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Hysteresis Loss in a Transformer and How It Affects AC Circuits

Key Takeaways

  • Hysteresis loss in a transformer occurs due to magnetization saturation in the core of the transformer.

  • Magnetic materials in the core will eventually become magnetically saturated when they are placed in a strong magnetic field, such as the magnetic field generated by an AC current.

  • To prevent distortion, transformers that are used for power electronics should be chosen so that they do not strongly saturate at the input magnetic flux value.

Hysteresis loss in the windings of a transformer

The magnetic core in this transformer will create hysteresis loss at high input current and magnetic field.

Transformers are one of those important pieces of equipment that make modern life possible, as they provide a critical power conversion function. They step up or step down AC voltage/current to useful levels, which then can be converted to DC and used to power your favorite electronics. If you want to plug anything into the wall and receive grid power, there are some important requirements you’ll need to satisfy, one of which relates to hysteresis in a transformer.

Unfortunately, with magnetic hysteresis comes hysteresis loss in a transformer. Every transformer exhibits some hysteresis loss as the input current oscillates back and forth, and these losses manifest as minor distortion and reduced efficiency in the output power. When you need to place power conversion directly on your PCB, or you just need to select a transformer for power conversion, pay attention to hysteresis loss in your transformer.

What Causes Hysteresis Loss in a Transformer?

Every transformer contains a ferromagnetic material as its core, and all magnetic materials will have some magnetic saturation that occurs at high magnetic field strength. When this occurs, the level of magnetization you’ve induced in the magnetic material has reached its maximum; you cannot make this material have any greater level of magnetism once saturation occurs. As a result, the induced magnetization in the transformer core stops increasing even though the input current and magnetic flux continue increasing.

Once the input flux switches direction, some amount of magnetic flux is needed to cause the magnetization in the transformer core to switch direction. This is the essence of hysteresis; although the magnetic field has switched direction, magnetization in the core (manifested in the B-field) is not fully reduced to zero until the field exceeds a certain threshold (called the coercive force). The effects of hysteresis on the B-field in the core due to the H-field created by current in the coils is shown in the image below.

Magnetic hysteresis loss and window graphic

Magnetic hysteresis window.

The H-field does not do work on magnetic domains in the core material, but it is still convenient to think of the magnetic field as experiencing a nonconservative force, known in many circles as magnetic friction. The analogy to friction is apt as power loss manifests itself in the core as heat. In reality, the magnetic field does actually shift magnetic domains in the core material. This leads to the familiar humming sound and vibration in large transformers that operate with very high fields. Due to dispersion, hysteresis losses differ as a function of frequency, which should be considered when selecting a transformer.

Can You Reduce Hysteresis Loss?

The simple answer is that hysteresis loss cannot be easily reduced by adding some components or adjusting the geometry. The hysteresis loss in the transformer core is proportional to the area enclosed in the hysteresis window for a given core material. For this reason, highly magnetically susceptible materials are used because they tend to have narrow hysteresis windows. Read this article to find a table with material properties and nominal losses at 100 kHz for common transformer core materials.

In addition to hysteresis loss, every transformer experiences the following sources of loss:

  • Leakage loss. Not all transformer designs are perfect and some field will leak away from the core of the transformer. This reduces the magnetic field seen at the secondary windings, so the input current will be reduced slightly. 

  • Conductor loss. The conductor used to form the windings around the core (usually copper) has some finite electrical conductivity, so there will be some IR drop in the windings. 

  • Eddy current loss. As the input magnetic flux switches continuously in time, an eddy current is induced in the core which creates Ohmic losses. The solution here is to use a core with a smaller cross-sectional area and higher conductivity. 

Not all SPICE models for transformers include all sources of losses. The most basic SPICE models are purely linear and don’t include any losses. To work with real transformers in standard SPICE simulations, you need to use a modeling utility to account for hysteresis or other losses in your power conversion system. This area of electronics design has been researched ever since SPICE simulators have existed. Take a look at this recent IEEE article to learn more about developing SPICE models for transformers with hysteresis.

SPICE simulation hysteresis loss

Example 3-phase voltage waveforms in a high current system. Note the distortion due to hysteresis.

Other Important Portions of Power Conversion

Power systems and electrical equipment must obey standards such as IEEE 519-2014, NEMA IS07 P1-2019, and IEC standards, all of which define acceptable upper limits on total harmonic distortion (THD) in power electronics. These standards affect other aspects of your system that are related to transformer hysteresis in various ways.

In addition to judicious transformer selection, you need to carefully select the following components and circuit topologies for power conversion, conditioning, and filtering. The table below shows a short list of important components and circuits that will need to be included in your AC input/conversion section:


Role in Power Conversion

Magnetics EMI filter

Uses a magnetic core with common-mode windings to eliminate common-mode conducted EMI on the input section of the device. Note that these filters are basically transformers and can also experience hysteresis loss.

PFC circuit

Smooths out the current waveform when a switching regulator draws power and when hysteresis loss in the transformer causes distortion.

Regulator topology (LDO or switching)

Provides stable DC output power with high efficiency. Some regulator topologies, such as forward and flyback converters, use a diode and 3-winding transformer to overcome hysteresis losses while generating stable DC output.

Rectifier diodes

Technically, any diode can be used in a rectifier as long as its forward voltage is sufficiently low. Many bridge rectifier ICs are rated for specific AC line voltages.


Once you select these other components and design regulation/conditioning circuits for power conversion, you can simulate all aspects of circuit behavior with the front-end design features from Cadence and the powerful PSpice Simulator. Once you’ve designed your circuits, you can use the PSpice modeling application and simulator tools to examine hysteresis loss in a transformer and other circuits in your system.

If you’re looking to learn more about how Cadence has the solution for you, talk to us and our team of experts.