An Analysis of k ii Coupling Coefficients

Abstract

The mutual inductance and the coupling coefficient for a couple of coils are usually described by simple parameters M and K respectively, instead of M₁₂, M₂₁ and k₁₂ and k₂₁. Many electric circuits theory books present at least a chapter about mutual inductance, in which a proof of M₁₂ = M₂₁ = M is usually described. Since most applications of M aim to transfer energy between coils, a coupling coefficient K is usually assumed without the rigorous analysis of k₁₂ and k₂₁. This paper presents an analysis of the mutual inductance between two coupled coils based on the linear magnetic circuit theory and a theoretical proof that it is not necessarily the case that k₁₂ = k₂₁ as many books assume. Finally, a practical experiment is presented to confirm the theoretical analysis.

Keywords

coupling coefficient magnetic circuits mutual inductance

Get full access to this article

View all access options for this article.

References

Lin

, ‘Proof of M₁₂ = M₂₁ based on stored energy is incorrect’, IEEE Trans. Circuits Systems, 36(9) (1989), 1153–1158.

Scott

R. E.

, Elements of Linear Circuits (Addison-Wesley, New York, 1966), ch. 12.

Nilsson

J. W.

, Electric Circuits, 2nd edn (Addison-Wesley, New York, 1986), ch 13.

Thomas

R. E.

and Rosa

A. J.

, The Analysis and Design of Linear Circuits, 5th edn (John Wiley, New York, 2006), ch. 15.

Edminister

J. A.

and Nahvi

, Schaum's Outline of Theory and Problems of Electric Circuits, 3rd edn (McGraw-Hill, New York, 1997), ch. 14.

Johnson

J. R.

, Electric Circuits part I: Direct Current (Holt, Rinehart and Winston, New York, 1970), ch. 11.

Siskind

C. S.

, Electrical Circuits, 2nd edn (McGraw-Hill, New York, 1965), ch. 8.

Guillemin

E. A.

, Introductory Circuit Theory (John Wiley, New York, 1953), ch. 8.

Desoer

C. A.

and Kuh

E. S.

, Basic Circuit Theory (McGraw-Hill, New York, 1969), ch. 8.

10.

Edminister

J. A.

, Schaum's Outline of Theory and Problems of Electric Circuits (Schaum, New York, 1965), ch. 13.

11.

Jackson

H. W.

, Introduction to Electric Circuits (Prentice-Hall, Englewood Cliffs, 1986), ch. 26–6.

12.

Hayt

W. H.

Jr. and Kemmerly

J. E.

, Engineering Circuit Analysis (McGraw-Hill, New York, 1962), ch. 16.

13.

Karris

S. T.

, Circuit Analysis II with MATLAB® Applications (Orchard Publications, Fremont, CA, 2003), ch. 8.

14.

Alexander

C. K.

and Sadiku

M. N. O.

, Fundamentals of Electric Circuits (McGraw-Hill, New York, 2000), ch. 13.

15.

Boast

W. B.

, Principles of Electric and Magnetic Circuits, 2nd edn (Harper & Brothers, New York, 1957), ch. 16.

16.

Kerchner

R. M.

and Corcoran

G. F.

, Alternating Current Circuits, 3rd edn (John Wiley, New York, 1951), ch. 7.