Low-Frequency Hysteresis Loop Experiment: Principles, Measurement Methods, and Applications

The low-frequency hysteresis loop experiment is a fundamental technique for characterizing the magnetic properties of ferromagnetic and soft magnetic materials by tracing the B-H curve under quasi-static or near power-frequency excitation. This article explains the measurement principles, standard test methods, sample requirements, key parameters such as coercivity, remanence, and hysteresis loss, and typical industrial and laboratory applications of low-frequency hysteresis loop testing.

Technical Overview

A hysteresis loop, or B-H curve, describes the relationship between the magnetic flux density B and the magnetizing force H in a ferromagnetic material as the applied field is cycled between positive and negative extremes. Because magnetization processes such as domain wall motion and domain rotation are irreversible, the flux density lags behind the field, producing a closed loop. The area enclosed by this loop represents the energy dissipated as heat per unit volume of material per magnetization cycle, expressed in joules per cubic meter.

In a low-frequency hysteresis loop experiment, the magnetizing field is swept slowly, typically from quasi-static rates of a few millihertz up to the power frequency range of 50/60 Hz or a few hundred hertz. Operating at low frequency suppresses dynamic eddy-current effects, so the measured loop approaches the intrinsic, quasi-static hysteresis loop of the material. This allows accurate determination of saturation flux density, remanence, coercive field, permeability, and the true hysteresis loss component, which is essential for material grading, core design, and quality control.

The classical experimental arrangement consists of a magnetizing circuit and a measuring circuit. In the ring-specimen configuration, a primary winding on a toroidal core is driven by a programmable current source to generate a controlled field H, while a secondary winding feeds an electronic integrator or digital fluxmeter whose output is proportional to the flux density B. The loop is displayed on an X-Y recorder, oscilloscope, or computer data-acquisition system. Standardized procedures for these measurements are defined in the IEC 60404 series, relevant ASTM standards such as ASTM A34/A34M and ASTM A596/A596M, and national standards including GB/T 3655 and GB/T 13789.

Testing Samples

Toroidal (Ring) Core Specimens

Ring cores are the preferred geometry for low-frequency hysteresis measurements because the magnetic path is closed and the demagnetizing field is essentially zero. Specimens are machined or wound from materials such as grain-oriented and non-oriented silicon steel, nickel-iron permalloy, cobalt-iron alloys, amorphous and nanocrystalline ribbons, soft ferrites, and iron powder or sendust compacts. To ensure uniform magnetization along the circumference, the ratio of mean diameter to radial thickness should generally be at least 8, as recommended in IEC 60404-6.

Strip and Sheet Specimens

Flat-rolled electrical steels are tested using standardized strip and sheet geometries, including 30 mm by 300 mm Epstein strips assembled in a 25 cm Epstein frame, and single-sheet specimens, typically 500 mm by 500 mm, tested in a single-sheet tester. These configurations replicate the magnetic path conditions found in transformer cores and rotating machine laminations and are specified in IEC 60404-2 and IEC 60404-3.

Specimen Conditioning

Before testing, specimens are usually stress-relief annealed to remove machining stresses that would distort the loop, electrically insulated where necessary, and demagnetized by applying a decaying alternating field or by thermal demagnetization. Proper conditioning is critical because residual stresses and remanent magnetization can significantly shift the measured coercivity and permeability values.

Testing Items

Low-frequency hysteresis loop experiments deliver a complete set of quasi-static magnetic characteristics, including:

• Saturation flux density Bs, in tesla, at the specified maximum field strength
• Remanence (residual flux density) Br, in tesla
• Coercive field strength (coercivity) Hc, in amperes per meter
• Initial permeability and maximum permeability of the commutation curve
• Hysteresis loop area and specific hysteresis loss Wh, in joules per kilogram per cycle
• Squareness ratio Br/Bs, indicating the rectangularity of the loop
• Normal magnetization curve obtained from loop tip points
• Temperature dependence of coercivity and remanence, when a thermal chamber is fitted

Testing Methods

Ring Specimen Method with Fluxmeter Integration

The specimen is wound with a primary coil of N1 turns and a secondary coil of N2 turns. A slow ramp, staircase waveform, or sinusoidal current drives the primary winding, and the field is calculated as H = N1·I / lm, where lm is the mean magnetic path length. The voltage induced in the secondary winding is integrated by a drift-compensated electronic fluxmeter to obtain the flux density B, with air-flux compensation applied via a mutual inductor or software correction. The specimen is first saturated and then cycled symmetrically between equal positive and negative field limits for several cycles until a stable, repeatable loop is recorded.

Oscilloscope-Based Display Method

In educational and routine laboratory settings, the secondary signal is passed through a simple RC integrator and applied to the vertical axis of an oscilloscope, while a voltage proportional to the primary current drives the horizontal axis. This produces a direct visual display of the hysteresis loop and is widely used in university physics experiments to demonstrate remanence, coercivity, saturation, and energy loss, although its quantitative accuracy is lower than that of fluxmeter-based systems.

Power-Frequency Methods: Epstein Frame and Single-Sheet Tester

For electrical steel at 50 or 60 Hz, the Epstein frame and single-sheet tester methods combine wattmeter loss measurement with the acquisition of B-H loops under controlled sinusoidal flux conditions. These standardized methods provide the specific total loss used for material grading and are the basis of product specifications in IEC 60404-2, IEC 60404-3, and corresponding GB standards.

Data Processing and Loss Separation

The hysteresis loss per cycle is obtained by numerically integrating the loop area, Wh = ∮H dB. By repeating measurements at several low frequencies and extrapolating the loss per cycle to zero frequency, the hysteresis component can be separated from eddy-current and anomalous losses. This separation validates whether the measured loop reflects the intrinsic quasi-static behavior of the material. Measurement uncertainty is typically within 2 to 3 percent for flux density and 3 to 5 percent for coercive field when standardized procedures are followed in accredited third-party laboratories.

Applications

Low-frequency hysteresis loop testing supports a broad range of engineering and scientific activities:

• Grading and incoming inspection of electrical steel for transformers, reactors, and motor laminations
• Design verification of toroidal and cut cores for inductors, current transformers, and magnetic amplifiers
• Characterization of amorphous and nanocrystalline ribbon cores for high-efficiency power electronics
• Material selection for magnetic shielding, relays, solenoid cores, and sensor elements
• Research and development of new soft magnetic alloys, ferrites, and powder composites
• Failure analysis and lifetime assessment, for example detecting degradation of coercivity after thermal aging or mechanical stress
• University teaching laboratories illustrating ferromagnetism, domain processes, and energy dissipation

FAQ

Why is the hysteresis loop measured at low frequency instead of at operating frequency?

Low-frequency excitation minimizes eddy-current and anomalous loss contributions, so the measured loop closely approximates the intrinsic quasi-static hysteresis loop. This isolates the fundamental hysteresis parameters, such as coercivity and remanence, and allows the hysteresis loss component to be separated from total loss through frequency extrapolation.

Which standards govern low-frequency hysteresis loop measurements?

Commonly referenced standards include IEC 60404-2 (Epstein frame), IEC 60404-3 (single-sheet tester), IEC 60404-4 (DC magnetic properties), IEC 60404-6 (ring specimens from 20 Hz to 200 kHz), ASTM A34/A34M, ASTM A596/A596M, ASTM A773/A773M, ASTM A804/A804M, and the Chinese national standards GB/T 3655 and GB/T 13789.

How is the loop area converted into a practical loss figure?

The loop area equals the energy dissipated per unit volume in one cycle, in J/m³. Dividing by the material density gives the specific loss per cycle in J/kg, and multiplying by the operating frequency gives the specific power loss in W/kg at that frequency.

What sample preparation is required before testing?

Ring specimens should meet the recommended ratio of mean diameter to radial thickness, be stress-relief annealed if machining was performed, and be thoroughly demagnetized with a decaying alternating field. Windings must be electrically insulated from the core, and the number of turns is selected to achieve the required maximum field strength without excessive winding resistance heating.

What accuracy and turnaround time can be expected?

With calibrated instrumentation and standardized procedures, typical uncertainties are 2 to 3 percent for flux density and 3 to 5 percent for coercive field. Routine single-condition measurements are usually completed within one to two working days, while multi-frequency or temperature-dependent characterization programs may require several additional days.