Transformer

A transformer is an electrical machine which changes a given alternating emf into larger or smaller alternating emf.

Transformer is one of the most useful electrical devices ever invented. It can use for increasing or decreasing the alternating voltage. It is a device which has large number of uses like electricity generation, transmission and distribution. In this chapter we shall discuss some of the basic properties of transformer and designing of transformer.

Principle:

                    It works on the principle of mutual induction between the coils. A changes current in the primary coil induces an emf in secondary coil.

Construction:

                    It consists of two windings primary winding to which source is applied and secondary winding from which stepped up or stepped down alternating voltage is obtained and an iron core over which primary and secondary windings are wound.

Working:

                     An alternating emf is applied to the primary, if the flux in the primary is changing at the rate of flux then this alternating flux links both windings and induces emf E1 and E2. The emf E1 is termed as primary emf and E2 is termed as secondary emf.

                    The emf induced in the primary will be back emf which will oppose the applied voltage if resistance of coil is negligible then back emf is opposite to applied voltage.

V = -E

According to Faraday’s law

E  = -N (change in flux)

V = - (-N (change in flux))

V =  (N (change in flux))

For primary coil

                                                                         V_p = N_P(change in flux)

For secondary coil

V_s = N_S(change in flux)

From (A) & (B)
 V_{p /}V_s  = N_P/N_S

Types of transformer:

Depending upon number of turns transformer is divided in to two types:

Step up transformer:

Such a transformer in which voltage across secondary is greater than primary is called step up transformer.

N_S > N_P

V_S > V_P

Step down transformer:

Such a transformer in which voltage across primary is greater than secondary is called step down transformer.

N_S < N_P

V_S < V_P

The transformer steps up or steps down but power remains same.

Primary power (P_p) = Secondary power (P_s)

                                                   Vp Ip        =            Vs Is

                                                  Vp / Vs       =            Is / Ip   

Losses in transformer:

Losses that occur in transformer are:

Core losses: Eddy current losses & Hysteresis losses.

Copper losses: Occurs in the winding.

Designing of transformer:

Let us we have to design a transformer of 12V and 3A output.

V_out = 12 V

I _out = 3A

Power of transformer = V x A

                                    = 12 x 3 = 36VA

V_in = 240 V

Step 1: Area of bobbin.

Area of bobbin can be calculated by following formula:

Area of bobin = sqrt(VA)/ 5.6

Size =   = 1.07 inch²
Step 2: Number of turns.

Copper windings = 8V per turn

Primary side =  = 30 turns

Secondary side =  = 1.5 turns

Now to decrease losses multiplying turns of both windings by a constant number.

Primary side = 30 x 20 = 600 turns

Secondary side = 1.5 x 20 = 30 turns

Step 3: Currents calculation.

Primary current:

I_p = VA/   Vp 

I_p = 36/240 = 0.15A

Secondary current:

I_s =VA/    Vs

I_s = 36/ 12 = 3A

Step 4: Calculation of S.W.G (Square wire gauge):

To calculate S.W.G, first of all calculate diameter which is given by following formula:

                          d = sqrt((4*A)/pi)                                                                       
Where A = Area
And area is given by:                                           A = i/ mu

Primary side:

A_p = 

Secondary side:

A_s = 

A_p =

A_s =

By using above formula:

d =  = 0.276 mm

d =  = 1.23 mm

To convert mm to S.W.G, you can use standard tables, according to given table:

d = 0.276mm     S.W.G = 32 SWG

d = 1.219            S.W.G = 18 SWG

As we have standard wire gauge corresponding to 1.219, so recalculating A_s, I_s.

A_s = 1.16

I_s = 2.91