[Explained] Transformer Size VS Frequency

We know that Transformer size decreases with increase in Frequency and the transformer size increases with decrease in frequency, but how it is possible? In this article, we will discuss this topic with a detail explanation. You may notice in mobile charger circuits, SMPS circuits very small size of transformers are used which step down the voltage from 230V to 12v or 6V. Those are the high-frequency transformers.

The answer to the above question can be given in different ways, all are given below.

(1) Let's Understand from the EMF equation.

The transformer EMF equation is,   E = 4.44fNΦ_m 

                                                   or,  E = 4.44fNABm  (As = B_m x A)

Here, f = frequency

         N = No. of Turns

         A = Area of Core

         Bm = Flux density

So if the Bm and N are taken as constant, then the Area of the Core depends upon the frequency for the same EMF. You may understand if we increase the frequency then the area of the core will decrease and if we decrease the frequency then the area of the core will increase.

Now, if we take both N and A as variables, then it can be said that if the frequency increases then the No. of Turns(N) and Area of Core(A) both decrease. If the frequency decreases the no. of turns and area of the core will increase.

As the size of the transformer depends upon the No. of turns and area of the core, so the transformer size will change with changing of the No. of turns and area of the core. High frequency transformer needs less coil and less core size that is why high frequency transformers have small size. So transformers are designed in such a way that their size will be appropriate for the particular applications with proper capacity.

(2) Let's understand from the Transformer Output Equation.

The output equation for single phase core type transformer is,

The output equation for three-phase single phase transformer is,

Remember that the above equations are only applicable for core type and shell type transformer.

Here,

Q = KVA Rating

δ= Current density (A/m2)

f = Frequency

Ai = Cross-sectional Area of Core

Bm = Maximum Flux Density in the Core

Aw = Window Area

Kw = Window Space Factor

In the above equation, the Flux density depends upon the material of the transformer core, and the current density depends upon the type of cooling.

Window Space Factor(Kw) is the ratio of the cross-sectional area of the copper conductor and the window area.

So, it is clear that Bm, δ, and Kw are constant.

Now, the size of the transformer is directly proportional to the product of the area of the window and the cross-sectional area of the limb.

As the Bm, δ, and Kw are constant, the KVA rating is directly proportional to the product of transformer size and the frequency.

So if the frequency increase then the transformer size will be decreased for the same KVA rating and if the frequency decrease then the transformer size will be increased. That is why you can see  high frequency switching principle are used for power supply devices to decrease the manufacturing cost as its transformer size decreases.

Read Also:

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• Why Transformer Cannot work on DC Supply?
• Why Three Phase Induction Motor Self-Starting but Synchronous Motor not?
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