0195136047.pdf

476 MAGNETIC CIRCUITS AND TRANSFORMERS

Flux φ Core

N-turn coil

Current I

(a)

Figure 11.2.1Simple magnetic circuit. (a) Mmf and

flux.(b)Leakage flux and fringing flux.

Core flux

I

(b)

Leakage

flux

Fringing flux

Air gap

lg

φl

of power). The current source is commonly a coil ofNturns, carrying a currentIknown as the

exciting current; the mmf is then said to beNIAt.

Figure 11.2.1(a) shows, schematically, a simple magnetic circuit with an mmf
(=NI)

and magnetic fluxφ. Note that theright-hand rulegives the direction of flux for the chosen

direction of current. The concept of a magnetic circuit is useful in estimating the mmf (excitation

ampere-turns) needed for simple electromagnetic structures, or in finding approximate flux and

flux densities produced by coils wound on ferromagnetic cores. Magnetic circuit analysis follows

the procedures that are used for simple dc electric circuit analysis.

Calculations of excitation are usually based onAmpere’s law, given by

∮

H ̄dl=ampere-turns enclosed (11.2.1)

whereH(|H ̄|=B/μ)is the magnetic field intensity along the path of the flux. If the magnetic

field strength is approximately constant(H =HC)along the closed flux path, andlCis the

average (mean) length of the magnetic path in the core, Equation (11.2.1) can be simplified as


=NI=HClC (11.2.2)

Analogous to Ohm’s law for dc electric circuits, we have this relation for magnetic circuits,

fluxφ=

mmf


reluctance

=

l/μA

(11.2.3)

whereμis the permeability,Ais the cross-sectional area perpendicular to the direction ofl, and

lstands for the corresponding portion of the length of the magnetic circuit along the flux path.

Based on the analogy between magnetic circuits and dc resistive circuits, Table 11.2.1 summarizes

the corresponding quantities. Further, the laws of resistances in series and parallel also hold for

reluctances.