What Is Step-Down Transformer and How It Works?

\[ \epsilon = -\frac{d}{dt} \phi_m\] 

where, \( E_{\epsilon mf} \) is the induced emf in the closed loop,

\( \frac{d}{dt} \phi_m \), is the rate of change of magnetic flux passing through the closed loop. 

The negative sign in the Faraday's Law equation indicates the if the magnetic flux,\( \frac{d}{dt} \phi_m \), is increasing then induced emf, \( \epsilon \) , is decreasing and vice versa. This is mathematical interpretation of Lenz's Law which states that "The direction of any magnetic induction effect is such as to oppose the cause of the effect."

Mutual Induction elucidates how a current is induced in a coil by another current-carrying coil in close proximity, experiencing varying magnetic flux. The induced current is directly linked to changes in the initial current's rate.

Consider the following picture of demonstration of mutual inductance:

Here, the ac current or changing current i1 flowing in the coil 1 with N1 turns produces a magnetic field B1 which flows through the coil 2. This in effect generates an induced and induced current emf in the coil 2. The induced emf in coil 2 is given by the Faraday's Law,

The magnetic flux through the secondary coil due to the current in the primary coil is given by:

${\mathrm{\Phi }}_2=M_{21}{I}_1$

Where:

• ${\mathrm{\Phi }}_2$ is the magnetic flux through the secondary coil,
• $M_{21}$ is the mutual inductance between the coils,
• $I_1$ is the current passing through the primary coil.

According to Faraday's law, the induced EMF in the secondary coil is:

${\mathcal{E}}_2=-\frac{d{\mathrm{\Phi }}_2}{dt}$

Now, if the current in the primary coil is changing with time ($\frac{d{I}_1}{dt}$), the rate of change of the magnetic flux through the secondary coil due to this changing current in the primary coil will induce an EMF in the secondary coil. So:

${\mathcal{E}}_2=-\frac{d{\mathrm{\Phi }}_2}{dt}=-\frac{d(M_{21}{I}_1)}{dt}$

By applying the product rule of differentiation:

${\mathcal{E}}_2=-M_{21}\cdot \frac{d{I}_1}{dt}-I_1\cdot \frac{d{M}_{21}}{dt}$

Comparing this with the equation for induced EMF in the secondary coil (${\mathcal{E}}_2=-\frac{d{\mathrm{\Phi }}_2}{dt}$), we can ignore the term $\frac{d{M}_{21}}{dt}$ because the mutual inductance is generally considered constant for stationary coils and their positions.

Therefore, we get:

${\mathcal{E}}_2=-M_{21}\cdot \frac{d{I}_1}{dt}$

Finally, if we consider the total induced voltage ($V_2=N_2\cdot {\mathcal{E}}_2$) in the secondary coil due to this induced EMF, we get:

$V_2=-M_{21}\cdot N_2\cdot \frac{d{I}_1}{dt}$

This equation relates the induced voltage in the secondary coil ($V_2$) to the rate of change of current in the primary coil ($\frac{d{I}_1}{dt}$) through the mutual inductance ($M_{21}$) and the number of turns in the secondary coil ($N_2$).

 The calculate primary current of transformer and transformer output current calculator can be used to calculate the transformer input and output current.

Transformer Construction

Transformers serve as marvels of electrical engineering, operating on the fundamental concept of mutual induction. Simply put, when there's a fluctuation in the current coursing through one coil, it triggers the creation of an electric current in another closely situated coil.

Each transformer consists of two vital components: the primary and secondary coils. The primary coil connects to the AC power source, while the secondary coil links to the load or the device receiving the electrical energy.

When the primary coil receives alternating current, it initiates the generation of a magnetic flux. This magnetic field completes its circuit through the transformer's core, crucial for the whole process.

As the secondary coil intersects with this magnetic flux, it induces an electromotive force (EMF) in itself. The potency of this induced EMF hinges upon the number of turns present in the winding of the secondary coil. The relationship is straightforward: the more turns in the coil, the higher the induced voltage.

Expressed mathematically as N1>N2, where N1 represents the number of turns in the first coil and N2 in the second coil, this disparity in turns directly impacts the induced voltage. The  transformer winding calculator online can be used the windings needed for the primary winding and secondary windings.

Transformer Equation 

There exists a proportional relationship between voltage and the number of turns in a coil, articulated by the following transformer equation:

\( \frac{V_s}{V_p} = \frac{N_s}{N_p} \)

Here, Vp denotes the voltage in the primary coil, Vs stands for the voltage in the secondary coil, Np represents the number of turns in the primary coil, and Ns signifies the number of turns in the secondary coil. This formula precisely quantifies how changes in coil turns correspond to variations in voltage across the transformer. The transformer calculator online

For a step-down transformer, the winding with more turns is typically the primary winding. The primary coil(Np) is the one connected to the higher voltage source, and it has more turns compared to the secondary coil(Ns). This configuration allows the transformer to step down the voltage from the primary side to the secondary side. The ratio of Np/Ns is called transformer's turn ratio which can be determined using the turn ratio of transformer calculator.

Animation of Step down Transformer

To understand the usage of step down transformer, consider the step down transformer working animation below. It demonstrates how the main power supply in homes are converted in DC voltage where step down transformer and rectifiers are used. 

Application Example of Transformer