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Experiment # 3

“AIR – CORE AND FERROMAGNETIC HYSTERISIS LOOP”

Introduction:

The objective of this experiment is to demonstrate the physical existence of “hysteresis loops” in both air and iron type cores (plungers). We will use a single phase transformer to obtain the hysteresis loop developed by the iron core as well as the loop developed by the air core. The loop developed by the air core will be by means of using two identical copper coils placed side by side.

Theory:

When measuring the Flux from the secondary windings (via voltage)on the transformer, in conjunction with a RC integrator, and the current from the primary coil, we can plot the B-H curves on our oscilloscope. The “B” represents the Flux on the dependent axis, while the “H” represents the magnetic field intensity on the independent axis.

The graph represented by plotting these two quantities yields a BH curve or a hysteresis loop. The quality of the core, whether air or iron, will determine the properties of the BH curve. The more inefficient the core, the greater the gap between the two curves. This gap between the two curves represents the energy losses in the transformer. In other words if you insert 100 watts into the transformer and only get 80 watts out, you will have 20 watts of power lost through the transformation process. This loss becomes apparent in the form of thermal energy, or heat.

The B-H curve is developed from two components, the magnetic Flux (B), and the Magnetic Field Intensity (H). The Flux is measured against time and will usually produce a smooth, consistent, sinusoidal function. The Magnetic Field Intensity is measured by the current readings as a function of time. It is this current measurement which determines how efficient, or the shape of the hysteresis loop as the current wave displays the quality of the sinusoid produced.

As described above, should the current curve experience distortion the plot of the Flux (B), and Magnetic Field (B) will contain a gap in their graphs, resembling a wide “S” shape. The broadness of this gap, if you were to integrate the area between the lines, accounts for the magnitude of the transformer losses and is a function of the permeability of the core. The permeability of the core is a product of the relative permeability of the core material and the permeability of free space (air). If the permeability is equal to that of free space then the B-H curve should resemble a straight line without any gaps. The slope of this line is equal to the permeability of free space.

Rough Data:

Procedure A:

Two copper coils were used and placed side by side. Air was used as the core, or you could simply say that a core was not used at all in this portion of the experiment. A resistor (2000 Ω load bank) was placed between the AC voltage supply and the primary coil. Channel 2 from our oscilloscope was set for “current” and placed across this 2000 Ω resistor. The secondary coil was wired directly to our RC integrator as shown in the diagram below. Channel 1 on our oscilloscope was set for “voltage” and placed across the capacitor within the RC integrator. This assembly enabled us to plot to magnetic flux density and magnetic field density on the oscilloscope upon supplying an AC voltage of 12.39 volts to the primary coil. A picture of this graph is shown below.

OSCILLOSCOPE

2000 OHM

RESISTOR

RC INTEGRATOR

COIL 1COIL 2

VOLTAGE CHANNEL

CURRENT CHANNEL

CH 1CH 2

AIR CORE CIRCUIT

Procedure B:

In this portion of this experiment a single phase transformer was used. The transformer used had an iron core built into it as needed. The transformer circuit was wired just as described in Part A, and our oscilloscope measured the same values across the same elements as also described in Part A. A detail of this circuit is shown below, accompanied by the digital photograph taken of the graph displayed by our oscilloscope.

OSCILLOSCOPE

2000 OHM

RESISTOR

RC INTEGRATOR

COIL 1COIL 2

VOLTAGE CHANNEL

CURRENT CHANNEL

CH 1CH 2

IRON CORE CIRCUIT

Questions and Answers:

Question: Draw, approximately, the signals generated in your oscilloscope. Indicate what they are.

Answer: The signals are shown above.

Question: In procedure A, why is the hysteresis loop linear? What does the slope mean?

Answer: The hysteresis loop is linear due to the undistorted sinusoidal produced by the air core. In other words, the sinusoidal produced by the primary coil is equal the sinusoidal produced by the secondary coil.

The slope of this line is equal to the permeability of free space, represented by μ0 . It follows the equation: B= μH (slope intercept form).

Question: In procedure B, why is the hysteresis loop non-linear?

Answer: The hysteresis loop is non-linear due to the ferromagnetic material used as the core of the transformer, or plunger as referred to in the first lab experiment.

Question: What is the main harmonic content (other than the fundamental) in the current signal?

Answer: This would be the 3rd harmonic, also referred to as a “Triplen” family member in the industry. The 3rd harmonic is the most destructive harmonic of them all. This is the sole reason why manufactures have developed K rated transformers.

Questions: What is its frequency?

Answer: As with any harmonic the harmonic frequency is the product of its order and the fundamental. In our case of the 3rd harmonic, it’s frequency is 3(60 Hz) = 180 Hz. Therefore, our 3rd harmonic has a frequency of 180 Hz.

Questions: Identify, approximately, the voltage at which saturation of the iron core occurred.

Answer: The saturation of the iron core occurred at approximately 620 millivolts. This does not make any since to me as saturation is usually defined by the amount of current.

CONCLUSIONS:

This experiment validated the energy losses produced when using an iron core, or ferromagnetic material, as the conduction medium between two conducting coils. We were able to cross reference this observation to the one made in the first procedure when an iron core was not used at all. We saw that using air as the conduction medium between the two conducting resulted in straight line, experiencing no energy losses between these two coils.

A second observation was also made when the instant the primary coils was energized, the inrush current. The inrush current is a result of a Lorenz Force which is developed form the magnetic field set up within the transformer by the input current. As this field is set up, it resists any change in flux it experiences during the establishment of this interior field. Needless to say, the inrush current settled within milliseconds as expected.

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