AC Excitation in Magnetic Circuits

Definition

AC excitation in a magnetic circuit is the process of energizing a magnetic core or magnetic path with an alternating current so that the magnetizing force and magnetic flux vary periodically with time, producing alternating magnetic flux and associated electromagnetic effects such as induced emf, hysteresis loss, and eddy current loss.

In simple terms, when an AC supply is applied to a coil wound on a magnetic core, the current changes continuously, causing the magnetizing force $H$ and flux density $B$ to alternate. This alternating flux is used for energy transfer, voltage transformation, or mechanical actuation in many electrical devices.

Main Content

1. Alternating Magnetizing Force and Flux

• When an alternating voltage is applied to a coil on a magnetic core, the current in the coil is alternating in nature, so the magnetizing force $H$ produced by the coil also alternates.
• The alternating magnetizing force creates an alternating magnetic flux $\phi$ in the core. As the current reverses direction every half cycle, the flux also reverses direction, producing a periodic magnetic field.

In AC excitation, the relationship between current and flux is not as straightforward as in a purely resistive circuit because the magnetic core has inductive properties. The flux often lags behind the exciting current due to energy storage in the magnetic field. The flux waveform is generally sinusoidal if the supply voltage is sinusoidal and the core is not heavily saturated. From Faraday’s law, the induced emf in the coil is proportional to the rate of change of flux:

$$e = -N \frac{d\phi}{dt}$$

where $N$ is the number of turns.

For example, in a transformer, the AC applied to the primary winding creates a time-varying flux in the iron core, which induces emf in the secondary winding. This is the fundamental principle of AC magnetic excitation in practical equipment.

2. Magnetic Characteristics under AC Conditions

• Under AC excitation, the magnetic circuit exhibits non-linear behavior because the B-H relationship of magnetic materials is not perfectly linear.
• The core undergoes repeated magnetization and demagnetization, resulting in a hysteresis loop and causing energy losses in each cycle.

The magnetic permeability of the core is not constant; it changes with flux density, frequency, and temperature. In AC operation, the flux density alternates through positive and negative values, and the magnetization process is repeatedly traced along the hysteresis loop. The area enclosed by the hysteresis loop represents the energy lost as heat per cycle per unit volume of the core material.

Also, the presence of alternating flux causes eddy currents to circulate in the conductive core material. These currents generate I²R losses and increase heating. To reduce these losses, laminated silicon steel cores are often used, because thin laminations increase the resistance to eddy current flow.

A practical consequence is that the current drawn by the exciting coil is not purely useful magnetizing current. It consists of:

• magnetizing current, which establishes flux, and
• core-loss component, which supplies the energy lost in the core.

Thus, AC excitation requires special core design considerations compared with DC excitation.

3. Flux, Induced EMF, and Losses in AC Magnetic Circuits

• The alternating flux produced in an AC magnetic circuit induces emf in the same coil or in neighboring coils according to Faraday’s law.
• This induced emf opposes the applied voltage and is the reason why an inductor or transformer limits current and transfers energy magnetically.

In an ideal magnetic circuit with AC excitation, if the flux varies sinusoidally:

$$\phi = \phi_m \sin \omega t$$

then the induced emf is:

$$e = N\omega \phi_m \cos \omega t$$

and the rms value becomes:

$$E = 4.44 f N \phi_m$$

where:

• $E$ = rms induced emf,
• $f$ = frequency,
• $N$ = number of turns,
• $\phi_m$ = maximum flux.

This equation is extremely important in transformer design. It shows that for a given voltage and frequency, the maximum flux is fixed. If frequency decreases while voltage remains constant, flux increases and may drive the core into saturation.

The main losses in AC-excited magnetic circuits are:

Hysteresis loss

• due to repeated magnetization of the core.

Eddy current loss

• due to induced circulating currents in the core.

Copper loss

• due to resistance of the winding carrying exciting current.

These losses reduce efficiency and must be minimized by proper material selection, lamination, and design. In high-frequency applications, ferrites are often used because they have high electrical resistance and low eddy current loss.

Working / Process

1. Application of AC supply to the coil

• An alternating voltage is applied to a winding wound around a magnetic core.
• This causes an alternating current to flow, depending on the winding impedance and circuit conditions.
• The current creates a time-varying magnetizing force in the core.

2. Establishment of alternating flux in the magnetic path

• The magnetizing force produces magnetic flux in the core material.
• The flux increases and decreases continuously, reversing direction every half cycle of the AC supply.
• This flux links the turns of the coil and any other coupled winding.

3. Induction of emf and energy transfer

• The changing flux induces emf in the same coil and in nearby coils according to Faraday’s law.
• The induced emf opposes the applied voltage, controlling current and enabling magnetic energy storage and transfer.
• During operation, losses such as hysteresis and eddy currents occur, converting part of the input energy into heat.

Advantages / Applications

Efficient voltage transformation in transformers

AC excitation is the basis of transformer operation, allowing voltage to be stepped up or stepped down efficiently in power systems.

Energy transfer without electrical contact

Magnetic coupling under AC excitation enables isolated transfer of power and signals, which is useful in inductors, transformers, and wireless energy systems.

Use in many electromechanical devices

AC-excited magnetic circuits are used in relays, solenoids, AC machines, chokes, electromagnets, and inductive sensors, making them essential in industrial and domestic equipment.

Summary

• AC excitation produces alternating magnetic flux in a magnetic circuit.
• The changing flux induces emf and causes core losses such as hysteresis and eddy current loss.
• The behavior of the magnetic circuit depends strongly on frequency, core material, and applied voltage.
• AC magnetic circuits are fundamental to transformers, inductors, and many electrical devices.