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 = 4.44fNÎ¦
or,  E = 4.44fNABm  (As = Bm 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 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 variable, then it can be said that if the frequency increases then the No. of Turns(N) and Area of Core(A) both decreases. If frequency decrease 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.

(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
Î´= 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, the Flux density depends upon the material of the transformer core, 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, Î´, 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, Î´, 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.