Name: b-h curves and inductor core limits
Uploaded: 2023-04-30T06:42:59.000Z
Duration: 10 min 41 s
Channel: JoVE

K12 Standards

Arizona Science Standards

High School

Physical Science

HS+Phy.P2

HS+Phy.P2U1.1

Characterization of Magnetic Components

1. Relative Permeability Identification
Follow the procedure to find the relative permeability of the small inductor (yellow/white ferrite core). The core dimensions are shown in Fig. 2, and the number of turns is N=75.
<ol>
	<li>Using a LCR meter, measure the inductance of the inductor at both 120 Hz and 1000 Hz.</li>
	<li>Build the circuit in Fig. 1 on a proto-board, but keep the function generator output disconnected from the proto-board.</li>
	<li>Check a differential voltage probe and a current probe for no offsets with the current probe connected on channel 1 and the voltage probe connected on channel 2.</li>
	<li>Note the scaling factors for the differential probe on the probe itself and on the scope. Set the differential probe to 1/20 for a better resolution.</li>
	<li>Set the current probe to 100 mV/A on the probe itself and 1X on the scope. Remember that these scaling factors need to be used when performing calculations.</li>
	<li>Set the function generator output (50 Ω BNC output connector) at 10 V peak and 1000 Hz sinusoidal waveform. Observe the waveform using the differential voltage probe.</li>
	<li>Leave the function generator on even when disconnected, but avoid shorting its terminals. Turning the function generator off resets many settings.</li>
	<li>Connect the current and voltage probes to measure vC and i.</li>
	<li>Check that the circuit is as desired and that all connections are maintained.</li>
	<li>Connect the function generator to the circuit.</li>
	<li>Take a screenshot of the measured current and voltage with at least three periods shown in addition to the peak or RMS values of the measured signals.</li>
	<li>From the "Display" menu on the scope, change the display format from "YT" to "XY".</li>
	<li>Observe the B-H curve by adjusting the channel 1 and channel 2 vertical adjustment knobs until the curve fits the scope screen.</li>
	<li>In order to see a steadier curve, use the "persist" option from the display menu at a setting of 1 or 2 s.</li>
	<li>Take a screenshot of the measured B-H curve.</li>
	<li>Adjust the function generator frequency to 120 Hz and retake the B-H curve screenshot after adjusting the curve settings as needed.</li>
	<li>Disconnect the function generator and remove the inductor. Keep the rest of the circuit intact.</li>
</ol>
<img alt="Annular ring diagram with dimensions: D&lt;sub&gt;in&lt;/sub&gt;=0.85cm, D&lt;sub&gt;out&lt;/sub&gt;=1.85cm, h=0.5cm." src="/files/ftp_upload/10164/10164fig2.jpg" data-altupdatedat="1761830439000" data-alt="Figure 2"> 
Figure 2: Dimensions of the smaller inductor core. <a href="//cloudfront.jove.com/files/ftp_upload/10164/10164fig2large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
2. Identifying the Number of Turns
The larger black inductor (Bourns 1140-472K-RC) has an unknown number of turns. To simplify calculations, assume the core to be an all-air-core solenoid with a radius of 1.5 cm and length of 2.5 cm. If this assumption is not taken, the geometry of the core will have to be considered and will complicate calculations. However, this assumption is still reasonable given that with a solenoid, flux has to pass through air on both sides of the device and air is the dominant flux path medium.
<ol>
	<li>Using the LCR meter, measure the inductance of the provided inductor at both 120 Hz and 1000 Hz.</li>
	<li>Place the inductor in the circuit shown in Fig. 1 , which should still be intact from the previous part of the experiment.</li>
	<li>Check a differential voltage probe and a current probe for no offsets with the current probe connected on channel 1 and the voltage probe connected on channel 2.</li>
	<li>Note the scaling factors for the differential probe on the probe itself and on the scope. Set the differential probe to 1/20 for a better resolution.</li>
	<li>Set the current probe to 100 mV/A on the probe itself and 1X on the scope. Remember that these scaling factors need to be used when doing calculations utilizing any measurements or data captures for further analysis.</li>
	<li>Set the function generator output (50 Ω BNC output connector) at 10 V peak and 1000 Hz sinusoidal waveform. Observe the waveform using the differential voltage probe.</li>
	<li>Leave the function generator on even when disconnected, but avoid shorting its terminals. Turning the function generator off resets many settings.</li>
	<li>Connect the current and voltage probes to measure vC and i.</li>
	<li>Check the circuit, and make sure that connections are as desired.</li>
	<li>Connect the function generator to the circuit.</li>
	<li>Take a screenshot of the measured current and voltage with at least three periods shown in addition to the peak or RMS values of the measured signals.</li>
	<li>From the "display" menu on the scope, change the display format from "YT" to "XY".</li>
	<li>Observe the B-H curve by adjusting the channel 1 and channel 2 vertical adjustment knobs until the curve fits the scope screen.</li>
	<li>In order to see a steadier curve, use the "persist" option from the display menu at a setting of 1 or 2 s.</li>
	<li>Take a screenshot of the measured B-H curve.</li>
	<li>Adjust the function generator frequency to 120 Hz and retake the B-H curve screenshot after adjusting the curve settings as needed.</li>
	<li>Turn off the function generator and disassemble the circuit.</li>
</ol>
3. B-H Curve of a 60 Hz Transformer
The transformer used in this demonstration steps down 115 V RMS to 24 V RMS, but can only be used for B-H curve characterization in this experiment, thus only the 120 V RMS terminals are used. The transformer dimensions are shown in Fig. 3.
<ol>
	<li>Using the LCR meter, measure the inductance of the 115 V-side winding at 120 Hz (closer to the rated 60 Hz).</li>
	<li>Make sure the three-phase disconnect switch is in the off position.</li>
	<li>Connect the three-phase cable to the VARIAC.</li>
	<li>Build the circuit shown in Fig. 4. Have the transformer sit on the side of the proto-board. Use banana cables to connect AC1 and N from the VARIAC to the proto-board.</li>
	<li>Make sure the VARIAC is set at 0%.</li>
	<li>Check a differential voltage probe and a current probe for no offsets with the current probe connected on channel 1 and the voltage probe connected on channel 2.</li>
	<li>Note down the scaling factors for the differential probe on the probe itself and on the scope. Set the differential probe scaling to 1/200.</li>
	<li>Set the current probe to 100 mV/A on the probe itself and 1X on the scope. Remember that these scaling factors need to be used when doing calculations.</li>
	<li>Connect the current and voltage probes to measure vC and i.</li>
	<li>Check the circuit.</li>
	<li>Turn on the three-phase disconnect switch, and slowly adjust the VARIAC until 90% is reached.</li>
	<li>Take a screenshot of the measured current and voltage with at least three periods shown in addition to the peak or RMS values of the measured signals.</li>
	<li>From the "Display" menu on the scope, change the display format from "YT" to "XY".</li>
	<li>Observe the B-H curve by adjusting the channel 1 and channel 2 vertical adjustment knobs until the curve fits the scope screen.</li>
	<li>In order to see a steadier curve, use the "persist" option from the display menu at a setting of 1 or 2 s.</li>
	<li>Take a screenshot of the measured B-H curve.</li>
	<li>Restore the VARIAC to 0%, turn the disconnect switch off, and disassemble the circuit.</li>
</ol>
<img alt="Rectangular prism diagram with dimensions X=6.3cm, Y=5.6cm, Z=3.1cm, W=1.25cm labeled." src="/files/ftp_upload/10164/10164fig3.jpg" data-altupdatedat="1761830439000" data-alt="Figure 3"> 
Figure 3: Dimensions of the transformer core. <a href="//cloudfront.jove.com/files/ftp_upload/10164/10164fig3large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Three-phase static equilibrium circuit diagram with VARIAC, resistor, capacitor, AC analysis setup." src="/files/ftp_upload/10164/10164fig4.jpg" data-altupdatedat="1761830439000" data-alt="Figure 4"> 
Figure 4: Test circuit to determine the B-H curve of a 60 Hz transformer. <a href="//cloudfront.jove.com/files/ftp_upload/10164/10164fig4large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>

Even though inductors and other electro-magnetic devices (e.g., transformers) are very common in many electrical, electronic, and mechanical systems, buying inductors for a specific application is not trivial. Even when an inductor is bought, datasheet information may still have ambiguities on the actual material, number of turns, and other details. The tests in this experiment are especially useful for engineers and technicians who plan to build their own inductors or characterize off-the-shelf ones. This is co...

characterization of magnetic components

Source: Ali Bazzi, Department of Electrical Engineering, University of Connecticut, Storrs, CT.
The objective of this experiment is to achieve hands-on experience with different magnetic components from design and material perspectives. This experiment covers B-H curves of magnetic material and inductor design through identifying unknown design factors. The B-H curve of a magnetic element, such as an inductor or transformer, is a characteristic of the magnetic material forming the core around which windings are wrapped. This characteristic provides information about the magnetic flux density that the core can handle with respect to the current flowing in the windings. It also provides information about limits before the core is magnetically saturated, i.e. when pushing more current through the coil leads to no further magnetic flux flow.

In order to find the relative permeability of the core material, two approaches can be used. The first approach is to use an LCR meter, where the inductance (L) of a coil made with a known number of turns (N) is measured, and then the relative permeability can be calculated as follows:
Reluctance of the core: <img alt="Mathematical formula for static equilibrium: ℜ = N²/L." src="/files/ftp_upload/10164/10164eq7...

Source: Ali Bazzi, Department of Electrical Engineering, University of Connecticut, Storrs, CT.
The objective of this experiment is to achieve hands-on ...

Magnetic elements, such as inductors or transformers, have characteristic properties that are dependent on the magnetic material forming the core inside of the coil. When current flows in an inductor or transformer coil, it creates a magnetic field. The ability of the core material to hold the magnetic field, called its permeability, determines the strength of the field, called its magnetizing force. The magnetizing force then produces magnetic flux in the inductor core. In inductors and transformer, the relationship between magnetizing force and flux density is defined as the magnetic flux through a cross-sectional area and can be analyzed using a B-H curve. The B-H curve describes the core material and identifies its magnetic saturation limit. This occurs when additional current through the windings no longer increases magnetic flux. This video illustrates the measurement of BH curves for inductors and transformers and the characterization of the core material and inductor windings.A B-H curve shows the relationship between magnetic flux density, B, and magnetic field strength, H. Initially, as the magnetic field strength is increased, the flux density also increases to a certain maximum value. After this point, any increase in magnetic field strength results in no significant increase in magnetic flux density and the material is considered saturated. Real magnetic materials exhibit hysteresis as the material is alternately magnetized in the positive and negative directions. This implies that as the magnetic field strength is reduced back to zero, some residual magnetism remains. The area inside the B-H curve is proportional to the energy loss as the material is magnetized in the positive and negative directions. A material with lower hysteresis loss, such as steel, is commonly used in transformer cores due to this property. The B-H curve can also be used to describe a material's permeability, calculated as the ratio of magnetic flux density to magnetic field strength. It is often related to the permeability of free space and thus termed relative permeability. Materials with very low magnetic susceptibility, like wood, have a low relative permeability. Where as materials with high magnetic susceptibility, like iron, have a high relative permeability. In order to create a B-H curve, the flux density, B, must first be determined. For this, the flux rate of change is measured, which is relative to the voltage across the coil using Faraday's Law. This can be identified using a simple RC circuit in parallel with the coil. For more detailed information on these calculations, please refer to the text protocol. The magnetic field strength, or H, can be found using Ampere's Law and measurable variables, the current in the coil, the number of winding turns, and the average length of the core. The B-H curve of a material can be estimated from measurements of current and the time integral of voltage across the element. When the number of turns and dimensions of the elements are also known, these can be scaled to actual quantities. Now, let's demonstrate how to measure relative permeability and calculate B-H curves.In these experiments, three magnetic components are measured, a small inductor with a ferrite core, a larger black inductor with an unknown number of turns, and a 60 Hz transformer. Start with the small inductor with dimensions as shown, and a winding turns number of 75. First, measure the inductor's inductance at 120 and 1,000 Hz using an LCR meter. Second, build the circuit as shown, keeping the function generator output at 50 ohm and the BNC connector cable disconnected. Next, connect the differential voltage and current probes and verify that there are no offsets. Set the differential probe to 120th for better resolution. Finally, set the current probe to 100 millivolts per amp on the probe and 1x on the scope. And note these scaling factors for later calculations. Set the function generator output to a 1,000 Hz sine soto wave form with a 10-volt peak. Measure VC and I, connect the function generator and verify that all circuit connections are as shown. Then, record the measured current and voltage. Finally, change the oscilloscope display format from yt to xy to display the B-H curve. Adjust the channel one and channel two vertical adjustment knobs until the curve fits the scope screen. Next, stabilize the curve by setting the persist option for the display. And then, take a screenshot of the curve. Last, adjust the function generator frequency to 120 Hz and retake the B-H curve screenshot after adjusting the curve settings as needed. Finally, disconnect the function generator and remove the inductor. Keep the rest of the circuit intact.To determine the number of turns for the larger inductor, let's first measure its B-H curve. In order to simplify calculations, assume the core is an all-air core. First, measure the inductor's inductance at 120 and 1,000 Hz using the LCR meter. Then, place the inductor in the RC circuit. Measure the B-H curve for the larger inductor using the same procedure described for the small inductor. Observe and record the measured current and voltage. Display the B-H curve. Adjust the function generator frequency to 120 Hz and adjust the curve settings as needed.Single phase transformers consist of two windings coupled by a magnetic core. Here, the B-H curve for 60 Hz transformer is measured. Using the LCR meter, measure the inductance of the 115-volt side winding at 120 Hz. Then, assemble the circuit by connecting AC1 and N from the variac to the transformer primary side through the protoboard circuit using banana cables. Adjust the scaling factors and function generator parameters as previously described. With the variac at 90 percent, measure the current and voltage. Then, display and record the B-H curve.If the number of turns for the coil, average core length, and cross-sectional area are known, then inductance of the coil is measured directly, and the relative permeability can be calculated. Alternatively, a measured B-H curve can be used to determine relative permeability of an element and then calculate the number of turns in the coil. In the linear region of the B-H curve, the relative permeability can be found from the slope. Using relative permeability, and given that the inductance and core dimensions are known, the number of turns can be easily calculated using the following relationship.Inductors and other electromagnetic devices, like transformers, are common in many electrical, electronic, and mechanical systems. The power grid provides electricity to consumers by distributing high voltage electricity over long distances via transmission lines. High voltages are required over long distances to compensate for energy losses. Transformers are used along power lines to step down the higher transmission voltages to the lower levels needed at distribution stations and for end user supply. Transformers transfer energy through electromagnetic induction, enabling the controlled step down of AC voltages. They are commonly designed with steel cores because of steel's high magnetic saturation point. The stator magnet induces a rotating magnetic field in the rotor causing the rotor to revolve. Effectively, the stator is the primary winding of a transformer, and the squirrel cage, the secondary winding. AC induction motors are used in a large variety of applications. The motor consists of an outer stationary wound magnet, and the inner ferromagnetic core of the rotor. Typically, a cylindrical arrangement of conductive bars forming the squirrel cage.You've just watched JoVE's Introduction to the Characterization of Magnetic Components. You should now understand how to measure B-H curves of inductors and transformers, while identifying unknown design factors, such as relative permeability and turn number. Thanks for watching.

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JoVE Science Education

Engineering

Electrical Engineering

b-h curves and inductor core limits

Magnetic components such as inductors and transformers depend on the core material around their windings. In this experiment, students get hands-on experience with these parts from both a design view and a material view.

The work focuses on B-H curves, which show the magnetic behavior of a material. A B-H curve describes the magnetic flux density the core can support as current flows through the windings. It also helps show the limit before magnetic saturation occurs.

Magnetic saturation means that adding more current to the coil no longer produces more magnetic flux in the core. The experiment also includes inductor design. Students identify unknown design factors by studying the magnetic component and its material response.

B-H Curves and Inductor Core Limits

electrical safety precautions and basic equipment

electrical-safety-precautions-and-basic-equipment

Safe Handling of High-Voltage Lab Power

Safe handling of high-voltage lab power is essential in electric machine and power electronics experiments. These labs involve electrical currents, voltages, power, and energy that require extreme care. The systems used in this work can include three-phase AC voltage at 208 V, 230 V, or 480 V. They may also use up to 250 V DC and currents that can reach 10 A. These levels can be dangerous if handled without proper attention. Electrocution can happen when electricity passes through the body.

Magnetic components such as inductors and transformers depend on the core material around their windings. In this experiment, students get hands-on experience with these parts from both a design view and a material view. The work focuses on B-H curves, which show the magnetic behavior of a material. A B-H curve describes the magnetic flux density the core can support as current flows through the windings. It also helps show the limit before magnetic saturation occurs. Magnetic saturation...

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Stepping Up DC Voltage with Boost Converters

DC voltage can be increased with a boost converter. This step-up circuit is useful in many applications where a DC source must be raised without first converting it to AC, using a transformer, and then rectifying the transformer output. A boost converter uses an inductor as an energy storage device. The inductor supports the output with extra energy in addition to the DC input source. That added energy raises the output voltage. This experiment studies several characteristics of a boost...

dc/dc buck converter

Buck Converter Step-Down DC Voltage

A DC/DC buck converter steps down DC voltage in an efficient, regulated way. Unlike transformers, which easily raise or lower AC voltage and current, DC systems need switching power converters to change voltage levels. The buck converter works by chopping the input DC voltage with a series input switch. An L-C low-pass filter then smooths the chopped signal and extracts the average output voltage. A diode gives the inductor current a path when the switch is off during part of the switching...

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Flyback Converter Voltage Step-Up and Step-Down

A flyback converter is a buck-boost converter that can both step voltage up and step it down. It also provides electrical isolation between the input and the output by using a coupled inductor, or flyback transformer. The coupled inductor acts like a transformer with a turns ratio, but it also stores energy through the air gap. This setup gives the converter both voltage step-up and step-down capability. In the experiment, the converter is studied in open-loop operation with a manually set...

single phase transformers

Single Phase Transformer Testing

Single-phase transformers step up or step down AC voltage in electric power systems. They are stationary electric machines with primary and secondary coils, also called windings. The primary winding receives the applied voltage, and the secondary winding delivers the changed voltage. Inside the transformer, current in one winding creates magnetic flux in the core. This flux links the two windings and transfers energy between them. With AC current, the changing flux induces voltage in the...

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AC to DC Conversion with Rectifiers

Rectifiers convert AC power into DC power for electronic circuits. A DC power supply provides unidirectional voltage and current. Batteries can do this, but they are limited by lifetime and cost. Using a rectifier is another way to turn AC line power into DC power. A rectifier is a device that lets current pass in one direction and blocks it in the other. It works after a forward voltage threshold is reached. Rectifiers may use a diode, a silicon controlled rectifier, or other silicon P-N...

thyristor rectifier

Controlling SCR Half-Wave Rectification

Thyristors, also called silicon controlled rectifiers (SCRs), are used to control current in a rectifier circuit. Like diodes, they let current pass from the anode to the cathode and block current in the opposite direction. Unlike a diode, a thyristor can be turned on with a gate terminal that receives a small current pulse. A thyristor is a four-layer device with alternating n-type and p-type layers. These layers form a PNPN structure with three junctions. The device has three terminals. The...

single phase inverter

DC to AC Conversion with Half-Bridge Inverters

DC to AC conversion is the main idea behind a power inverter. DC power flows in one direction, while AC current changes direction at about 50-60 Hz. Many electronic devices are designed to run on AC power, so a DC source must be inverted before it can be used with them. An inverter makes this change through switching action. The switches repeatedly flip the polarity of the input DC source at the output, or load side, for part of a switching period. A typical power inverter needs a stable DC...

dc motors

DC Motors and Generator Action

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Three-Phase Motor Equivalent Circuit Tests

Three-phase induction motor testing can be used to find equivalent circuit parameters. The experiment uses the per-phase equivalent circuit to model the motor. This model keeps the important behavior of the original system and makes calculations easier. The procedure uses tests similar to those used in transformer characterization. These measurements help estimate the motor's circuit values from its electrical response. The experiment also aims to operate the motor in the linear torque-speed...

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Variable Frequency Drive Speed Control

Variable frequency drives, or VFDs, control the speed of AC induction motors. They are a type of adjustable speed drive and are becoming standard equipment for powering most AC induction motors. In industrial and automation settings, VFDs can provide strong control of motor speed, torque, or position. This experiment focuses on speed control with open-loop operation. It uses constant voltage-to-frequency ratio control, also called V/f control. The motor usually operates at a rated stator flux,...

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Grid Connection of AC Synchronous Generators

AC synchronous generators are a major source of electrical power worldwide. They are three-phase, wound-rotor machines that are used in many power plants. These generators need a prime mover and an exciter to produce power. A prime mover is the device that spins the generator, often a turbine driven by fluid. That fluid can come from water flowing from a dam through a long nozzle or from steam made by burning coal. Most power plants use synchronous generators, including coal, nuclear, natural...

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Three-Phase Synchronous Motor Starting and V-Curves

Three-phase synchronous motors and generators are important AC machines. Wound-rotor synchronous motors are less common than permanent magnet rotor synchronous motors because the rotor field uses brushes. Synchronous generators are much more common. They are used in most existing power plants because they provide excellent frequency and voltage regulation. A synchronous motor runs at the same speed as the stator magnetic field. This gives it almost 0% speed regulation, so the rotor speed stays...

electrical engineering

This collection starts with an electrical safety video that introduces the best practices for commonly used equipment in an electrical laboratory. Subsequent videos introduce elements such as inductors, transformers, convertors, rectifiers, and inverters.

Explore B-H curves, magnetic saturation, and inductor design as students study how core materials affect inductors and transformers in this hands-on experiment.

B-H Curves and Inductor Core Limits | JoVE K12

Ali Bazzi

Overview

Principles of Magnetic Component Characterization

Measuring Relative Permeability

Identifying the Number of Turns

B-H Curve of a 60 Hz Transformer

Representative Results

Applications

Summary

Electrical Safety Precautions and Basic Equipment

Source: Ali Bazzi, Department of Electrical Engineering, University of Connecticut, Storrs, CT.
Electric machines and power electronics experiments ...

Magnetic Fields

Source: Yong P. Chen, PhD, Department of Physics &#38; Astronomy, College of Science, Purdue University, West Lafayette, IN
Magnetic fields can be ...

A moving charge or a current creates a magnetic field in the surrounding space, in addition to its electric field. The magnetic field exerts a force on ...

Solenoids

A solenoid is a conducting wire coated with an insulating material, wound tightly in the form of a helical coil. The magnetic field for a solenoid is the ...

Induction

An emf is induced when the magnetic field in a coil is changed by pushing a bar magnet into or out of the coil. emfs of opposite signs are produced by ...

Faraday's Law

Faraday&#39;s law state that the induced emf is the negative change in the magnetic flux per unit of time. Any change in the magnetic field or change in ...

Lenz's Law

The direction in which the induced emf drives the current around a wire loop can be found through the negative sign. However, it is usually easier to ...

Electric Generator: Alternator

Electric generators induce an emf by rotating a coil in a magnetic field. A simple alternator is an AC generator that creates electrical energy that ...

Magnetic Field due to Moving Charges

A stationary charge creates and interacts with the electric field, while a moving charge creates a magnetic field.
Consider a point charge moving with a ...

Magnetic Field of a Solenoid

A solenoid is a conducting wire coated with an insulating material, wound tightly in the form of a helical coil. The magnetic field due to a solenoid is ...

Magnetic Flux

The magnetic flux measures the number of magnetic field lines passing through a given surface area. The SI unit for magnetic flux is the weber (Wb). ...

Magnetic Force

In addition to the electric forces between electric charges, moving electric charges exert magnetic forces on each other. A magnetic field is created by a ...

DC Generator

An alternator converts mechanical energy into electrical energy that varies sinusoidally, resulting in AC current. Meanwhile, a DC generator converts ...

Plan and carry out investigations to design, build, and refine a device that works within given constraints to demonstrate that an electric current can produce a magnetic field and that a changing magnetic field can produce an electric current.

B-H Curves and Inductor Core Limits

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