Download 150LECTURE11CHAPTER11INDUCTORS Lecture Notes Page

FOWLER CHAPTER 11
LECTURE 11 INDUCTANCE
INDUCTANCE, CHAPTER 11
OPPOSES 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 EXPANDING
FIELD 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.
Inductor basics
http://www.youtube.com/watch?v=NgwXkUt3XxQ
DC Theory 13 Segment 3A - Inductance & the Inductor http://www.youtube.com/watch?v=X2e9x104AnE
MUTUAL INDUCTANCE P278
OCCURS WHEN THE MAGNETIC FIELD FROM ONE WIRE INDUCTS A CURRENT IN A SEPARATE
WIRE. TRANSFORMERS WORK USING MUTUAL INDUCTANCE.
YOU TUBE:DC THEORY 13 SEGMENT 3B
http://www.youtube.com/watch?v=aphgli-RHm0
CONTERELECTROMOTIVE FORCE (CEMF) P.278
IS THE VOLTAGE INDUCED IN A CONDUCTOR BY
ITS OWN MAGNETIC FIELD IS CALLED
COUNTER EMF OF BACK EMF.
LENZ’S LAW
A 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 ELECTRICAL
ENERGY.
INDUCTANCE DOES NOT CONVERT ELECTRCIAL ENERGY INTO HEAT, ONLY RESISTANCE CAN.
MAKE presents: The Inductor
http://www.youtube.com/watch?v=STDlCdZnIsw
FOR THESE 2 QUARTER CYCLES,ENERGY IS TAKEN
FROM THE CURRENT. (ELECTRICAL TO MAGNETIC)
I
FOR THESE 2 QUARTER CYCLES, ENERGY IS RETURNED TO
THE CURRENT. (MAGNETIC TO ELECTRICAL)
INDUCTORS CAUSE NO NET ENERGY LOSS.
HENRY P. 280
1 HENRY (H) PRODUCES 1 V OF CEMF THE WHEN
CURRENT CHANGES AT A RATE OF 1A/S.
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.
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.282
CLASSIFIED 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 THE
SAME AS AIR.)
OTHER AIR CORE MATERIALS USED:CERAMIC, PHENOLIC (HARD RESIN, MADE
OF 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 INDUCTORS
ARE INCASED IN INSULATION MATERIAL TO PROTECT WINDINGS,
CORES CAN BE AIR, FERRITE, POWERED Fe.
Band
1
2
3
4
Meanin
g
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%
+/-20%
Black
0
0
x1 (No Zeros)
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 CORES.
3 PHASE TRANSFORMER
FILTER CHOKES P. 285
AKA LAMINATED Fe CORE INDUCTORS
USED 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 = 6.28fL
XL IS DIRECTLY PROPORINAL TO FREQUENCY f AND INDUCTANCE L
WHY?
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 = ILXL
DO 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° = 0
THEREFORE 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/R
THE 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 INDUCTORS
SKIN 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 WIRE
MULTICONDUCTOR 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 INDUCTORS
1. 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
GENERAL METHOD
1
1 1
1
1
   .... 
LT L1 L2 L3
Ln
TWO INDUCTORS IN PARALLEL
N EQUAL INDUCTORS IN PARALLEL
L1  L2
LT 
L1  L2
L
LT 
n
INDUCTIVE REACTANCE IN PARALLEL
GENERAL METHOD
X LT 
1
1
1
1
1


... 
X L1 X L 2 X L 3
X Ln
TWO INDUCTORS IN PARALLEL
X LT
N EQUAL INDUCTORS IN PARALLEL
X L1  X L 2

X L1  X L 2
X LT
XL

n
YOU CAN FIND XLT BY THE ABOVE METHOD OR
X LT  6.28  f  LT
IN PARALLEL INDUCTOR CIRCUITS THE LOWEST VALVE INDUCTOR CARRIES THE MOST CURRENT.
INDUCTORS IN SERIES P.295
SERIES INDUCTANCES AND REACTANCES USE THE SAME FORMUALS AS SERIES RESISTORS.
LT  L1  L2  L3 ...  Ln
X LT  X L 1  X L 2  X L 3 ...  LL n
YOU CAN FIND XLT BY THE ABOVE METHOD OR
X LT  6.28  f  LT
OHM’S LAW
VLT  I LT  X LT
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
RL TIME CONSTANT
http://www.youtube.com/watch?v=-vznuNkEBto
RL Time Constant -- Rising I
% of final current
100
0
0
1
2
5
3
4
Time constants
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.
RL Time Constant -- Falling I
% of starting current
100
0
36.8%
13.5%
0
1
5.0%
2
3
Time constants
1.8%
4
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.
0.7%
5
PREVENTING MUTUAL INDUCTANCE
1. BY ORIENTATION OF THE AXIS.
2. PHYSICAL SEPARATION
3. SHEILDING
INDUCTORS IN SERIES P.295
SERIES INDUCTANCES AND REACTANCES USE THE SAME FORMUALS AS SERIES RESISTORS.
TOTAL INDUCTANCE
INDUCTIVE REACTANCE
LT  L1  L2  L3 ...  Ln
X LT  X L 1  X L 2  X L 3 ...  LL n
YOU CAN FIND XLT BY THE ABOVE METHOD OR
OHM’S LAW FOR INDUCTORS
X LT  6.28  f  LT
VLT  I LT  X LT
TOTAL CURRENT
I LT  I L1  I L2  I L3
INDUCTORS IN PARALLEL ( FINDING TOTAL INDUCTANCE)SAME AS RESISTORS IN PARALLEL
1
1 1
1
1



....

GENERAL METHOD
LT L1 L2 L3
Ln
L1  L2
L

TWO INDUCTORS IN PARALLEL
T
L1  L2
N EQUAL INDUCTORS IN PARALLEL LT 
L
n
X LT 
GENERAL METHOD
X LT 
XL
n
YOU CAN FIND XLT BY THE ABOVE METHOD OR
X LT  6.28  f  LT
1
1
1
1


... 
X L1 X L 2 X L 3
X Ln
TWO INDUCTORS IN PARALLEL
TOTAL CURRENT
N EQUAL INDUCTORS IN PARALLEL
1
X LT
X L1  X L 2

X L1  X L 2
I LT  I L1  I L2  I L3  I LN