Understanding the 90-Degree Phase Lag in Transformer Flux Induced by EMF

Electromagnetic induction plays a crucial role in the core functioning of transformers. In this article, we delve into the principles that explain why EMF in a transformer induces a phase shift of 90 degrees in the flux, a phenomenon rooted in the behavior of alternating current (AC) circuits and inductor properties.

Alternating Current (AC) and Magnetic Flux

In an AC circuit, both the current and voltage vary sinusoidally over time. This behavior is fundamentally different from direct current (DC), where these quantities remain constant. When AC flows through the primary winding of a transformer, it generates a time-varying magnetic field in the transformer's core. This magnetic field is a critical component in understanding the relationship between EMF and flux.

Induction and Lenz's Law

The principles of electromagnetic induction, as described by Faraday's law, provide a framework for understanding how EMF is induced in the secondary winding of a transformer. Faraday's law states that the induced EMF in the secondary winding is proportional to the rate of change of magnetic flux through that winding. Lenz's law further reinforces this by asserting that the direction of the induced EMF opposes the change in magnetic flux that produced it. Together, these laws elucidate why the EMF and magnetic flux exhibit a 90-degree phase shift in a transformer.

Phase Relationships in Inductive Circuits

Considering a purely inductive circuit, such as the primary winding of a transformer, we observe a key characteristic: the current lags the voltage by 90 degrees. This phenomenon is a result of the inherent characteristics of inductors. In an inductor, the voltage reaches its peak value before the current reaches a corresponding peak due to the time required for the magnetic field to build up. As a consequence, the magnetic flux, which is directly proportional to the current in the primary winding, also lags the voltage by 90 degrees.

Mathematical Representation

To illustrate this concept mathematically, we can represent the voltage in the primary winding as:

Vt  V0 sin(omega;t)

The current It can be expressed as:

It  I0 sin(omega;t - 90°)  I0 cos(omega;t)

Since magnetic flux Phi;t is related to the current, it also lags the voltage by 90 degrees, as shown in the equation below:

Phi;t  Phi;0 sin(omega;t - 90°)  Phi;0 cos(omega;t)

This sinusoidal relationship and the 90-degree phase shift align with the principles of AC circuit analysis.

Conclusion

The 90-degree phase lag observed in the induced EMF and the magnetic flux in a transformer is a direct result of the inductive properties of the windings and the characteristics of AC circuits. The time required for the magnetic field to build up in response to the applied voltage is the primary cause of this phase difference. Understanding these principles is essential for optimizing transformer performance and minimizing harmonic distortion.

Additional Considerations

While the primary relationship between EMF and flux in a transformer is well understood, the interpretation can become more complex due to the non-linearity of the core material (BH curve). In high-flux density conditions, the magnetic field can distort, introducing harmonic sine waves such as the 3rd and 5th harmonics. These harmonics can be particularly significant in three-phase systems. Proper practices, such as ensuring a pathway for the 3rd harmonic currents (zero phase sequence currents) in star-connected transformers, mitigate these distortions and maintain system stability.