Sensor Magnet Maximum Energy Product (BH)max Testing and Determination

The maximum energy product (BH)max is the primary figure of merit for permanent magnets used in Hall effect, magnetoresistive, reed, and inductive sensors, directly determining air-gap flux density, signal amplitude, and sensor miniaturization potential. Accurate determination of (BH)max requires standardized measurement of the complete second-quadrant demagnetization curve using a hysteresisgraph, vibrating sample magnetometer, or pulsed field magnetometer. This article provides a comprehensive technical guide to sensor magnet maximum energy product testing, covering sample types, measured parameters, measurement methods, industry standards, and applications.

Technical Overview

The maximum energy product, denoted (BH)max, is the highest value of the product of magnetic flux density (B) and magnetic field strength (H) at any point along the second-quadrant demagnetization curve of a permanent magnet. Expressed in kJ/m³ in the SI system or MGOe in the CGS system (1 MGOe = 7.96 kJ/m³), it represents the maximum magnetic energy that a unit volume of magnet material can deliver to an external circuit, and it is universally accepted as the most important single performance index for permanent magnet materials.

In sensor systems, the (BH)max of the bias magnet or rotary target directly determines the flux density available in the working air gap. This in turn governs the output amplitude, sensitivity, switching threshold accuracy, temperature margin, and signal-to-noise ratio of Hall effect, anisotropic and giant magnetoresistive (AMR/GMR/TMR), inductive, reed, and Wiegand sensors. A higher energy product allows engineers to obtain identical gap flux from a substantially smaller magnet volume, which is decisive for miniaturized automotive, industrial, and consumer sensor packages. Because the operating point of a magnet in a real circuit is the intersection of the demagnetization curve with the load line defined by the permeance coefficient, reliable determination of (BH)max requires measurement of the entire demagnetization curve under controlled, standardized conditions, principally in accordance with IEC 60404-5, ASTM A977/A977M, and GB/T 3217.

Testing Samples

Sintered NdFeB Magnets

Neodymium-iron-boron is the dominant sensor magnet material, offering (BH)max values from approximately 200 to 450 kJ/m³ (25 to 56 MGOe) across commercial grades N35 through N55. Test samples are typically ground cylinders or rectangular blocks with parallel end faces and a uniform cross-section. High-coercivity grades such as 38UH or 42SH, which are widely specified for automotive sensors, require correspondingly stronger saturation fields during specimen preparation. Nickel-copper-nickel or epoxy protective coatings must be excluded from the effective magnetic length calculation.

Sintered SmCo Magnets

Samarium-cobalt magnets based on the SmCo5 or Sm2Co17 phases deliver (BH)max values of roughly 120 to 260 kJ/m³ combined with exceptional thermal stability at continuous operating temperatures of 250 to 350 °C. They are the preferred choice for engine-compartment position sensors, aerospace actuator feedback, and oil-level detection. Their low temperature coefficient of remanence, approximately -0.03 percent per °C, makes full-temperature demagnetization curve determination particularly valuable for these applications.

Bonded and Injection-Molded Magnets

Compression-bonded NdFeB magnets reach 60 to 90 kJ/m³, while injection-molded NdFeB and ferrite compounds deliver 25 to 50 kJ/m³. Because these composites are often formed into complex multipole rings for encoders, they are commonly characterized by open-circuit VSM measurement with demagnetization-factor correction. The intrinsic J-H loop is converted to the normal B-H curve, from which (BH)max is calculated for the magnetically effective direction.

Hard Ferrite Magnets

Anisotropic strontium and barium ferrites provide (BH)max values between approximately 10 and 40 kJ/m³, combining very low material cost with outstanding corrosion resistance. They are extensively used in reed switches, float-type liquid level sensors, water and gas flow meters, and general-purpose proximity sensors. The relatively high length-to-diameter ratios typical of ferrite designs must be respected when preparing closed-circuit permeameter specimens.

Alnico Magnets

Alnico alloys offer (BH)max values from 10 to 75 kJ/m³, characterized by high remanence but low coercivity. They must usually be magnetized while assembled in their magnetic circuit and are susceptible to partial demagnetization by external fields. Alnico remains in service for selected reed sensors and legacy instrumentation where a very low temperature coefficient of Br is required.

Testing Items

A complete determination of the energy product capability of a sensor magnet includes the following measured and derived quantities:

• Remanence (Br): the residual flux density at zero applied field, typically 200 to 1480 mT depending on material class
• Normal coercivity (Hcb): the demagnetizing field at which flux density B falls to zero
• Intrinsic coercivity (Hcj): the field at which intrinsic polarization J reaches zero, the key indicator of resistance to demagnetization
• Maximum energy product (BH)max: the peak of the B·H product along the demagnetization curve
• Knee point (Hk) and squareness ratio Hk/Hcj, which quantify the shape of the curve and the margin against irreversible loss
• Recoil permeability, needed for circuit modeling after partial demagnetization events
• Operating point data at specified permeance coefficients relevant to the sensor air gap
• Temperature coefficients alpha(Br) and beta(Hcj), and hot demagnetization curves at 80, 120, 150, or 180 °C

Testing Methods

Hysteresisgraph (Permeameter) Closed-Circuit Method

The hysteresisgraph is the reference method for (BH)max determination. The specimen is clamped between the pole shoes of an electromagnet yoke to form a closed magnetic circuit. Flux density B is measured by a search coil wound directly on the sample and connected to an integrating fluxmeter, while field strength H is measured by a calibrated Hall probe positioned adjacent to the specimen. The sample is first saturated by an impulse magnetizer at a field of at least three times Hcj, typically 3 T or more for NdFeB grades, and the demagnetizing field is then swept to record the complete second quadrant. The B·H product is computed point by point, and its maximum value is reported. Typical expanded uncertainties are 1 percent on Br, 2 percent on Hcj, and 2 to 3 percent on (BH)max, in accordance with IEC 60404-5 and ASTM A977.

Vibrating Sample Magnetometer (VSM) Method

The VSM is an open-circuit technique in which a small specimen vibrates within a uniform field produced by an electromagnet or superconducting magnet, with the magnetic moment calibrated against a certified nickel standard. The instrument records the intrinsic M-H loop, which is converted to the intrinsic J-H curve and then corrected for the self-demagnetizing field using the geometry-dependent demagnetization factor N to obtain the normal B-H curve and (BH)max. The method is preferred for small, irregular, bonded, coated, and thin-film specimens that cannot form a closed circuit. Because the accuracy of the demagnetization factor strongly influences the result, ellipsoidal or high aspect-ratio samples are recommended.

Pulsed Field Magnetometer (PFM) Method

In the PFM method, a capacitor bank discharged into a solenoid generates pulsed fields of 4 to 10 T, sufficient to saturate the highest-coercivity NdFeB sensor grades. Intrinsic polarization is captured by coaxial pickup coils, and the full loop is acquired within tens of milliseconds. The technique is ideal for high-throughput production quality control. For electrically conductive sintered specimens, eddy-current and dynamic field corrections must be applied, and periodic cross-validation against a hysteresisgraph is recommended.

Sample Preparation and Test Conditions

• Grind end faces parallel within 0.05 mm and verify a uniform cross-section along the magnetic length
• Measure all dimensions to within 0.1 percent, since volume and area errors propagate directly into reported flux values
• Fully demagnetize the specimen by AC field decay or thermal demagnetization before testing
• Saturate with a pulsed field of at least three times Hcj, with a minimum of 2.5 to 3 T for NdFeB materials
• Condition and test at 23 ± 5 °C with documented ambient humidity for moisture-sensitive ferrites
• Perform a minimum of three valid runs and report the mean together with the observed deviation

Applications

Certified (BH)max data for sensor magnets underpins design, simulation, and incoming quality control across a wide range of industries:

• Automotive wheel speed sensors for ABS and ESC, crankshaft and camshaft position sensors, transmission speed and gear position sensors, and brake pedal travel sensors
• Linear and rotary magnetic encoders using multipole bonded NdFeB or ferrite rings
• Reed-switch security contacts and float-type liquid level sensors in fuel tanks, brake reservoirs, and appliance water tanks
• Water, gas, and heat meters employing Wiegand wires or inductive pickup with ferrite bias magnets
• Current sensors, brushless DC motor commutation sensors, and seat or door position detection modules
• Consumer electronics, including lid-closure detection in laptops and true wireless earbuds, and door and window sensors for smart home systems

Verified demagnetization curves and energy product values are routinely imported into finite-element magnetic simulations to predict sensor output, air-gap tolerance, and demagnetization immunity, and they serve as the acceptance basis between magnet suppliers and sensor manufacturers.

FAQ

Question: Why is the maximum energy product so important for sensor magnet selection?

Answer: The (BH)max value fixes the maximum flux density a given magnet volume can deliver into an air gap. A higher energy product directly increases sensor signal amplitude and signal-to-noise ratio, or allows the magnet to be made smaller and cheaper while preserving performance, which is essential for miniaturized sensor packages.

Question: What is the difference between Hcb and Hcj?

Answer: Hcb is the field at which the normal flux density B reaches zero on the demagnetization curve, while Hcj is the field at which the intrinsic polarization J falls to zero. Hcj measures the material's true resistance to irreversible demagnetization and is the critical parameter when the magnet is exposed to counterfields from coils, adjacent magnets, or high operating temperatures.

Question: What measurement accuracy can be expected for (BH)max?

Answer: A properly calibrated hysteresisgraph typically achieves expanded uncertainties of 1 percent on Br, 2 percent on Hcj, and 2 to 3 percent on (BH)max. VSM results on small or bonded samples carry additional geometry-related uncertainty from the demagnetization factor correction.

Question: Can a bonded multipole encoder ring be tested directly?

Answer: A complete multipole ring cannot be clamped into a closed magnetic circuit. Standard practice is to measure material coupons by VSM or hysteresisgraph to establish the (BH)max of the compound, and then to verify the finished ring by scanning surface flux density pole by pole with a calibrated Hall probe.

Question: How does temperature influence the measured energy product?

Answer: (BH)max decreases with temperature because Br declines as temperature rises. For NdFeB the temperature coefficient of Br is approximately -0.11 percent per °C, so hot-curve testing at the sensor's maximum operating temperature is mandatory for automotive grades. SmCo and Alnico exhibit substantially lower coefficients and retain more of their energy product at elevated temperatures.

Question: How are MGOe and kJ/m³ converted?

Answer: One MGOe equals 7.96 kJ/m³. For example, a grade N42 magnet with (BH)max of 42 MGOe corresponds to approximately 334 kJ/m³.