Lesson 25 Magnetism and Transformers 1 Learning Objectives

Lesson 25: Magnetism and Transformers 1

Learning Objectives • Analyze the relationship between the transformation ratio, voltage ratio, current ratio, and impedance ratio. • Construct a circuit equivalent of a transformer and calculate primary and secondary voltage, current and polarity. • Explain the relationship between the power developed in the primary and secondary of a transformer. 2

Transmission of Power 3

Transformer Overview • A transformer is a magnetically coupled circuit whose operation is governed by Faraday’s Law. 4

Faraday’s Experiment #3: Mutually Induced Voltage • Voltage is induced across Coil 2 when i 1 is changing. • When i 1 reaches steady state, voltage across Coil 2 returns to zero. − NOTE: The coil to which the source is attached is the primary and the coil attached to the load is the secondary. 5

Transformer Overview • A time-varying current in the primary windings induces a magnetic flux (field) in the iron core. • The flux flows through the core and induces a current the secondary windings. • Thus power flows via the magnetic field without the windings being electrically connected. 6

Winding Direction • The polarity of ac voltages can be changed by changing the direction of the windings. 0º phase shift 180º phase shift 7

Iron-Core Transformers • Two basic types of iron-core transformers are the core type and the shell type. • In both, the core is constructed of laminated sheets of steel to reduce eddy current losses. Core Type 8 Shell Type

Iron-Core Transformers • We will consider the ideal transformer which − − Neglects coil resistance. Neglects core losses. Assumes all flux is confined to the core. Assumes negligible current required to establish core flux. • Transformer operation is governed by Faraday’s Law. 9

Transformation Ratio • According to Faraday’s Law, voltage (e) is directly related to the number of turns (N) in the primary or secondary windings: • For each winding we can write: • Because the flux ( m) is the same through both windings, we can write: 10

Transformation Ratio • “The ratio of the primary voltage to secondary voltage is equal to the ratio of primary turns to secondary turns. ” • This ratio is called the transformation ratio (or turns ratio) and given by the symbol a. 11

Step-up and Step-down • Transformers are used to change or “transform” voltage. • Step-Up transformer: − The secondary voltage is higher than the primary voltage. − There are fewer primary windings than secondary windings (a < 1). • Step-Down transformer: − The secondary voltage is lower than the primary voltage. − There are more primary windings than secondary windings (a > 1). 12

Step-up and Step-down Step-Up Step-Down 13

Example Problem 1 Suppose the transformer depicted below has 4000 turns on its primary winding and 1000 turns on its secondary. a. Determine it’s turns ratio (a). Is it step-up or step-down? b. If the primary voltage epri = 480 sin t, what is it’s secondary voltage? => Step-Down since a > 4 Remember, this is a Step-Down for voltage, but a step-up for current. => esec = 120 V sin (Ѡt) 14

Current Ratio and Power • Because we are considering an ideal transformer, power in equals power out (Pin = Pout). • If the voltage is stepped up, then the current is stepped down, and vice versa. 15

Impedance • The impedance of the primary of an ideal transformer is the transformation ratio (a) squared times the impedance of the load (secondary winding) and is derived as below: − NOTE: If the load is capacitive or inductive, the reflected impedance is also capacitive or inductive. 16

Example Problem 2 For the figure below Eg = 120 V 0º, the turns ratio is 6: 1, and ZLD = 100100 j. The transformer is ideal. Find: N a. load voltage b. load current c. generator current d. Active power to the load Note that Ohm’s law and regular power equations are used here. 17

The Dot Convention • The direction of the windings is not obvious looking at a transformer, therefore we use the dot convention. • Dotted terminals have the same polarity at all instants of time. Used for phase shifting (180). 18

Example Problem 3 For the figure below Ig = 25 30ºm. A, the turns ratio is 4: 1, and VLD = 60 0ºV. The transformer is ideal. Find: a. b. c. d. Load current Load impedance Generator voltage Real and Reactive load power a) b) c) d) 19

Example Problem 4 For the figure below i 1 = 100 sin (ωt) m. A and the transformer is ideal. Determine the secondary currents i 2 and i 3. Why -180⁰ 20 Note the dot convention here, which switches the polarity 180⁰

Power Transformer Ratings • Just like ac motors and generators, power transformers are rated in terms of voltage and apparent power. − For example, a transformer is rated at 2400/120 volt, 48 k. VA has: • On the primary winding, the current rating is 48, 000 VA / 2400 V = 20 A. • On the secondary winding, the current rating is 48, 000 VA / 120 V = 400 A. 21