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
Mutual Inductance L M Transformers Core Losses Types of Cores Variable Inductance Topics Covered in Chapter 20 (continued)
Inductances in Series or Parallel Stray Inductance Energy in Magnetic Field of Inductance Troubles in Coils Topics Covered in Chapter 20 (continued)
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.
Top view Front view Inductors and Schematic Symbols
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. + + - -
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
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)
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:
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
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
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
Coefficient of Coupling (k) k approaching 1 k between 0 and 1 k approaching 0 21 LL L k M
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.
Secondary Circuit Transformers Have Mutual Inductance (magnetic coupling) Primary Circuit Induced Voltage
PrimarySecondary Load PrimarySecondary Load Step-up and Step-down Transformers Step-up (V LOAD > V SOURCE ) Step-down (V LOAD < V SOURCE )
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
Voltage Ratio PrimarySecondary Load 3:1 120 V 40 V PrimarySecondary Load 1:3 120 V 360 V
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
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
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
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:
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
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.
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.
Inductors in Series and Parallel with k = 0 321 LLLL T 321 111 1 LLL L EQ