Sérgio Francisco Pichorim & Paulo José Abatti
CPGEI / CEFET-PR - Paraná Federal Center of Technological Education
Av. Sete de Setembro, 3165 CEP : 80230-901 - Curitiba - Paraná - Brazil

INTRODUCTION Practical biotelemetry system design commonly requires the determination of optimal size of the coils involved on power and/or information transmission. In principle, coils optimal size can be determinated using the Neumann mutual inductance general formula. However, the latter involves elliptic integrals [1], from which solutions are usually obtained using tabulated or graphical values [2]. The aim of this work is to present the derivation of mutual inductance simplified equations, useful to compute optimal size of circular-circular and circular-solenoid (including solenoid with ferrite core) pair of coils.

(1) (2)

METHODS Calculating the magnetic flux density (B) due to a current in primary coil using Biot-Savart law, and assuming that r²>>a² (where, r is the distance between primary coil center and secundary coil, and a is the primary coil radius), it is possible to obtain simplified equations of mutual inductance (M) between two circular coils (eq. 1), and between a solenoid and circular coil (eq. 2). In these equations n₁ and n₂ are the coils' number of turns, D distance between them, b radius of secundary circular coil, L solenoid length, and gm a constant related to solenoid core (gm=1 for air). Since eq. 1 and 2 do not employ elliptic integrals, the secundary coil radius (b), yielding maximum mutual inductance, can be calculated for a given set of geometrical parameters (a, D or L).

RESULTS The proposed equations have been compared with the general equations and measured values, giving results with negligible errors for D/a>10. Calculations using eq. 1 and 2, for D/a=5, yield results with errors less than 4%. For D/a<5, these equations cannot be considered useful to calculate the maximum mutual inductance.

CONCLUSIONS Observing that most biotelemetry systems use weakly coupled coils, i.e. the coils are within the above conditions (D/a>5), the authors believe that simplified equations are useful for optimal coil design.
[1] - Soma, M., Galbraith, D. C. & White, R. L., "Radio frequency coils in implantable devices: misalignment analysis and design procedure". IEEE Trans. Biom. Eng., 34, 276-282, 1987.
[2] - Terman, F. E., "Radio engineering handbook". McGraw-Hill, New York, 1943.