Electronics Technology Fundamentals Chapter 10 Inductors

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved Inductance – P1 Inductance – the ability of a component with a changing current to induce a voltage across itself or a nearby circuit by generating a changing magnetic field Inductor – a component designed to provide a specific measure of inductance

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved Inductance – P2 The Effect of Varying Current on a Magnetic Field When current passes through an inductor, magnetic flux is generated Flux density is found as where B = the flux density, in webers per square meter (Wb/m 2 )  m = the permeability of the core material NI= the ampere-turns product ℓ = the length of the coil, in meters

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved Inductance – P3

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved Inductance – P4 Faraday’s Laws of Induction Law 1: To induce a voltage across a wire, there must be a relative motion between the wire and the magnetic field. Law 2: The voltage induced is proportional to the rate of change in magnetic flux encountered by the wire. Law 3: When a wire is cut by 10 8 perpendicular lines of force per second, 1 V is induced across that wire.

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved Inductance – P5 Faraday’s Laws of Induction (Continued)

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved Inductance – P6 Lenz’s Law 1834, Heinrich Lenz – derived the relationship between a magnetic field and the voltage it induces Lenz’s Law – an induced voltage always opposes its source

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved Inductance – P7 Lenz’s Law (Continued) An increase in the inductor current causes the magnetic field to expand. As the magnetic field expands, it cuts through the coil, inducing a voltage. The polarity of the voltage opposes the increase in current.

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved Inductance – P8 Lenz’s Law (Continued)

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved Inductance – P9 Lenz’s Law (Continued) An decrease in the inductor current causes the magnetic field to collapse. As the magnetic field collapses, it cuts through the coil, inducing a voltage across the component. The polarity of the voltage opposes the decrease in current.

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved Inductance – P10 Induced Voltage can be found as where v L = the instantaneous value of induced voltage L = the inductance of the coil, measured in henries (H) = the instantaneous rate of change in inductor current (in amperes per second)

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved Inductance – P11 Unit of Measure – henry (H) Inductance is measured in volts per rate of change in current When a change of 1A/s induces 1V across an inductor, the amount of inductance is said to be 1 H

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved Inductance – P12

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved The Phase Relationship Between Inductor Current and Voltage – P1 Sine-Wave Values of reaches its maximum value when i = 0

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved The Phase Relationship Between Inductor Current and Voltage – P2 The Phase Relationship Between Inductor Voltage and Current Voltage leads current by 90° Current lags voltage by 90°

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved Connecting Inductors in Series and Parallel – P1 Series-Connected Inductors where L n = the highest-numbered inductor in the circuit

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved Connecting Inductors in Series and Parallel – P2 Parallel-Connected Inductors where L n = the highest-numbered inductor in the circuit

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved Connecting Inductors in Series and Parallel – P3 Mutual Inductance – when one inductor is placed in close proximity to another, the flux produced by each coil can induce a voltage across the other

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved Connecting Inductors in Series and Parallel – P4 Mutual Inductance (Continued) Amount of mutual inductance: Coefficient of Coupling (k) – a measure of the degree of coupling that takes place between two or more coils where  1 = the amount of flux generated by L 1  2 = the amount of  1 that passes through L 2 at a 90° angle to the turns of the coil

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved Connecting Inductors in Series and Parallel – P5 The Effects of Mutual Inductance on L T

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved Inductive Reactance (X L ) – P1 Inductors Oppose Current. For the circuit below,

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved Inductive Reactance (X L ) – P2 Inductive Reactance (X L ) – the opposition (in ohms) that an inductor presents to a changing current Calculating the Value of X L

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved Inductive Reactance (X L ) – P3 X L and Ohm’s Law Example: Calculate the total current below

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved Inductive Reactance (X L ) – P4 Series and Parallel Reactances Insert Figure 10.19

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved Transformers – P1 Transformer – a two-coil component that uses electromagnetic induction to pass an ac signal from its input to its output while providing dc isolation between the two

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved Transformers – P2 Transformer Construction and Symbols Construction - Two coils Primary – input Secondary - output

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved Transformers – P3 Transformer Construction and Symbols (Continued) Schematic Symbols

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved Transformers – P4 Transformer Classifications

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved Transformers – P5 Transformer Operation Changing magnetic field in the primary windings induces a voltage in the secondary windings Primary and secondary windings are not physically connected

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved Transformers – P6 Turns Ratio Insert Figure 10.25

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved Transformers – P7 Secondary Voltage (V S ) Determined by the primary voltage and turns ratio

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved Transformers – P8 Power Transfer Ideal Conditions: P P = P S or I P V P = I S V S In Practice: Secondary power is always slightly lower because of a number of power losses Losses Copper Loss (I 2 R loss) Loss Due to Eddy Currents Hysteresis Loss

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved Transformers – P9 Transformer Input and Output Current Current varies inversely with turns ratio For an ideal transformer:

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved Transformers – P10

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved Transformers – P11 Primary Impedance (Z P ) Proportional to the square of the turns ratio where Z S = the total opposition to current in the secondary (generally assumed to equal the opposition provided by the load)

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved Transformers – P12 Transformer as an impedance-matching circuit

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved Transformers – P13 Center-Tapped Transformer

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved Related Topics – P1 Apparent Power (P APP ) Energy in an inductor is actually stored in the electromagnetic field generated by the inductor Energy not dissipated Called reactive power – units of measure: volt-ampere-reactive (VAR) Power is dissipated only through resistance – winding resistance, R W Energy dissipated as heat Called true power – units of measure: watts (W) Apparent Power – the combination of resistive (true) and reactive (imaginary) power – units of measure: volt- amperes (VA)

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved Related Topics – P2 Inductor Quality (Q) – is a figure of merit that indicates how close the inductor comes to the power characteristics of an ideal component where P X = the reactive power of the component, measured in VARs P Rw = the true power dissipation of the component, measured in watts

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved Related Topics – P3 Inductor Quality (Continued)

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved Related Topics – P4 Types of Inductors Air-Core: low Q Iron-core: higher Q, limited to low frequencies due to power losses Ferrite Core: highest Q, used in higher frequencies, low power loss

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved Related Topics – P5 Types of Inductors (Continued) Toroids

Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ All Rights Reserved Related Topics – P6 Types of Inductors (Continued) Chokes