CHAPTER 14 TRANSFORMER CHAPTER OBJECTIVES Explain mutual inductance Describe how a transformer in constructed and how it works Explain how a step-up transformer works Explain how a step-down transformer works Discuss the effect of a resistive load across the secondary winding Discuss the concept of a reflected load in the transformer CHAPTER OBJECTIVES Discuss impedance matching with transformers Explain how the transformer acts as an isolation device Describe a practical transformer Describe several types of transformers THE BASIC TRANSFORMER A basic transformer is an electrical device constructed of two coils placed in close proximity to each other so that there is a mutual inductance. One coil is called the primary winding and the other is called the secondary winding as indicated. 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. When a second coil is placed vary close to the first coil so that the changing magnetic lines of force cut through the second coil When two coils are magnetically coupled, they provide electrical isolation because there is no electrical connection between them. Mutual Inductance The amount of voltage induced in the second coil as a result of the current in the first coil is dependent on the mutual inductance, LM The mutual inductance is established by the inductance of each coil and by the amount of coupling (k) between two coils Coefficient of Coupling Coefficient of coupling (k) between two coils is the of the lines of force (flux) produced by coil 1 that link coil 2 to the total flux produced by coil 1 φ 1− 2 k = φ1 A greater value of k (no unit) means that more voltage is induced in coil 2 for a certain rate of change of current in coil 1. Formula for Mutual Inductance The three factors that influence mutual inductance are ( k, L1 and L2 ) and the formula for mutual inductance is LM = k L1 L 2 THE BASIC TRANSFORMER The winding of a transformer are formed around the core. Three general categories of core material are air, ferrite, and iron. The schematic symbol for each type is CORE MATERIALS Air-core and ferrite-core Air-core and ferrite-core transformer generally are used for high-frequency applications and the wire is typically covered by vanish-type coating to prevent the winding from shorting together. The amount of magnetic coupling between the primary winding and the secondary winding is set by the type of core material and by the relative positions of the winding tighter the coupling, the greater the The induced voltage in the secondary for a given current in the primary CORE MATERIALS Iron-core Iron-core transformer generally are used for audio frequency (AF) and power applications. A core constructed from laminate sheets of ferromagnetic material. The core type has more room for insulation and can handle higher voltages, and the shell type can produce higher core flux. Types of transformers Turns Ratio The turns ratio (n) is defined as the ratio of the number of turns in the secondary winding (Nsec) to the number of turns in the primary winding (Npri) n = N sec N pri 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 winding STEP-UP TRANSFORMER The secondary voltage is greater than the primary voltage, and the amount that the voltage is stepped up depends on the turns ratio. The ratio is illustrated as : Vsec V pri = N sec N pri Vsec = nV pri Primary Secondary STEP-DOWN TRANSFORMER The secondary voltage is less than the primary voltage, and the amount that the voltage is stepped up depends on the turns ratio which is always less than 1. Primary Secondary LOADING THE SECONDARY When a load is connected to the secondary winding of the transformer, the power delivered to the load can never be greater than the power delivered by the primary winding. For an ideal transformer Psec = Ppri LOADING THE SECONDARY The power delivered by the primary is Ppri = Vpri Ipri The power delivered by the secondary is Psec = Vsec Isec I pri I s ec I s ec = n 1 = I pri n REFLECTED LOAD The load (RL) in the secondary of a transformer is reflected into the primary by transformer action. The actual load is essentially ‘reflected’ into the primary determined by the turns ratio. R pri RL = V pri I pri V sec I sec ⎛ V pri =⎜ ⎜V ⎝ sec ⎞ ⎛ I sec ⎟⎜ ⎟⎜ I ⎠ ⎝ pri 2 R pri ⎞ ⎛ 1 ⎞⎛ 1 ⎞ ⎛ 1 ⎞ 2 ⎟ = ⎜ ⎟⎜ ⎟ = ⎜ ⎟ ⎟ ⎝ n ⎠⎝ n ⎠ ⎝ n ⎠ ⎠ ⎛1⎞ = ⎜ ⎟ RL ⎝n⎠ MATCHING THE LOAD AND THE SOURCE RESISTANCE Using the concept of maximum power transfer Recall the maximum power transfer theorem When a source is connected to a load, maximum power is delivered to the load when the load resistance is equal to the internal source resistance Impedance Matching A special type of wide-band transformer that make the load resistance appear to have the same value as the source resistance is called an impedance-matching transformer, and this technique is called impedance matching Impedance Matching An antenna system has a characteristic resistance of 75 Ω which is not equal to the 300 Ω TV input, and thus we need a matching transformer for matching and maximum power will be delivered to the input of the TV THE TRANSFORMER AS AN ISOLATION DEVICE DC Isolation When a direct current voltage is supplied to the primary of transformer, nothing happens in the secondary circuit. A small transformer can be used to keep the dc voltage on the output of an amplifier stage from affecting the dc bias of the next amplifier Power Line Isolation To prevent the shock hazard, if the 220 V or 110V line is connected to the metal chassis of the equipment. NONIDEAL TRANSFORMER CHARACTERISTICS Winding resistance Both the primary and the secondary winding of a practical transformer have winding resistance. Loss in the core There is always some energy conversion in the core material of a practical transformer because of the continuous reversal of the magnetic field due to the changing direction of the primary current; this component of the energy conversion is called hysteresis loss NONIDEAL TRANSFORMER CHARACTERISTICS Magnetic flux leakage Some of magnetic flux line produced by the primary current break out of the core and pass through the surrounding air back to the other end of the winding Winding capacitance Transformer Power rating A power transformer is typically rated in volt-amperes (VA) For example: 2 kVA, 500/50, 60 Hz. The transformer rating can be helpful in selecting the proper transformer for a given application Transformer efficiency ⎛ Pout η = ⎜⎜ ⎝ Pin ⎞ ⎟⎟100 % ⎠ OTHER TYPE OF TRANSFORMER Tapped Transformer OTHER TYPE OF TRANSFORMER Tapped Transformer OTHER TYPE OF TRANSFORMER Multiple-winding transformers OTHER TYPE OF TRANSFORMER Autotransformers SUMMARY A transformer generally consists of two or more coils that are magnetically coupled on a common core. 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 secondary winding determine the turns ratio. The relative polarities of the primary and secondary voltages are determined by the direction of the windings around the core. SUMMARY A step-up transformer has a turns ratio greater than 1. A step-down transformer has a turns ratio less than 1. A transformer cannot increase power. 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. SUMMARY A load connected 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 selection of the proper turn ratio. A transformer does not respond to constant dc. Conversion of electrical energy to heat in an actual transformer results from winding resistances, hysteresis loss in the core, eddy currents in the core, and flux leakage.