3657 0.3382 0.3144 0.1828 0.0801 0.05 12 0.0412

0.4321 0.3948 0.3631 0.3360 0.3124 0.1821 0.0799 0.051 1 0.0412

0.4308 0.4305 0.4304 0.4303 0.3937 0.3935 0.3934 0.3933 0.3622 0.3620 0.3619 0.3619 0.3352 0.3350 0.3350 0.3349 0.3118 0.3117 0.3116 0.3116 0.1819 0.1819 0.1819 0.1819 0.0799 0.0799 0.0799 0.0799 0.051 1 0.0511 0.0511 0.0511 0.0412 0.0412 0.0412 0.0412

113

a = (2) which in this case yields a= 0.0679 length units. The semitransverse axis of the equivalent oblate spheroid is b=na= 1.849 length units.

A circular cylinder particle of unit volume and aspect ratio m,=0.02 similarly yields the following equivalent oblate spheroid: n=24.44, a=0.0735, and b= 1.796. For this latter calculation, tables in [6] were utilized, since the tables in [5 J, while of small increment, only have values in the range 25.0<n<129.0.

R. MOSKOWITZ E. DELLA TORRE R. M. M. CHEN

Dept. of Elec. Engrg. Rutgers University

New Brunswick, N. J.

REFERENCES [I I R. Moskowitz and E. Della Tom, "Demagnetization factors of non-ellipsoidat sam-

pks,” submitted to IEEE Transactwnr on Mamtics. I21 F. W. Grover, Inductance Calculntwm Working Formuku and Tabk-s. New York:

Dover, 1%2, pp. 172-173. I31 W. F. Bream, Jr., and A. H. Morrisb, “EBect of a cavity on a single4omain magnetic

panicle,”Phyr.Rev.,voL 105, PP. 1198-1201, February 1957. [41 R. Moslrowitz and E. Della Tom, ‘Thsoretical aspefts of demagnetization tcnsors,”

submitted w IEEE Transacriom on Magiwi~s, [SI L. B. Schmidt, W. E. Case, and R. D. Harrington, “Demagnetidng factors for oblate

spheroids used in ferrimagnetic rrsonanaexperimemts,” National Bureau of Standards,

[61 E. C. Stoner, ‘Tbe factors for ellipsoids,” PhiL Mag., vol. 36, pp. 80s Boulder, Colo., Tech. Note 221, Scptanbcr 1964.

821, Decgnba 1945.

Low-Fqnen~y Noise in dc Amplifiers Noise, like zero drift (aging, or irreversible change of zero level with

time) or zero shift (reversible change of zero level due to various causes, e.g., temperature) is a limiting factor to the sensitivity of an amplifier. The noise limit has traditionally been associated with ac amplifiers only and zeri, drift and zero shift exclusively with dc amplifiers, but due to recent improvements in compensation techniques [l ] and m semiconductor tech- nology, it seems appropriate to reconsider the importamx of noise in dc

Manumipt dved June 30,1966. M a n d p t received June 13,1966.