1	Chapter 23 Transformers and Coupled Circuits
2	Transformer Construction Transformer is a magnetically coupled circuit It consists of two coils wound on a common core
3	Transformer Construction Power flows from one circuit to the other circuit Through the medium of the magnetic field
4	Transformer Construction There is no electrical connection between the two coils Coil (winding) on side of the transformer to which we apply power is called primary
5	Transformer Construction Coil on side to which we connect the load is called the secondary
6	Transformer Construction Iron-core transformers Generally used for low-frequency applications (such as audio and power) Iron core provides an easy path for magnetic flux
7	Transformer Construction Two basic construction types Core and shell Each type uses laminated sheets of metal to reduce eddy currents
8	Transformer Construction Air-core and ferrite-core types Used for high-frequency applications (such as radio frequencies)
9	Transformer Construction These do not have high hysteresis and eddy-current losses of iron-core transformers Ferrite Increases coupling between coils while maintaining low losses
10	Transformer Construction Transformer may be used to change polarity of an ac voltage Depending on the directions of its windings
11	Transformer Construction If most of the flux produced by one of the coils links the other Coils are tightly coupled Otherwise loosely coupled All transformer operations are described by Faraday’s law
12	Voltage Ratio for Ideal Transformers If we apply Faraday’s law, where N is the number of turns and f is the flux, then
13	Voltage Ratio for Ideal Transformers Ratio of primary voltage to secondary voltage Equal to ratio of the number of turns
14	The Turns Ratio Turns ratio (or the transformation ratio) a = N_p/N_s Also, e_p/e_s = a
15	The Turns Ratio A step-up transformer Secondary voltage is higher than the primary voltage (a < 1) A step-down transformer Secondary voltage is lower (a > 1)
16	The Current Ratio In an ideal transformer Power in equals power out (η = 100%) Ratios of the current are
17	The Current Ratio If voltage is stepped up Current is stepped down, and vice versa
18	Reflected Impedance A load impedance Z_L connected directly to a source is seen as Z_L Impedance will be seen by the source differently If a transformer is connected between the source and the load
19	Reflected Impedance Reflected impedance, Z_p, is given by Z_p = a²Z_L
20	Reflected Impedance Load characteristics do not change Capacitive loads still look capacitive, etc. A transformer can make a load look larger or smaller Depending on the turns ratio
21	Reflected Impedance Using a transformer We can match loads to sources (such as amplifiers) Relates to the maximum power theorem discussed in a previous section
22	Transformer Ratings Transformers are rated in terms of voltage and apparent power Rated current can be determined from these ratings
23	Transformer Ratings By dividing the apparent power rating by the voltage rating Rated current is determined, regardless of the power factor
24	Power Supply Transformers Used to convert the incoming 120 V source to voltage levels required by circuit Some have a multi-tapped secondary winding to provide different voltages for different applications
25	Power Supply Transformers Typically, an incoming voltage is Stepped down Rectified Smoothed by a filter Passed through a voltage regulator
26	Transformers in Power Systems Transformers are used at generating stations to raise voltage for transmission This lowers losses in the transmission lines At the user end Voltage is stepped down
27	Transformers in Power Systems Transformers have a split secondary This permits both 120-V and 240-V loads to be supplied from the same transformer For residential use Single phase is used
28	Isolation Applications Transformers are sometimes used to isolate equipment Isolation transformers are often used to make measurements involving high voltages
29	Isolation Applications They can also ensure that a grounded metal chassis is not connected to a hot wire
30	Isolation Applications Readings can be made on an oscilloscope Must have a grounded lead without shorting circuit components across ground connections by using a 1:1 transformer
31	Impedance Matching A transformer can be used to raise or lower apparent impedance of a load Impedance matching Sometimes used to match loads to amplifiers to achieve maximum power transfer
32	Impedance Matching If load and source are not matched A transformer, with the proper turns ratio, can be inserted between them
33	Autotransformers In autotransformers Primary circuit is not electrically isolated from its secondary They cannot be used as isolation transformers
34	Autotransformers Smaller and cheaper than conventional transformers with the same load kVA
35	Practical Iron-Core Transformers Non-ideal transformers have several effects that cause loss of power Leakage flux Will appear as small inductances in series with the windings
36	Practical Iron-Core Transformers Winding resistance Core losses due to eddy currents and hysteresis Magnetizing current
37	Transformer Efficiency Efficiency is ratio of output power to input power Given as a percentage. Losses Due to power losses in the windings and in core
38	Transformer Efficiency Large transformers can have efficiencies of 98 to 99 percent Smaller transformers have efficiencies of about 95 percent
39	Transformer Tests Losses may be determined by making tests on transformers Short-circuit tests Determine losses due to resistance of windings Open-circuit tests will determine core losses
40	Voltage and Frequency Effects As applied voltage increases, core flux increases, causing greater magnetization current Therefore, transformers should be operated only at or near their rated voltage
41	Voltage and Frequency Effects At very low frequencies Core flux and the magnetizing current increases Causing large internal voltage drops At very high frequencies Stray capacitances and inductances cause voltage drops
42	Loosely Coupled Circuits Circuits without an iron core, where only a portion of the flux produced by one coil links another Cannot be characterized by turns ratios They are characterized by self- and mutual inductances
43	Loosely Coupled Circuits Expressed by coefficient of coupling Air-core Ferrite-core transformers General inductive circuit coupling
44	Loosely Coupled Circuits Self-induced voltage in a coil is v = L di/dt Mutually induced voltage of a coil is v = M di/dt M is mutual inductance between coils
45	Loosely Coupled Circuits In each coil Induced voltage is the sum of its self-induced voltage Plus voltage mutually induced due to the current in the other coil
46	Loosely Coupled Circuits Coefficient of coupling, k Describes degree of coupling between coils Mutual inductance depends on k:
47	Loosely Coupled Circuits Coupled impedance is