 # Step Down Transformer Equation Study

Step-down transformers are used to reduce the Voltage in electric power generation, transmission, and distribution. Step down transformer equation follows electromagnetic induction rule so that it is used in electronic devices. This article is about all the equations and formulas for the Step-Down transformer.

## Step Down Transformer Equation And Formula

Step-down transformer mainly has transmission formula; transformer ratio, voltage ration, and current ratio. All the formal is the main topic of this article. Continue reading for the details.

### Step Down Transformer Formula

Step down transformer follows Ns/Np = Vs/Vp when Ns < Np. The Step-Down Transformer formula used to design a Step-Down Transformer is given below with details.

Step Down Transformer Equation is, Ns/Np = Vs/Vp

Where,

Ns= Number of turns in secondary
Np= number of turns in the primary
Vs= Voltage in secondary
Vp= Voltage in primary

For a voltage step-down transformer, the number of turns in secondary winding always be less than the number of turns in the primary winding.

So the point is here, because of less turn in the secondary winding, induced EMF and hence the output voltage in the secondary will also be less than the primary input voltage.

### Step Down Transformer EMF Equation

Let’s discuss the step-down transformer EMF equation. Step down transformer EMF equation depends on the number of turns in both primary and secondary coil, flux in the magnetic core, and supply frequency.

Np = Turns in the primary coil.
Ns = Turns in the secondary coil.
Φm = Induced flux in the magnetic core (in Wb) = (Bm x A)
f = Supply frequency (in Hz)

Here,
change of flux = Φm /(T/4) = Φm /(1/4f)

So,
Average rate of change of flux = 4f Φm(Wb/s).

Now,
Induced EMF per turn = change of flux per turn

So, the average induced EMF per turn = 4f Φm(V).

Now, we know, Form factor = RMS value/average value

So, the RMS value of emf per turn = Form factor X average induced EMF per turn.

As the flux Φ varies sinusoidally, the form factor of a sine wave is 1.11

Therefore, RMS value of emf per turn = 1.11 x 4f Φm = 4.44f Φm.

RMS value of induced emf in whole primary winding (Ep) = RMS value of EMF per turn X Turns in the primary winding

Now, equation 01 is, Ep = 4.44f Np Φm.

Similarly, RMS induced emf in the secondary winding (Es) can be given as

Equation 02 is, Es = 4.44f Ns Φm.

So, Step Down EMF equation is, Ep/Np=Es/Ns=4.44fΦm

This equation is Step Down transformer EMF equation, which shows that the EMF/number of turns is the same for both primary and secondary winding.

For an ideal transformer on no load, Ep=Vp, and Es=Vs.

Where Vp = Input voltage in the primary coil.
Vs. = Output voltage in the secondary coil.

### Step-Down Transformer Turns Ratio

Transformer turns ratio expressed by a constant K. K equals the number of turns in the primary coil divided by the number of turns in the secondary coil K=N2/N1.  For a voltage step-down transformer, it must be N2< N1, i.e., K < 1. So, the step-down transformer turns ratio K=N1/N2.

Here,

• N1= Primary coil turns
• N2= Secondary coil turns
• K= Constant

Say, a step-up transformer has primary coil turn = 220
Secondary coil turn = 140

So, the transformer ratio of this transformer

K= 220/140
K= 1.57

### Step-Down Transformer Voltage Current Ratio

Step down transformer follows tuns ratio. Here is the step-down transformer voltage and current ratio:

• Step down transformer voltage ratio = Vp/Vs=Np/Ns
• Step down transformer current ration = Ip/Is=Np/Ns

## Conclusion

Every transformer follows the same formula, but the difference here is turning in the coil. Fewer turns in the primary coil than the secondary make a transformer voltage step up.

• So, Step Down transformer equation is, Ns/Np = Vs/Vp.
• Turns ratio K=N1/N2.
• EMF equation is, Ep/Np=Es/Ns=4.44fΦm
• Voltage ratio = Vp/Vs=Np/Ns.
• Current ration = Ip/Is=Np/Ns.

All the information is collected from various sources like a book, electrical blog. I hope this article helps. Read more related to an electrical transformer.