# Transformer Core Loss Lissajous

• fonz
In summary, the Lissajous figure closely resembles the B-H hysteresis loop due to the similarity in frequency of the two signals. The current in the primary is the current that establishes the flux in the core, which in turn produces the magnetomotive force. The voltage lags the flux by 90 degrees, due to the presence of an RC load.
fonz

## Homework Statement

[/B]
A single phase transformer circuit is assembled with an RC load. A voltmeter is connected to across the capacitor and an ammeter in series with the primary. The output of the ammeter is connected to the X-channel of an oscilloscope and the output of the voltmeter is connected to the Y-channel.

The oscilloscope is set to X-Y mode and the resulting display is a Lissajous figure that closely resembles the B-H hysteresis loop.

Explain why this is the case...

N/A

## The Attempt at a Solution

The current in the primary is the current that establishes the flux in the core i.e. provides the magnetomotive force which effectively represents the behavior of the H field.

Since the e.m.f. produced by the transformer windings is proportional to the rate of change of flux the voltage lags the flux by 90deg.

Lissajous figures represent phase differences between two signals. In this case the frequency of the two signals is the same but anti-phase. If the current was perfectly sinusoidal the figure would be an ellipse however due to saturation effects the current is not perfectly sinusoidal which is observed by the resulting Lissajous figure.

I think this answer is on the right lines however I'm confused as to why the need for an RC load? Also, the magnetising current should be more prominent under no load however in this there is a 150kohm and 2microF capacitor which represents some load impedance on the transformer.

Have you calculated the phase of the sinusoid across the capacitor, relative to the voltage applied to the RC combo for your powerline frequency?

How would you describe in words the shape of the BH 'loop' for an ideal power transformer core?
fonz said:
voltage lags the flux by 90deg.

Lissajous figures represent phase differences between two signals. In this case the frequency of the two signals is the same but anti-phase.
You seem to be saying a phase difference of "90 deg" is being in "antiphase"?

fonz
fonz said:
The output of the ammeter is connected to the X-channel of an oscilloscope and the output of the voltmeter is connected to the Y-channel.
That seems an unusual usage of the terms ammeter and voltmeter but I understand what they intend.

fonz

I haven't calculated the phase of the volt-drop across the capacitor since in this arrangement I am only supplied with the magnitude of the volt-drop across the capacitor. Also, I wouldn't be sure how to analyse this since there will be some impedance in the transformer windings which will influence the power factor. I suppose just by observation the capacitor would have the effect of correcting the power factor slightly but I'm confused as to why the capacitor is needed for the B-H curve analysis.

Also, to answer your second question; in an ideal transformer the B-H curve would be linear for all values of H in other words the magnetic permeability is a true constant. Also since the hysteresis contributes to losses in the core an ideal transformer core would not exhibit coercivity.

Also, thank you for spotting that mistake.

fonz said:
I haven't calculated the phase of the volt-drop across the capacitor
But you know R and C, so you could?
fonz said:
Also, to answer your second question; in an ideal transformer the B-H curve would be linear for all values of H in other words the magnetic permeability is a true constant.
It might be best to initially focus on what is needed to set up this x-y display so with an ideal transformer your setup would be displaying a recognizable linear B-H relationship. (B=μH)

fonz said:
I'm confused as to why the need for an RC load?

it has nothing to do with the transformer.

Nascent is giving you a hint by asking about phase. At risk of meddling, i'll strengthen the hint a little bit...

For the moment ignore the transformer and go to the basics of your RC circuit.
You said R is 150 K ohms. What is Xc of your 2μf capacitor at line frequency ? I wager it's small compared to 150 KΩ .
Which means the capacitor has little effect on current through the RC circuit.
Which means current through the capacitor is very nearly in direct proportion to voltage across the RC circuit;
Now, voltage across a capacitor being the integral of current through it, means what ?
It means your RC circuit makes an integrator where voltage across capacitor very nearly represents the integral of voltage applied to the RC circuit. Certainly as close to a perfect integral as you can see by eye on a 'scope screen that has probably 3% accuracy.

So your RC circuit is an integrator. That's the key to this homework exercise.
I can tell you from real world practical experience that an integrator is a handy tool to have when studying inductance . I've done exactly this experiment myself for studying iron cores.

So you think real practical now,
why might whoever set up this homework exercise want you to think about observing the integral of voltage?

@NascentOxygen: it's counterintuitive to beginners so i thought he needed a nudge in right direction... no offense meant...

Try it with non-sine magnetizing current, like a triangle wave...

jim hardy said:
A circular reference.

I seem to recall a thread similar to this one somewhere recently.

## What is transformer core loss Lissajous?

Transformer core loss Lissajous is a graph that shows the relationship between the input voltage and current of a transformer. It is used to measure the core losses in a transformer, including hysteresis and eddy current losses.

## Why is transformer core loss Lissajous important?

Transformer core loss Lissajous is important because it helps us understand the efficiency of a transformer. By analyzing the shape and size of the Lissajous pattern, we can determine the amount of core losses and make necessary adjustments to improve the transformer's efficiency.

## How is transformer core loss Lissajous measured?

Transformer core loss Lissajous is measured by applying a sinusoidal voltage to the primary winding of the transformer and measuring the current on the secondary winding. The resulting Lissajous pattern is then analyzed to determine the core losses.

## What is the difference between hysteresis and eddy current losses?

Hysteresis losses occur due to the magnetization and demagnetization of the core material, while eddy current losses are caused by induced currents in the core material. Both types of losses contribute to the overall core loss in a transformer.

## How can we reduce transformer core loss?

To reduce transformer core loss, we can use materials with lower hysteresis and eddy current losses, such as laminated silicon steel. We can also design the transformer with a tighter air gap and minimize the number of turns in the windings, which can reduce the magnetic flux and thus reduce core losses.

• Electrical Engineering
Replies
8
Views
1K
• Mechanics
Replies
77
Views
5K
• Electrical Engineering
Replies
8
Views
874
• Engineering and Comp Sci Homework Help
Replies
1
Views
1K
• Electrical Engineering
Replies
64
Views
5K
• Engineering and Comp Sci Homework Help
Replies
1
Views
1K
• Electrical Engineering
Replies
36
Views
10K
• Engineering and Comp Sci Homework Help
Replies
4
Views
3K
• Engineering and Comp Sci Homework Help
Replies
4
Views
2K
• Electrical Engineering
Replies
3
Views
948