Presentation on theme: "DC/AC Fundamentals: A Systems Approach"— Presentation transcript:
1 DC/AC Fundamentals: A Systems Approach Thomas L. FloydDavid M. BuchlaTransformersChapter 14
2 Mutual Inductance Ch.14 Summary When two coils are placed close to each other, the changing flux in one coil will induce a voltage in the second coil. The coils are said to have mutual inductance (LM), which can either add or subtract from the total inductance, depending on whether the fields are aiding or opposing.The coefficient of coupling is a measure of how well the coils are linked; it is a number between 0 and 1.
3 Mutual Inductance (LM) Ch.14 SummaryMutual Inductance (LM)The formula for mutual inductance isk = the coefficient of coupling (dimensionless)L1, L2 = inductance of each coil (H)The coefficient of coupling depends on factors such as the orientation of the coils to each other, their proximity, and if they are on a common core.
4 Basic Transformer Ch.14 Summary The basic transformer is formed from two coils that are usually wound on a common core to provide a path for the magnetic flux. Schematic symbols indicate the type of core.Air coreFerrite coreIron coreSmall power transformer
5 Ch.14 SummaryTurns RatioA useful parameter for ideal transformers is the turns ratio, defined asNsec = number of secondary windingsNpri = number of primary windingsMost transformers are not marked with turns ratio, however it is a useful parameter for understanding transformer operation.A transformer has 800 turns on the primary and a turns ratio of How many turns are on the secondary?200
6 Direction of Windings Ch.14 Summary The direction of the windings determines the polarity of the voltage across the secondary winding with respect to the voltage across the primary. Phase dots are sometimes used in schematic diagrams to indicate the input/output polarity relationship.The dots identifythe primary andsecondary windingswhose voltages arein phase with eachother.In phaseOut of phase
7 Step-up and Step-Down Transformers Ch.14 SummaryStep-up and Step-Down TransformersA step-up transformer provides a secondary voltage that is greater than the primary voltage (n > 1).A step-down transformer provides a secondary voltage that is less than the primary voltage (n < 1).What is the secondary voltage?4:1Vpri30 Vrms?120 VrmsWhat is the turns ratio?0.25
8 Isolation Transformers Ch.14 SummaryIsolation TransformersA transformer with a turns ratio of 1 is called an isolation transformer. Because n =1, the secondary voltage is equal to the primary voltage.The isolation transformer breaks the dc path between two circuits while maintaining the ac path. The dc is blocked by the transformer, because magnetic flux does not change with dc.
9 Coupling Transformers Ch.14 SummaryCoupling TransformersCoupling transformers are used to pass high frequency signals from one stage to another. They are typically are configured with a resonant circuit on the primary and the secondary. Some specialty isolation amplifiers use transformer coupling to isolate power.
10 Transformer Current Ch.14 Summary Transformers cannot increase the applied power. If the secondary voltage is higher than the primary voltage, then the secondary current must be lower than the primary current and vice-versa.The ideal transformer turns ratio equation for current isNotice that the primary current is in the numerator.
11 Transformer Power Ch.14 Summary The ideal transformer does not dissipate power. Power delivered from the source is passed on to the load by the transformer. This important idea can be used to define the transformer voltage and current relationships:These last ratios are the turns ratio, n.
12 Reflected Resistance Ch.14 Summary Most transformers change both the voltage and current on the primary side to different values on the secondary side. This makes a load resistance appear to have a different value on the primary side.Applying Ohm’s law:Taking the ratio of Rpri to RL:
13 Reflected Resistance Ch.14 Summary The resistance “seen” on the primary side is called the reflected resistance.If you “look” into the primary side of the circuit, you see an effective load that is changed by the reciprocal of the turns ratio squared.You see the primary side resistance, so the load resistance is effectively changed.
14 Impedance Matching Ch.14 Summary A special impedance matching transformer can be used to match a load resistance to internal resistance of its source (and hence transfer maximum power to the load).Impedance matching transformers are designed for a wider range of frequencies than power transformers, hence tend to be not ideal.RintVsRL
15 Impedance Matching Ch.14 Summary The balun is a specialized transformer to match a balanced line to an unbalanced line and vice-versa. A balanced signal is composed of two equal-amplitude signals that are 180o out-of-phase with each other. An unbalanced signal is one that is referenced to ground. In the illustration, an unbalanced signal is converted to a balanced signal by the balun transformer.
16 Impedance Matching Ch.14 Summary One common application of a balun is in matching a balanced dipole antenna to a coax line, as illustrated below.Beside making the conversion from a balanced line to an unbalanced line, the balun can also match two different impedances. For example, a dipole antenna of 300 W can be matched to a 75 W coax using a balun.
17 Non-Ideal Transformers Ch.14 SummaryNon-Ideal TransformersAn ideal transformer has no power loss; all power applied to the primary is all delivered to the load. Actual transformers depart from this ideal model. Some loss mechanisms are:Winding resistance; causing power to be dissipated in the windings.Hysteresis loss; due to the continuous reversal of the magnetic field.Core losses; due to circulating current in the core (eddy currents).Flux leakage; flux from the primary that does not link to the secondaryWinding capacitance; that has a bypassing effect for the windings.
18 Transformer Efficiency Ch.14 SummaryTransformer EfficiencyThe efficiency of a transformer is the ratio of power delivered to the load (Pout) to the power delivered to the primary (Pin). That is20 mAWhat is the efficiency of the transformer?VpriRL100 W15 Vrms120 Vrms94%
19 Transformer Efficiency Ch.14 SummaryTransformer EfficiencyWhat is the efficiency of the transformer?94%20 mAVpriRL100 W15 Vrms120 Vrms
20 Tapped and Multiple-Winding Transformers Ch.14 SummaryTapped and Multiple-Winding TransformersMultiple windings can appear on either the primary or secondary side of a transformer. Tapped and multiple windings allow a transformer to provide more than one secondary (output) voltage, or accept more than one primary (input) voltage.Secondary with center-tapPrimary with multiple-windings
21 Tapped and Multiple-Winding Transformers Ch.14 SummaryTapped and Multiple-Winding TransformersUtility companies frequently use multiple-tapped transformers. By selecting different taps, on theprimary side, the voltage delivered to the customer can be adjusted.The center-tapped secondary allows household wiring to select either 120 V or 240 V, depending on the circuit.
22 Three-Phase Transformers Ch.14 SummaryThree-Phase TransformersThree-phase power is used for power transmission and industrial applications. Three-phase transformers are wired in either a wye or a delta configuration or a combination of both. The names refer to the schematic representation of the windings.This transformer is a wye-to-delta configuration, which is generally used in step down cases. The delta-wye (not shown) is generally used in step up cases.
23 Key Terms Ch.14 Summary Mutual inductance Transformer Primary winding The inductance between two separate coils, such as in a transformer.TransformerAn electrical device constructed of two or more coils that are magnetically coupled to each other so that there is mutual inductance from one coil to the other.Primary windingThe input winding of a transformer; also called primary.Secondary windingThe output winding of a transformer; also called secondary.
24 Key Terms Ch.14 Summary Magnetic coupling Turns ratio The magnetic connection between two coils as a result of the changing magnetic flux lines of one coil cutting through the second coil.Turns ratioThe ratio of the turns in the secondary winding to the turns in the primary winding.Reflected resistanceThe resistance of the secondary circuit reflected into the primary circuit.Impedance matchingA technique used to match a load resistance to a source resistance in order to achieve maximum transfer of power.
25 Quiz Ch.14 Summary The measurement unit for the coefficient of coupling isa. ohmb. wattc. meterd. dimensionless
26 Quiz Ch.14 Summary 2. A step-up transformer refers to one in which the voltage across the secondary is higher than the primary.the current in secondary is higher than the primary.the power to the load is higher than deleivered to the primary.all of the above.
27 Quiz Ch.14 Summary 3. An isolation transformer a. blocks both ac and dc.b. blocks ac but not dc.c. blocks dc but not ac.d. passes both ac and dc.
28 Ch.14 SummaryQuiz4. If the current in the secondary is higher than in the primary, the transformer is aa. a step-up transformer.b. an isolation transformer.c. a step-down transformer.d. not enough information to tell.
29 Quiz Ch.14 Summary 5. An ideal transformer has a. no winding resistance.b. no eddy current loss.c. power out = power in.d. all of the above.
30 Ch.14 SummaryQuiz6. Assume a step-down transformer is used between a source and a load. From the primary side, the load resistance will appear to bea. smaller.b. the same.c. larger.
31 Ch.14 SummaryQuiz7. A transformer that can deliver more power to the load than it receives from the source is a(n)a. step-up type.b. step-down type.c. isolation type.d. none of the above.
32 Ch.14 SummaryQuiz8. Generally, the purpose of an impedance matching transformer is toa. make the load voltage appear to be the sameas the source voltage.b. make the load resistance appear to be thesame as the source resistance.c. make the load current appear to be the sameas the source current.d. provide more power to the load than isdelivered from the source.
33 Ch.14 SummaryQuiz9. A type of transformer that tends to not be ideal because it is designed for a good frequency response is aa. step-up type.b. step-down type.c. isolation type.d. impedance matching type.
34 Ch.14 SummaryBlank Slide10. A transformer that could be used for 110 V or 220 V operation is aa. multiple-winding type.b. center-tapped type.c. isolation type.d. all of the above.
35 Answers Ch.14 Summary 1. d 2. a 6. c 3. c 7. d 4. c 8. b 5. d 9. d