. The Bell System technical journal . I Fig. 2. cylinders should be in a geometric progression to give the most efficientshield. That is, we should have qi — qi — qz = qn = §23 = q- Equa-tion (2) then becomes g = 1/4 m(1 - g + 1/16 fx^n -f M« + 3/4 m«) + 1. (7) For two cylinders we get g = 1/4 m(1 -2^ + 1/4 M«^) + 1. (8) In these equations, the following relations hold between n and Rsfor (7) and ri and R2 for (8) Rs = rJ^[i^ R, = rif^\ (9) The effect upon the shielding efficiency of varying 5 (Fig. 3) from 422 BELL SYSTEM TECHNICAL JOURNAL zero to P keeping rijRi = r^jRi can be obtained by me
. The Bell System technical journal . I Fig. 2. cylinders should be in a geometric progression to give the most efficientshield. That is, we should have qi — qi — qz = qn = §23 = q- Equa-tion (2) then becomes g = 1/4 m(1 - g + 1/16 fx^n -f M« + 3/4 m«) + 1. (7) For two cylinders we get g = 1/4 m(1 -2^ + 1/4 M«^) + 1. (8) In these equations, the following relations hold between n and Rsfor (7) and ri and R2 for (8) Rs = rJ^[i^ R, = rif^\ (9) The effect upon the shielding efficiency of varying 5 (Fig. 3) from 422 BELL SYSTEM TECHNICAL JOURNAL zero to P keeping rijRi = r^jRi can be obtained by means of thefollowing equation g- 1/4m where 1 -^ + 1/4m(i --^Xn,,912 \ Vgi2/ R2 + 1> (10) If Ri/r2 (that is Vgi2) is varied from 1 to R^/ri the desired result isobtained. Assume in Fig. 3 the thickness of the two cylinders to be the same,that is, R\ — r\ = R2 — ^2- The variation in shielding efficiency vs. 5. FiR. 3. or Vgi2, is then given by equation (5), with §2 expressed in terms of512 and q\ as follows: Vg2 = 1 + Vgi2[l - Vgi] (11) In an article in the Philosophical Magazine of February 1933 L. has developed relations for the shielding efficiency of sphericaland cylindrical shells taking into account the effect of induced following equations for an infinitely long metallic cylinder havebeen picked from his paper. For a non-magnetic shell, the thicknessof which is small compared to its radius, the shielding ratio, g, isgiven by g = 1 cosh {ka) + 1/2 ka sinh {kd) |, (12) » MAGNETIC SHIELDING OF TRANSFORMERS 423 where a is the radius and d the thickness in cm. k is given by where/is frequency in cycles and p is resistivity in ohms per centimetercube. At low frequencies (12) reduces to 1+,-M^io- (14) which is good up to about 10^ cycles. The direction of the disturbingmagnetic field in (12) and (14) has been assumed perpendicular tothe axis of the cylinder. Other form
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