Chapter 14. Transformers ISU EE. C.Y. Lee

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1 Chapter 14 Transformers

2 Objectives Explain mutual inductance Describe how a transformer is constructed and how it works Explain how a step-up and -down transformer works Discuss the effect of a resistive load across the secondary winding Discuss impedance matching with transformers Explain how the transformer acts as an isolation device Describe a tapped transformer 2

3 Mutual Inductance When two coils are placed close to each other, a changing electromagnetic field produced by the current in one coil will cause an induced voltage in the second coil because of the mutual inductance, L M 3

4 Coefficient of Coupling The coefficient of coupling (k) between two coils is the ratio of the lines of force (flux) produced by one coil linking the second coil (φ 1-2 ) to the total flux produced by the first coil (φ 1 ): φ k = 1 2 φ The coefficient of coupling depends on the physical closeness of the coils and the type of core material on which they are wound The formula for mutual inductance: L M = k L 1 L 2 1 4

5 The Basic Transformer Source voltage is applied to the primary winding The load is connected to the secondary winding 5

6 The Basic Transformer The core (air, ferrite or iron) provides a physical structure for placement of windings and a magnetic path so that the magnetic flux lines are concentrated close to the coils 6

7 Turns Ratio Turns ratio (n) is defined as the ratio of the number of turns in the secondary winding (N sec ) to the number of turns in the primary winding (N pri ) n = N N sec pri 7

8 Direction of Windings The direction of the windings determines the polarity of the voltage across the secondary winding with respect to the voltage across the primary 8

9 Direction of Windings Phase dots are used to indicate polarities 9

10 Step-Up Transformers A transformer in which the secondary voltage is greater than the primary voltage is called a stepup transformer The ratio of secondary voltage (V sec ) to primary voltage (V pri ) is equal to the ratio of the number of turns in the secondary winding (N sec ) to the number of turns in the primary winding (N pri ) V V N N sec sec = = pri 10 pri n

11 Step-Up Transformers Example: The transformer has a turns ratio of 3. What is the voltage across the secondary? V sec = (3/1)(120V) = 360 V 11

12 Step-Down Transformer A transformer in which the secondary voltage is less than the primary voltage is called a stepdown transformer The amount by which the voltage is stepped down depends on the turns ratio The turns ratio of a step-down transformer is always less than 1 12

13 Step-Down Transformers Example: The transformer is part of a laboratory power supply and has a turns ratio of 0.2. What is the secondary voltage? V sec = (0.2)(120V) = 24 V 13

14 Primary Power Equals Load Power For an ideal transformer, the power delivered in the secondary equals the power in the primary In a real transformer, some power is dissipated in the transformer, so primary power is always greater than secondary power In an ideal transformer, power transfer is not related to the turns ratio P pri = V pri I pri = V sec I sec = P sec 14

15 Loading the Secondary Winding When a load resistor is connected to the secondary winding, there is a current through the resulting secondary circuit because of the voltage induced in the secondary coil This secondary current results in a primary current I I sec pri = N N pri sec 15

16 Loading the Secondary Winding Example: The two transformers have loaded secondaries. If the primary current is 100 ma in each case, what is the current through the load? (a) (b) I L = (1/10)(100mA) = 10 ma I L = (2/1)(100mA) = 200 ma 16

17 Reflected Load This reflected load is what the primary source effectively see, and it determines the amount of primary current The effective resistance that the primary sees is R pri = N N pri sec 2 R L = 1 n 2 R L 17

18 Reflected Load Example: What is the reflected resistance seen by the source R pri = (1/4) 2 (100Ω) = 6.25 Ω 18

19 Impedance Matching When a source is connected to a load, maximum power is delivered to the load when the load impedance is equal to the fixed internal source impedance 19

20 Matching Transformer One application of transformers is in the matching of a load resistance to a source resistance in order to achieve maximum transfer of power R 1 n 2 = 75 ( 300 ) pri R L = n = = 4 = 2 n 75 20

21 DC Isolation A transformer does not pass dc, therefore a transformer can be used to keep the dc voltage on the output of an amplifier stage from affecting the bias of the next amplifier The ac signal is coupled through the transformer between amplifier stages 21

22 Tapped Transformers The center tap (CT) transformer is equivalent to two secondary windings with half the voltage across each 22

23 Tapped Transformers Power company step down the high voltage from the power line to 100V/220V service for residential and commercial customers 23

24 Summary There is mutual inductance between two magnetically coupled coils When current in one coil changes, voltage is induced in the other coil The primary is the winding connected to the source, and the secondary is the winding connected to the load The number of turns in the primary and the number of turns in the secondary determine the turns ratio 24

25 Summary The relative polarities of the primary and secondary voltages are determined by the direction of the windings around the core A step-up transformer has a turns ratio greater than 1 A step-down transformer has a turns ratio less than 1 In an ideal transformer, the power from the source (input power) is equal to the power delivered to the load (output power) If the voltage is stepped up, the current is stepped down, and vice versa 25

26 Summary A load across the secondary winding of a transformer appears to the source as a reflected load having a value dependent on the reciprocal of the turns ratio squared An impedance-matching transformer can match a load resistance to an internal source resistance to achieve maximum power transfer to the load by selecting the proper turns ratio A typical transformer does not respond to dc 26

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