How to Plot the B-H Curve for Ferrite Magnets: A Comprehensive Guide

1. Introduction to the B-H Curve

The B-H curve, also known as the magnetic hysteresis loop, is a graphical representation of the relationship between magnetic flux density (B) and magnetic field strength (H) in a ferromagnetic material. For ferrite magnets, this curve is crucial for understanding their magnetic properties, including remanence (Br), coercivity (Hc), intrinsic coercivity (Hci), and maximum energy product (BHmax). These parameters determine the magnet's performance in applications such as motors, generators, and loudspeakers.

2. Fundamental Concepts

Before plotting the B-H curve, it is essential to understand the key terms:

• Magnetic Flux Density (B): Measured in Tesla (T) or Gauss (G), it represents the magnetic field generated within the material.
• Magnetic Field Strength (H): Measured in Amperes per meter (A/m) or Oersteds (Oe), it is the external magnetic field applied to the material.
• Remanence (Br): The residual magnetic flux density remaining in the magnet after the external field is removed.
• Coercivity (Hc): The external field required to reduce the remanence to zero.
• Intrinsic Coercivity (Hci): A measure of the magnet's resistance to demagnetization, often higher than Hc.
• Maximum Energy Product (BHmax): The point on the demagnetization curve where the product of B and H (absolute values) is maximized, indicating the magnet's energy storage capacity.

3. Equipment Required

To plot the B-H curve, the following equipment is necessary:

• Permeameter: A device used to measure the magnetic properties of materials. It typically consists of a DC magnetizer, a fluxmeter, and a search coil.
• DC Magnetizer: Generates a strong, controlled magnetic field to magnetize the sample.
• Fluxmeter: Measures the magnetic flux linked with the search coil, which is proportional to B.
• Search Coil: A coil wound around the sample to detect changes in magnetic flux.
• Sample Preparation Tools: To machine the ferrite magnet into a precise shape (usually a cube or cylinder) for consistent measurements.
• Data Acquisition Software: To record and process the B and H values during the test.

4. Sample Preparation

The accuracy of the B-H curve depends on the sample's dimensions and alignment. Follow these steps:

1. Select the Material: Choose a ferrite magnet with known composition (e.g., SrO or BaO-Fe2O3 based).
2. Machine the Sample: Cut the magnet into a precise geometric shape (e.g., a cube or cylinder) to ensure uniform magnetic properties.
3. Align the Magnetization Direction: For anisotropic ferrite magnets, align the sample's easy axis of magnetization with the direction of the applied field. Isotropic magnets do not require alignment.
4. Clean the Sample: Remove any contaminants or burrs that may affect the magnetic measurements.

5. Experimental Setup

Set up the permeameter as follows:

1. Mount the Sample: Place the machined sample between the pole pieces of the DC magnetizer to create a closed magnetic circuit.
2. Wind the Search Coil: Wrap the search coil tightly around the sample, ensuring good electrical contact and minimal leakage flux.
3. Connect the Fluxmeter: Link the search coil to the fluxmeter to measure the induced voltage, which is proportional to the rate of change of magnetic flux (dB/dt).
4. Calibrate the System: Zero the fluxmeter and ensure the DC magnetizer is functioning correctly.

6. Data Collection Procedure

Follow these steps to collect B-H data:

1. Initial Demagnetization: Apply an alternating magnetic field to the sample to reduce its residual magnetism to near zero. This ensures a consistent starting point for the test.
2. Magnetization Cycle:
   • First Quadrant (Saturation): Gradually increase the DC magnetic field (H) from zero to a value sufficient to saturate the magnet (i.e., B no longer increases with H). Record B and H values at regular intervals.
   • Second Quadrant (Demagnetization): Decrease H from saturation to zero, then reverse the field to a negative value. Continue decreasing H until the magnet is fully demagnetized in the opposite direction. Record B and H values throughout this process.
   • Third and Fourth Quadrants (Reverse Saturation and Remagnetization): Repeat the process in the opposite direction to complete the hysteresis loop.
3. Data Recording: Use the data acquisition software to record B and H values continuously or at discrete intervals during the entire cycle.

7. Data Processing and Curve Plotting

After collecting the data, process it as follows:

1. Smooth the Data: Apply smoothing algorithms (e.g., moving average) to reduce noise in the B-H measurements.
2. Normalize the Data: Scale the B and H values to appropriate units (e.g., Tesla for B and A/m for H).
3. Plot the Hysteresis Loop: Use graphing software (e.g., Excel, MATLAB, or Origin) to plot B versus H. The resulting curve should resemble a closed loop, with the second quadrant representing the demagnetization curve.
4. Identify Key Parameters:
   • Remanence (Br): The B value at H = 0 in the second quadrant.
   • Coercivity (Hc): The H value at B = 0 on the negative H-axis.
   • Intrinsic Coercivity (Hci): The H value at the "knee" of the demagnetization curve, where B begins to drop rapidly.
   • Maximum Energy Product (BHmax): The point on the demagnetization curve where the product of B and H (absolute values) is maximized. This can be calculated as BHmax = |B| × |H| at the peak point.

8. Factors Affecting the B-H Curve

Several factors can influence the shape and position of the B-H curve for ferrite magnets:

• Material Composition: The type and ratio of oxides (e.g., SrO, BaO, Fe2O3) affect the magnet's coercivity and remanence.
• Temperature: Magnetic properties vary with temperature. For example, coercivity typically decreases with increasing temperature.
• Sample Geometry: The shape and size of the sample can influence the demagnetizing field, altering the B-H curve.
• Magnetization Direction: Anisotropic magnets exhibit different B-H curves depending on the alignment of the magnetization direction with the applied field.
• External Fields: Stray magnetic fields during testing can distort the B-H curve. Ensure a controlled environment to minimize interference.

9. Applications of the B-H Curve

The B-H curve is a valuable tool for engineers and scientists in various fields:

• Magnet Selection: Engineers use the B-H curve to select the appropriate magnet for a specific application based on its magnetic properties.
• Motor and Generator Design: The curve helps optimize the design of magnetic circuits to maximize efficiency and performance.
• Quality Control: Manufacturers use B-H curves to verify the consistency and quality of magnet batches.
• Research and Development: Scientists study the B-H curves of new materials to develop advanced magnetic systems with improved properties.

10. Advanced Considerations

For more sophisticated applications, consider the following:

• Temperature-Dependent B-H Curves: Plot B-H curves at different temperatures to understand how the magnet's properties change with thermal conditions.
• Dynamic B-H Curves: Measure the B-H response under alternating magnetic fields to study eddy current losses and hysteresis losses.
• Numerical Modeling: Use finite element analysis (FEA) software to simulate the B-H behavior of complex magnetic systems, validating results with experimental data.