1. 1 Magnetic Circuits and Transformers Discussion D10.1 Chapter 6

2. 2 Hans Christian Oersted (1777 – 1851) Ref: http://chem.ch.huji.ac.il/~eugeniik/history/oersted.htmhttp://chem.ch.huji.ac.il/~eugeniik/history/oersted.htm 1822 In 1820 he showed that a current produces a magnetic field. X

3. 3 André-Marie Ampère (1775 – 1836) French mathematics professor who only a week after learning of Oersted’s discoveries in Sept. 1820 demonstrated that parallel wires carrying currents attract and repel each other. attract repel A moving charge of 1 coulomb per second is a current of 1 ampere (amp).

4. 4 Michael Faraday (1791 – 1867) Self-taught English chemist and physicist discovered electromagnetic induction in 1831 by which a changing magnetic field induces an electric field. Faraday’s electromagnetic induction ring A capacitance of 1 coulomb per volt is called a farad (F)

5. 5 Joseph Henry (1797 – 1878) American scientist, Princeton University professor, and first Secretary of the Smithsonian Institution. Discovered self- induction Built the largest electromagnets of his day Unit of inductance, L, is the “Henry”

6. 6 Magnetic Fields and Circuits A current i through a coil produces a magnetic flux, , in webers, Wb. H = magnetic field intensity in A/m. B = magnetic flux density in Wb/m 2.  = magnetic permeability Ampere's Law: Magnetomotive force reluctance

7. 7 Magnetic Flux Magnetic flux, , in webers, Wb. Current entering "dots" produce fluxes that add.

8. 8 Faraday's Law Faraday's Law: induced voltage in coil 1 is Sign of induced voltage v 1 is such that the current i through an external resistor would be opposite to the current i 1 that produces the flux  1. Total flux linking coil 1: i Example of Lenz's law Symbol L of inductance from Lenz

9. 9 Mutual Inductance Faraday's Law In linear range, flux is proportional to current self-inductance mutual inductance

10. 10 Mutual Inductance Linear media Let

11. 11 Ideal Transformer - Voltage  The input AC voltage, v 1, produces a flux This changing flux through coil 2 induces a voltage, v 2 across coil 2

12. 12 Ideal Transformer - Current  The total mmf applied to core is Magnetomotive force, mmf For ideal transformer, the reluctance R is zero.

13. 13 Ideal Transformer - Impedance Input impedance Load impedance Turns ratio

14. 14 Ideal Transformer - Power Power delivered to primary Power delivered to load Power delivered to an ideal transformer by the source is transferred to the load.

15. 15 L.V.D.T. Linear Variable Differential Transformer http://www.rdpelectronics.com/displacement/lvdt/lvdt-principles.htm Position transducer http://www.efunda.com/DesignStandards/sensors/lvdt/lvdt_theory.cfm

16. 16 LVDT's are often used on clutch actuation and for monitoring brake disc wear LVDT's are also used for sensors in an automotive active suspension system