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Basic Electronics Ninth Edition Basic Electronics Ninth Edition ©2002 The McGraw-Hill Companies Grob Schultz
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Basic Electronics Ninth Edition Basic Electronics Ninth Edition ©2003 The McGraw-Hill Companies 20 CHAPTER Inductance
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Topics Covered in Chapter 20 Induction by Alternating Current Self-Inductance L Self-Induced Voltage v L How v L Opposes a Change in Current
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Mutual Inductance L M Transformers Core Losses Types of Cores Variable Inductance Topics Covered in Chapter 20 (continued)
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Inductances in Series or Parallel Stray Inductance Energy in Magnetic Field of Inductance Troubles in Coils Topics Covered in Chapter 20 (continued)
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Inductor Action Variations in current level induces voltage in a conductor. Lenz’ Law states that the induced voltage produces current that opposes the changes in the current causing the induction. The ability of a conductor to induce a voltage across itself when the current varies is self-inductance, or simply inductance.
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Top view Front view Inductors and Schematic Symbols
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Most Inductors Have Multiple Turns to Increase the Effect. As the flux expands and contracts, it cuts across the coils (multiple turns). The self-induced voltage opposes the source. + + - -
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The Unit of Inductance The henry (H) is the basic unit of inductance. One henry causes 1 V to be induced when the current is changing at the rate of 1 A per second. Practical inductor values are in these ranges: 1 H to 10 H 1 mH (millihenry) = 1 10 -3 H 1 (microhenry) = 1 10 -6 H
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Calculating the Inductance of a Long Coil Hx l AN L r 610 2 26.1 Where L is the inductance in henrys: r is the relative permeability of the core N is the number of turns A is the area in square meters l is the length in meters d l 10d air-core symbol r = 1) iron-core symbol r >> 1)
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Amount of Induced Voltage Induced voltage is proportional to inductance (L). Induced voltage is proportional to the rate of current change. vL di dt L di dt Formula:
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Inductor Voltage as a Function of di/dt v L = 1x10 -3 (6000) = 6 V Triangle current generator 1 mH 0 A 6 A 1 ms + 6 V - 6 V v L = L(di/dt) v L = 1x10 -3 (-6000) = -6 V vLvL vLvL iLiL time
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Energy Stored in the Field 2 2 LI Energy Where the Energy is in joules: L is the inductance in henrys I is the current in amperes
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Mutual Inductance Mutual inductance (L M ) occurs when current flowing through one conductor creates a magnetic field which induces a voltage in a nearby conductor. Two coils have a mutual inductance of 1 H when when a current change of 1A/s induces 1 V in the other coil. Unit: Henrys (H) Formula: LkLL M 12
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Coefficient of Coupling (k) k approaching 1 k between 0 and 1 k approaching 0 21 LL L k M
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A transformer has two or more windings with mutual inductance. The primary winding is connected to a source of ac power. Transformer The secondary winding is connected to the load. A transformer can step up or step down the voltage level from the ac source.
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Secondary Circuit Transformers Have Mutual Inductance (magnetic coupling) Primary Circuit Induced Voltage
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PrimarySecondary Load PrimarySecondary Load Step-up and Step-down Transformers Step-up (V LOAD > V SOURCE ) Step-down (V LOAD < V SOURCE )
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The voltage ratio is the same as the turns ratio: V P / V S = N P / N S V P = primary voltage, V S = secondary voltage N P = number of turns of wire in the primary N S = number of turns of wire in the secondary When transformer efficiency is 100%, the power at the primary equals the power at the secondary. Power ratings refer to the secondary winding in real transformers (efficiency < 100%). Transformers Ratios and Power
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Voltage Ratio PrimarySecondary Load 3:1 120 V 40 V PrimarySecondary Load 1:3 120 V 360 V
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Current Ratio PrimarySecondary Load 3:1 120 V 40 V PrimarySecondary Load 1:3 120 V 360 V 0.3 A 0.1 A 0.3 A
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Power Ratio (100 % Efficiency) PrimarySecondary Load 3:1 120 V 40 V PrimarySecondary Load 1:3 120 V 360 V 0.3 A 0.1 A 0.3 A P PRI = 120 x.3 = 36 W = P SEC = 360 x 0.1 = 36 W P PRI = 120 x.1 = 12 W = P SEC = 40 x 0.3 = 12 W
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Efficiency PrimarySecondary Load 3:1 120 V 40 V 0.12 A 0.3 A P PRI = 120 x.12 = 14.4 WP SEC = 40 x 0.3 = 12 W %83%100 4.14 12 %100 xx P P Efficiency PRI SEC
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Transformer Impedance A transformer can be used to reflect a secondary load impedance back to the primary: Z N N Z P P S S 2 N N Z Z P S P S Transformer impedance matching is related to the turns ratio:
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Impedance Ratio PrimarySecondary Load = 9 The load on the source is 1 . 1:3 Z RATIO = 1/9 PrimarySecondary Load = 9 3:1 The load on the source is 81 . Z RATIO = 9/1
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Eddy Currents Eddy-currents are induced in the iron core of an inductor or transformer. Eddy currents raise the temperature of the core. Losses increase with frequency. Losses can be reduced by using a laminated core or a powered-iron core.
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Combining Inductance Values With no mutual coupling: For series circuits, inductances add just like resistances. For parallel circuits, inductances combine according to a reciprocal formula as with resistances.
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Inductors in Series and Parallel with k = 0 321 LLLL T 321 111 1 LLL L EQ
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