Modeling & Calculation of the Magnetic Field Given by an Helmholtz Coil for Orthoferite Daniel Victoras ENE Vice-Chair of the IEEE-CPMT SBC Department of Electronic Technology Politehnica University of Bucuresti Splaiul Independentei 313, 77206, Bucharest, Romania Phone , Fax WWW: WWW: WWW: Daniel Victoras ENE Vice-Chair of the IEEE-CPMT SBC Department of Electronic Technology Politehnica University of Bucuresti Splaiul Independentei 313, 77206, Bucharest, Romania Phone , Fax WWW: WWW: WWW: IEEE-CPMT Student Branch Chapter Meeting November, 1 st, 2002

Goals  Biot-Savart formula  Numerical and Analytical Computation  1 st Model  Variation of the Magnetic Field Components  2D and 3D Model  Simulation Results IEEE-CPMT Student Branch Chapter Meeting November, 1 st, 2002

Modeling of the Magnetic Field for Half of a Winding Diagram for evaluating the vectors from Biot-Savard formula IEEE-CPMT Student Branch Chapter Meeting November, 1 st, 2002

Vectorial Product Calculation IEEE-CPMT Student Branch Chapter Meeting November, 1 st, 2002

Comparation between Numerical and Analytical Methods Analytical formula r=d/2 Our case x=z1 r=d/2 Our case x=z1 IEEE-CPMT Student Branch Chapter Meeting November, 1 st, 2002

Comparation between Numerical and Analytical Methods Both of them The relative error obtained when using the numerical method IEEE-CPMT Student Branch Chapter Meeting November, 1 st, 2002

Modeling of the Magnetic Field for More Windings IEEE-CPMT Student Branch Chapter Meeting November, 1 st, 2002

Modeling of the Magnetic Field for More Windings Up side: diameter(n) = 2*[raz+(n-1)*D1] diameter(n) = 2*[raz+(n-1)*D1] shift in y = 0 shift in y = 0 Down side: diameter(n) = 2*[raz+0.5*(2*n-1)*D1] diameter(n) = 2*[raz+0.5*(2*n-1)*D1] shift in y = -0.5*D1 shift in y = -0.5*D1 IEEE-CPMT Student Branch Chapter Meeting November, 1 st, 2002

Variation of the B components along x,y and z axis are for the Up side. IEEE-CPMT Student Branch Chapter Meeting November, 1 st, 2002

Variation of the B components along x,y and z axis are for the Down side. IEEE-CPMT Student Branch Chapter Meeting November, 1 st, 2002

Modeling of the Magnetic Field – 2 sides of the Coil IEEE-CPMT Student Branch Chapter Meeting November, 1 st, 2002

Bztotal along x axis (TOP) Bytotal along y axis(TOP) Bxtotal along y axis (TOP) Variation of the Btotal components along x,y and z axis for TOP & BOTTOM side. Fig 9. Bztotal along x axis (BOTTOM) Bytotal along y axis (BOTTOM) Fig 11. Bxtotal along y axis (BOTTOM) Bztotal along z axis (BOTTOM) Bxtotal along y axis (BOTTOM) IEEE-CPMT Student Branch Chapter Meeting November, 1 st, 2002

Modeling of the Magnetic Field – one dimension IEEE-CPMT Student Branch Chapter Meeting November, 1 st, 2002

Modeling of the Magnetic Field – two dimension IEEE-CPMT Student Branch Chapter Meeting November, 1 st, 2002

Variation of the Magnetic Field on Number of Windings IEEE-CPMT Student Branch Chapter Meeting November, 1 st, 2002

Inductance of the Planar Inductor IEEE-CPMT Student Branch Chapter Meeting November, 1 st, 2002

Variation of the Inductance on Number of Windings IEEE-CPMT Student Branch Chapter Meeting November, 1 st, 2002

What is needed?  Induction of the Coil 1mT….10mT  for 1mmX1mm square  Constant Value of the Magnetic Field  no more than 10% relative error  Low Value of the Inductance IEEE-CPMT Student Branch Chapter Meeting November, 1 st, 2002

Simulation Results zp=0 the field in the XOY plane; raz=0.001 the radius of the first half circle D1= distance between the radius; N1=3 number of windings; h=0.001 the thickness of the substrate; t= the thickness of the track coil; w= the width of the cooper pellicle; n1=n2=10 the number of the divisions I1=1A current pulse IEEE-CPMT Student Branch Chapter Meeting November, 1 st, 2002

Simulation Results IEEE-CPMT Student Branch Chapter Meeting November, 1 st, 2002

Design: Daniel Victoras Ene Design: Daniel Victoras Ene Thank you for your attention ! Thank you for your attention !