WORKING PRINCIPLE OF TRANSFORMER

A transformer is a static (or stationary) piece of apparatus by means of which electric power in one circuit is transformed in to electric power of the same frequency in another circuit. It can raise or lower the voltage in a circuit but with a coresponding decrease or increase in current. The physical basis of a transformer is mutual induction between two circuits linked by a common magnetic flux*. In its simplest form, it consists of two inductive coils which are electrically seperated but magenetically linked through a path of low reluctance. The two coils posses high mutual inductance. If one coil is connected to a source of alternating voltage, an alternating flux is set up in the laminated core, most of which is linked with the other coil in which it produces mutually induced e. m. f (according to Faradays law of electro magnetic induction) If the second coil circuit is closed, a current fiows in it and so electric energy is transfered (entirely magnetically) from the first coil to the second ceil The first coil in which electric energy is fed from the Ac supply mains, is called primary winding and the other from which energy is drawn out is called secondary.

In brief, a transformer is a device that,

(1) Transfer electric power from one circuit to another

(2) It does so without change in frequency

(3) It accomplishes it by electromagnetic induction and,

(4) Where the two electric circuits are in mutual inductive influence of each other.

B.H-F- EQUATION OF A TRANSFORMER

Let N1 = Number of turns in the primary.

N2 — Number of turns in ire seconr'a /

Qm - Max. flux in core in Was = 8m. A

f r: Frequency of AC input in Hz.

The fiux increases from its zero value to maximum value (Om) in one quarter of the cycle (1/4f second)

. • . Average rate of change of flux E" Om/1/4f E" 40mf Wb/s. or volt Now, rate of change of fiux/ turn meens induced e. m. f. in volts ,

• . Average e. m. f/ turn ~ 40mf volts.

If flux 0 varies sinusoidally/then r. m s. value of induced e. m. f is obtained by multiplying the average value with from facto*-.

FORM FACTOR = R.M-S VALUE / AVERAGE VALUE

For sinusoidal wave Form factor = I- II c. m. s. value of e. m. f / turn =1.11 40m f = 4. 44 0m f volts

Now, RMS value of induced tmf in the whole [of primary turns = (indueed emf/turn) * numbtr of primary turns.

E1 = 4. 44 Om f nl = 4. 44 Dm A f n1 volts.

Similarly rms value of emf induced in secondary is

E2 = 4. 44 Om f n1 = 4. 44 Bm A f n1 volts.

In an ideal transformer V1 =" E1 and E2 = V2 where VI is the terminal voltage.

CLASSIFICATION OF TRANSFORMER ACCORDING TO CONSTRUCTION

1- CORE TYPE TRANSFORMER: When the magnetic circuit take the form of a single wing encorded

by two or more groups of primary and secondary windings distributed around the periphery of a ring, the transformer is called a core type transformer.

2- SHELL TYPE TRANSFORMER: When the primary and secondary windings take the form of a

common ring which is encorded by two or more rings of magnetic materials distributed around its preiphery, the transformer is termed a shell type transformer.In small power application, shell type transformers are more preferable.

TRANSFORMER ASSEMBLY PARTS

1-WINDiNG W!RE_: It is made up of copper and enamled with fine varnish for good insulation. The wire wjll obtain in different diameters. The current capacity of this type of copper wire can be

taken as 200 to 250ampere per sq. cm.

2-CORE LAMINATION: Sheet steel lamination with 4% silicon are used for the manufacture of the core. The lamination used are about 0 35mm thick. Colled Railed Grain Oriented (ORGO) stampings are mostly used for core construction. This has a higher allowable flux density and lower losses.

3-BOBPINS: It is used as a winding former. This will obtain in differend dimensions as in table 3, The material used for manufacturing bobbins are nylon, rubber plastic', fibre sheet and bekelite sheets are ussually termed as former.

4-U-CLAMPS: This is made up of tin or mild steel. It is used to fix the transformer.

5-NSULATiON: Insulation materials obtain in different classess (class A,B.C etc). This classification is according with their temperature capacity and directric ability. Commonly used insulating materials are varnished paper, letheroid paper, polyster etc.

PRELIMINARY DESIGN

As the first step to the design of a transformer, the primary and secondary voltage ratings and secondary current rating must be clearly stated. Then decide on the core material to be used ordi­nary steel stampings or cold rolled grain

SECONDARY TURNS = 1.03 (TURNS PER VOLT X SECONDARY VOLTS) The windoe area required for the secondary winding is found from Tadle 1 as

SECONDARY WINDOW AREA=r. SECONDARY TURNS/TURNS PER sq. cm. FROM TABLE i

CORE SIZE

The main criterion in selecting the core is the total window is arc of winding space available

•

TOTAL WINDOW AREA=PRIMARY WINDOW AREA+SUM OF SECONDARY WINDOW AREA+SPACE FOR FORMER & INSULATION.

Some extra area is required to accomodate the former and insulation between windings. The actual amount of extra area varies, although 30% may be taken to start with but may have to be modified later. The suitable core sizes having a larger window area are selected ficm table 2

Taking in to account the gap between laminations while stacking than (the core stacking factor taken as 0.9), we have:

GROSS CORE AREA- CORE AREA/0.9 sq. cm.

In general, a square central limb is preferred. For this, the width of the tongue of iamination is

TONGUE WIDTH = / GROSS CORE AREA cm.

Now refer to Table 2 again arid finallay select the proper core sixe, with sufficient window area and a close value of the tongue width as calculated. Adjust the stack height as required to obtain the required core section.

I

STACK HEIGHT * GROSS CORE AREA / ACTUAL TONGUE WIDTH Cm.

The stack should not be much less than the tongue width but may be more. However, it should be more than 1.5 times the tongue width.

ASSEMBLY

The windings are wound on an innsulating former which fits over the centre limb of the core. The primary is usually wound first, than the secondary, with insul­ation between windings. A final insulating layer is provided over the windings to protect them from mechanical damage.

When thin wires are used, their ends must be soldered to thicker wires for bringing the terminals outside the former. The laminations are assembled over the former with alternate laminations reversed in assembly. The laminations must be held together tightly by a suitable claimping frame or by screws (if holes are provided in)

oriented (C. R. G. O) Stampings. CRGO has a higher allowable flux dencity and lower losses.

The optimum cross-sectional area of tha core is approximately given by

GORE AREA=» 1.152/Out put voltage X Out put current sq. cm

. For transformer with multiple secondaries, the sum of the out put volt-amp

product of each winding is to be used. The number of turns on the primary and secondary windings is decided by the turns per volt ratio as:

TURNS PER VOLT = I/(4.41X10-4 frequency X core area X flux density)

Here, the frequency is 50Hz for indian di n ^stic miins supply. The flux density can be taken as about 1.0 wb/sq.m for ordinary steel stampings and about 1.3 ^wb/sq. cm for CRGO stampings.

PRIMARY WINDING DESIGN

The curent in the primary winding is given by :

PRIMARY CURRENT=(V2. 12) / (VI. Efficiency)

Here V2 — Secondary voltage 12==- Secondary current V1 = Primary voltage

The efficiency of small transformer varies between 0.8 to 0.96. A value of 0.9 can be used for ordinary transformers. The proper wire size has to be selected for the winding. The wire diameter depends on the current to be supply by the winding and the allowable current density of the wire. The current density may be as high as 233 Amp.s/sq. cm. in small transformers and as low as 155 Amps/sq. cm. in large ones. Usually a value of 200 Amps/sq. cm. can be taken, on whole basis table 1 is given.

The number of turns in the prim try winding is given by:

PRIMARY TURNS = TURNS PER VOLT X PRIMARY VOLTS

The space taken by the winding will depend on the insulation thickness, method of winding and wire diameter. Table 1 gives the approximate values of the turns per sq. cm. from which we can estimate the window area occupied by the primary winding.

PRIMARY WINDING AREA *> PRIMARY TURNS/TURNS PER Sq. cm. FROM TABLE 1.

SECONDARY WINDING DESIGN

Since we have assumed that we know the secondary curent rating, we can ftnd out the wire size for the winding by referring to table 1 directly.

The number of turns on the secondary is calculated in the same way as for the primary, but about 3% extra turns are to be added to compensate for the internal drop of secondary voltage of transformer, upon loading.

TABLE 1 WINDING DATA ON ENAMELLED COPPER WIRE (200 Araps/Sq. cm)

SWG	Max. current capacity (Amps)	Turns/sq.cm.	SWG	Max. current capacity I Amps)	Turns/sq.cm.
10	16-60	8.7	30	.1558	881
11	13.638	10-4	31	.1364	997
12	10.961	12.8	32	• 1182	1137
13	8.579	16.1	3d	• 1013	1308
14	6-487	21-5	34	• 0858	1608
15	5-254	26-8	35	• 0715	1902
16	4.151	35.2	36	.0586	2286
17	3.178	45.4	37	.0469	2800
18	2.335	60.8	38	.0365	3507
19	1-622	87.4	39	.0274	4838
20	1.313	106	40	.0233	5595
21	1.0375	137	41	.0197	6543
22	.7945	176	42	-0162	7755
23	.5838	242	43	.0131	9337
24	.4906	286	44	.0104	11457
25	.4054	341	45	.0079	14392
25	.3284	415	46	.0059	20223
27	.2726	504	47	.0041	27546
28	.2219	609	48	.0026	39706
29	.1874	711	49	.0015	62134
			50	.0010	81242

TABLE 2 DIMENSIONS OF TRANSFORMER STAMPINGS

Type No.		Tongue Window Type No. Tongue width (cm) area (cm2) width (cm)				Window area (cm2)
17	(E-I)	1.270	1.213	9 (U— T)	2.223	7-865
12A	(E-I)	1.588	1.897	9A(U— T)	2.223	7.865
74	(E-I)	1.748	2.284	11 A (E-I )	1.905	9.072
23	(E-I)	1.905	2.723	4A(E— I )	3.335	10.284
30	(E-I)	2.000	3.000	. 2 (E-T )	1.905	10.891
21	(E-I)	1.588	3.329	16 (K— I )	3.810	10.891
31	(E-l)	2.223	3.703	5 (E-I )	3.810	12-704
10	(E-I)	1.588	4.439	4AX(U— T)	2.383	13.039
15	(E-I)	2.540	4.839	13 (E-I )	3.175	14.117
33	(E-I)	2.800	5.880	75 (U— T)	2.540	15.324
1	(E-I)	2.461	6.555	4 (E-l )	2.540	15.865
14	(E-I)	2.540	6.555	7 (E-I )	5.080	18.969
11	(E-T)	.1.905	7.259	6 (E-I) }	3.810	19 356
34	(U-T)	1.588	7.259	35A(U — T)	3.810	39.316
3 »j	(E-I)	3.175	7.562	8 (E-I )	5.080	49.803

TABLE 3

BOBBONS – INNER HOLE DIMENSIONS

TYPE NO. LENGTH AVAILABLE BREADTH

1 7.9375 X 11.906

74 17.463 X 17.463

30 19.844 X 19.844 X 25.400

45 22.225 X 25.400 X 31.750

80 4.7625 X 4.7625 X 7.1440 X 9.5250

32 6.3500 X 6.3500 X 9.5250 X 12.700

17 6.3500 X 6.3500 X 15.875 X 19.050

12A 15.875 X 6.3500 X 15.875 X 19.050

33 28.575 X 28.575 X 31.750 X 34.924 X 38.100

3 31.750 X 31.750 X 38.1 X44.450 X 50.8

23 15.875 X 15.875 X 25.400 X 28.575 X 31.750 X 38.100

15 25.400 X 25.400 X 31.750 X 38.100 X 44.450 X 50.800