FOWLER CHAPTER 11 LECTURE 11 INDUCTANCE. INDUCTANCE, CHAPTER 11 OPPOSES CHANGE OF CURRENT IN A CIRCUIT. DEVICES THAT USE INDUCTANCE (L) ARE CALLED INDUCTORS.

FOWLER CHAPTER 11LECTURE 11 INDUCTANCE

INDUCTANCE, CHAPTER 11OPPOSES CHANGE OF CURRENT IN A CIRCUIT.DEVICES THAT USE INDUCTANCE (L) ARE CALLED INDUCTORS.A.K.A. AS CHOKES, REACTORS, COILS.INDUCTANCE IS THE RESULT OF A VOLTAGE INDUCTED IN A CONDUCTOR FROM A MAGNETIC FIELD.

CES 2009 - Kitchen of the Future From Powermat

http://www.youtube.com/watch?v=Z9a_Ihhtnx4

WHEN CURRENT FLOWS A MAGNETIC FIELD IS CREATED AROUND THIS WIRE. THIS EXPANDINGFIELD INDUCES ITS OWN SMALL VOTAGE IN THE WIRE.IF THE FLUX IS EXPANDING, POLARITY IS IN THE SAME DIRECTION AS THE CURRENT FLOW IN THE WIRE.IF THE FLUX IS COLLASPING, THE FLUX INDUCED IN THE WIRE IS OF THE OPPOSITE POLARITY.

IF THE FLUX IS COLASPING, THE FLUX INDUCES A CURRENT IN THE WIRE OF THE OPPOSITE POLARITY.THIS IS CALLED SELF INDUCTANCE.

INDUCTANCE OF A WIRE CAN BE INCREASED BY FORMING THE WIRE IN A COIL.

http://www.youtube.com/watch?v=NgwXkUt3XxQInductor basics

http://www.youtube.com/watch?v=X2e9x104AnEDC Theory 13 Segment 3A - Inductance & the Inductor

MUTUAL INDUCTANCE P278

OCCURS WHEN THE MAGNETIC FIELD FROM ONE WIRE INDUCTS A CURRENT IN A SEPARATEWIRE. TRANSFORMERS WORK USING MUTUAL INDUCTANCE.

YOU TUBE:DC THEORY 13 SEGMENT 3B http://www.youtube.com/watch?v=aphgli-RHm0

CONTERELECTROMOTIVE FORCE (CEMF) P.278IS THE VOLTAGE INDUCED IN A CONDUCTOR BY ITS OWN MAGNETIC FIELD IS CALLEDCOUNTER EMF OF BACK EMF.

LENZ’S LAWA CEMF POLARITY ALWAYS OPPOSES THE CURRENT THAT CREATED IT.

Eddy Currents and Lenz's Law http://www.youtube.com/watch?v=kU6NSh7hr7Q

ENERGY STORAGE AND CONVERSION. P.279

CURRENT FLOW THRU A CONDUCTOR CREATES A MAGNETIC FIELD.

INDUCTORS CONVERT ELECTRICAL ENERGY INTO MAGNETIC ENERGY.

AS CURRENT DECREASES MAGNETIC ENERGY IS CONVERTED BACK TO ELECTRICALENERGY.

INDUCTANCE DOES NOT CONVERT ELECTRCIAL ENERGY INTO HEAT, ONLY RESISTANCE CAN.

http://www.youtube.com/watch?v=STDlCdZnIswMAKE presents: The Inductor

FOR THESE 2 QUARTER CYCLES,ENERGY IS TAKEN FROM THE CURRENT. (ELECTRICAL TO MAGNETIC)

FOR THESE 2 QUARTER CYCLES, ENERGY IS RETURNED TO THE CURRENT. (MAGNETIC TO ELECTRICAL)

INDUCTORS CAUSE NO NET ENERGY LOSS.

I

INDUCTANCE OF A INDUCTOR DEPENDS ON 4 FACTORS.

1. TYPE OF CORE MATERIAL; AIR OR IRON CORE. Fe IS BETTER THEN AIR, SINCE ITS PERMEABILITY IS HIGHER ( ABILITY TO CONDUCT FLUX). CARRIES MORE FLUX. MORE FLUX CHANGE, MORE CEMF.

HENRY P. 2801 HENRY (H) PRODUCES 1 V OF CEMF THE WHEN CURRENT CHANGES AT A RATE OF 1A/S.

2.THE # OF TURNS OF WIRE; MORE TURNS, GREATER THE MAGNETIC FIELD.

3.THE DIAMETER OF THE COIL (CORE): WITH LARGER COIL DIAMETERS ALL THE FLUX LINES GO THRU THE COIL, WHICH INCREASES THE FLUX DENSITY.

4.SPACING BETWEEN TURNS OF WIRE: WHEN DISTANCE DECREASES, FIELD STRENGTH INCREASES,SINCE FLUX LINES LINK TOGETHER.

TYPES OF INDUCTORS P.282CLASSIFIED BY THE TYPE OF MATERIAL USED FOR THE CORE. CAN BE FIXED OR VARIABLE.CORES CAN MAGNETIC OR NONMAGNETIC.

INDUCTOR SYMBOLS

IN VARIABLE INDUCTORS, INDUCTION IS CHANGED BY MOVING THE POSITION OF THE CORE.

AIR CORE

OFTEN WAPPED AROUND NONMAGENTIC FORM WITH HIGH RELUCTANCE (ABOUT THESAME AS AIR.) OTHER AIR CORE MATERIALS USED:CERAMIC, PHENOLIC (HARD RESIN, MADEOF PHENOL) , USUALLY LESS THAN 5mH.

FERRITE (Fe ALLOY ), POWERED CORE, L LESS THAN 200mH

FERRITE CORE IN AM RADIO ANTENNAS

TOROID CORE: FLUX LOOPS ALL EXIST INSIDE THE CORE.

SMD INDUCTORS: L RANGES FROM nH TO mH

Fig. 11-11 Surface mount inductor positioned in the end of a small paper clip.

MOLDED INDUCTORSARE INCASED IN INSULATION MATERIAL TO PROTECT WINDINGS,CORES CAN BE AIR, FERRITE, POWERED Fe.

Band 1 2 3 4

Meaning

1st Digit

2nd Digit

Multiplier (No. of zeros)

Tolerance %

Gold     x 0.1 (divide by 10) +/-5%

Silver     x 0.01 (divide by 100) +/-10%

Black 0 0 x1 (No Zeros) +/-20%

Brown 1 1 x10 (0)  

Red 2 2 x100 (00)  

Orange 3 3 x1000 (000)  

Yellow 4 4 x10000 (0,000)  

Green 5 5    

Blue 6 6    

Violet 7 7    

Grey 8 8    

White 9 9    

SHIELDED INDUCTORS

SHIELDED FROM EXTERNAL MAGNETIC FILEDS TO PREVENT INTERFERENCE.SHEILD ITSELF IS MADE FROM MAGNETIC MATERIAL.

LAMINATED Fe CORE.L RANGES FROM 0.1 H TO 100H.MADE FROM E AND I LAMINATIONS, STACKED TOGETHER FOR DESIRED THICKNESS.

WINDINGS ARE PLACED ON THE CENTER OF THE “E”. THIS SECTION IS TWICE AS THICK,SINCE IT CARRIES TWICE AS MUCH FLUX.

INDUCTION DEPENDS ON THE AMOUNT OF CURRENT FLOWING THRU IT.PERMABILITY DECREASES AS FLUX INCREASES.WHEN SATURATED ALMOST NO CHANGE IN FLUX OCCURS.

l

3 PHASE TRANSFORMER

3 PHASE TRANSFORMER CORES.

FILTER CHOKES P. 285

AKA LAMINATED Fe CORE INDUCTORSUSED IN POWER SUPPLIES TO SMOOTH OUT PULSATING D.C.

RF CHOKES USED IN HIGH FREQUENCY RADIO’S ETC.

RATING OF INDUCTORS.RATED BY:1. DC RESISTANCE: THE RESISTANCEOF WIRE IN THE COIL, CALLED OHMIC RESISTANCE.

2. CURRENT: AMOUNT OF CURRENT INDUCTOR CAN CARRY WITHOUT HEATING.

3. VOLTAGE: HOW MUCH VOLTAGE THE WINDING INSULATION CAN HANDLE BEFORE BREAKING DOWN.

4. QUALITY: RATIO OF REACTANCE TO RESISTANCE. HIGHER THE QUALITY THE BETTER.

5.TOLERANCE: +/- 1% COSTLY +/- 10% TYPICAL

INDUCTORS IN DC CIRCUITS.

INDUCTORS IN DC CIRCUITS FORCE CURRENT TO RISE SLOWLY.THIS IS DUE TO THE INDUCTORS CEMF.THE TIME FOR THIS TO OCCUR DEPENDS ON THE AMOUNT OF INDUCTANCE AND RESISTANCE.

IDEAL INDUCTORS IN AC CIRCUITS

IDEAL INDUCTORS HAVE NO RESISTANCE.NO ENERGY CONVERSION TAKES PLACE.NO ELCTRICAL ENERGY IS CONVERTED TO HEAT.INDUCTORS CONTROL CIRCUIT CURRENT WITHOUT POWER LOSS.

INDUCTIVE REACTANCE ( XL)

OPPOSITION OF AN INDUCTOR TO AC. XL COMES FROM THE CEMF OF THE INDUCTOR.VOLTAGE LEADS CURRENT BY 90° IN A IDEAL INDUCTOR.

XL

INDUCTIVE REACTANCE EQUATION

XL =2πfL = 6.28fLXL IS DIRECTLY PROPORINAL TO FREQUENCY f AND INDUCTANCE LWHY?1. AS f INCREASES I CHANGES MORE RAPIDLY, MORE CEMF AND REACTANCE ARE PRODUCED.2. AS L INCREASES THE MORE FLUX CHANGES AS THE CURRENT CHANGES. DO E. 11-1 P.289

OHM’S LAW FOR XL

VL = ILXLDO E.11-3 P.290

POWER IN INDUCTORS

IDEAL INDUCTOR USES NO POWER SINCE I AND V ARE 90° OUT OF PHASE.

P = IVcosØ , SINCE I AND V ARE 90° OUT OF PHASE COS90° = 0THEREFORE P = IV(0) = 0W

NO NET CONVERSION OF ENERGY TAKES PLACE.

ENERGY IS TRANSFERED BACK AND FORTH BETWEEN THE SOURCE AND THE INDUCTOR.F.11-23 P.291

REAL INDUCTORS IN AC CIRCUITS.REAL INDUCTORS USE POWER, SINCE THEY HAVE RESISTANCE AS WELL AS REACTANCE.

QUALITY: Q = XL/RTHE HIGHER THE Q OF A COIL ,THE LESS POWER IT USES.

IMPEDANCE (Z)COMBINATION OF RESISTANCE AND REACTANCE.SINCE INDUCTORS HAVE BOTH RESISTANCE AND REACTANCE, THERE IS IMPEDANCE IN AC CIRCUITS. SINCE REACTANCE IS HIGH AND RESISTANCE IS LOW. WE CAN SPECIFIC ANY INDUCTOR INTERMS OF ITS REACTANCE ONLY.

POWER LOSS IN INDUCTORSSKIN EFFECT :ELECTRONS MOVE TO OUTER SURFACE OF A CONDUCTOR AT HIGHER f, CAUSES INCREASED RESISTANCE WHICH CAN BE MEASURED WITH A VOM.

EFFECTIVE RESISTANCE AT INCREASED f IS GREATER THEN THAT MEASURED WITH A VOM.

LITZ WIREMULTICONDUCTOR CABLE OF APPROX. 44 GAUGE, INSULATED WIRE TWISTED TOGETHER, WHICH PROVIDES MORE SURFACE AREA THEN A SINGLE STRANDED CONDUCTOR, WHICH RESULTS IN LOWER RESISTANCE AT HIGHER f.

POWER LOSS IN Fe CORE INDUCTORS1. LOSS FROM CORE MATERIAL, CAUSED BY CURRENT HEATING FROM INDUCTED

VOLTAGES. 2.LOSS IN WINDINGS, HEATING CAUSED BY THE REVERSALS OF MAGNETIC FIELD.

INDUCTORS IN PARALLEL ( FINDING TOTAL INDUCTANCE)SAME AS RESISTORS IN PARALLEL

nT LLLLL

1....

1111

321

21

21

LL

LLLT

GENERAL METHOD

TWO INDUCTORS IN PARALLEL

N EQUAL INDUCTORS IN PARALLEL

n

LLT

INDUCTIVE REACTANCE IN PARALLEL

LnLLL

L

XXXX

XT 1

...111

1

321

21

21

LL

LLL XX

XXX

T

n

XX LLT

GENERAL METHOD

TWO INDUCTORS IN PARALLEL

N EQUAL INDUCTORS IN PARALLEL

YOU CAN FIND XLT BY THE ABOVE METHOD OR

TL LfXT

28.6IN PARALLEL INDUCTOR CIRCUITS THE LOWEST VALVE INDUCTOR CARRIES THE MOST CURRENT.

INDUCTORS IN SERIES P.295SERIES INDUCTANCES AND REACTANCES USE THE SAME FORMUALS AS SERIES RESISTORS.

nT LLLLL ...321

nLLLLTL LXXXX ...321

YOU CAN FIND XLT BY THE ABOVE METHOD OR

TL LfXT

28.6

OHM’S LAW

TTT LLL XIV

DC Electronics Theory 13 Segment 5 - Connecting Inductors http://www.youtube.com/watch?v=GXcxswDcUbI

TIME CONSTANTS FOR RL CIRCUITS

SIMILAR TO RC TIME CONSTANT, EXCEPT SUBSITUDE CURRENT FOR VOLTAGE

TIME CONSTANT(T) T = L/R

http://www.youtube.com/watch?v=-vznuNkEBtoRL TIME CONSTANT

1 2 3 4 5

100%

of

fin

al c

urr

ent

Time constants0

0

RL Time Constant -- Rising I

After 1 T, the inductor’s current is 63.2 % of final value. After 2 T, the inductor’s current is 86.5 % of final value.

After 3 T, the inductor’s current is 95.0 % of final value.After 4 T, the inductor’s current is 98.2 % of final value.

After 5 T, the inductor’s current is 99.3 % of final value.

The current has essentially reached its final value after 5 T.

After 1 T, the current is reduced by 63.2 % .After 2 T, the current is reduced by 86.5 % .

After 3 T, the current is reduced by 95.0 % .After 4 T, the current is reduced by 98.2 % .

After 5 T, the current is reduced by 99.3 % .

The current is essentially zero after 5 T.

Time constants0 1 2 3 4 5

100

0

% o

f st

arti

ng

curr

ent

RL Time Constant -- Falling I

36.8%

13.5%5.0% 1.8% 0.7%

PREVENTING MUTUAL INDUCTANCE

1. BY ORIENTATION OF THE AXIS.2. PHYSICAL SEPARATION3. SHEILDING

INDUCTORS IN SERIES P.295SERIES INDUCTANCES AND REACTANCES USE THE SAME FORMUALS AS SERIES RESISTORS.

nT LLLLL ...321

nLLLLTL LXXXX ...321

YOU CAN FIND XLT BY THE ABOVE METHOD OR TL LfXT

28.6OHM’S LAW FOR INDUCTORS

TTT LLL XIV

TOTAL INDUCTANCE

INDUCTIVE REACTANCE

INDUCTORS IN PARALLEL ( FINDING TOTAL INDUCTANCE)SAME AS RESISTORS IN PARALLEL

nT LLLLL

1....

1111

321

21

21

LL

LLLT

GENERAL METHOD

TWO INDUCTORS IN PARALLEL

N EQUAL INDUCTORS IN PARALLELn

LLT

LnLLL

L

XXXX

XT 1

...111

1

321

21

21

LL

LLL XX

XXX

T

n

XX LLT

GENERAL METHOD

TWO INDUCTORS IN PARALLEL

N EQUAL INDUCTORS IN PARALLEL

YOU CAN FIND XLT BY THE ABOVE METHOD OR

TL LfXT

28.6

321 LLLL IIIIT

TOTAL CURRENTNT LLLLL IIIII

321

TOTAL CURRENT