Download Fields and Waves I Lecture - Rensselaer Polytechnic Institute

Fields and Waves I
Lecture 1
Introduction to Fields and Waves
K. A. Connor
Electrical, Computer, and Systems Engineering Department
Rensselaer Polytechnic Institute, Troy, NY
These Slides Were Prepared by Prof. Kenneth A. Connor Using
Original Materials Written Mostly by the Following:
 Kenneth A. Connor – ECSE Department, Rensselaer Polytechnic
Institute, Troy, NY
 J. Darryl Michael – GE Global Research Center, Niskayuna, NY
 Thomas P. Crowley – National Institute of Standards and
Technology, Boulder, CO
 Sheppard J. Salon – ECSE Department, Rensselaer Polytechnic
Institute, Troy, NY
 Lale Ergene – ITU Informatics Institute, Istanbul, Turkey
 Jeffrey Braunstein – Chung-Ang University, Seoul, Korea
Materials from other sources are referenced where they are used.
Those listed as Ulaby are figures from Ulaby’s textbook.
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Overview




Why study E&M?
Review of 5 experiments
Introduction to transmission lines
Introduction to the course webpages
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Why Study E&M?
 Some good sources
• http://www.ece.northwestern.edu/ecefacul
ty/taflove/WhyStudy.pdf Some info from
this document follows. (Taflove)
• Others?
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Why take Fields and Waves?
• E and B are fundamental to Electrical Engineering
• if you have “V”, there is an “E”
• if you have “I”, there is a “B”
V is Voltage
I is Current
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E is Electric Field Intensity
B is Magnetic Flux Density
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Relationship with Circuit Theory
• Circuit Theory uses simplified (lumped) Models of components
The model, however, does not include:
• Details on how the components work
• Components are not made up of C,L,R
• Distributed Properties for example Transmission Lines
• Electromagnetic Waves - like mWaves, Radio Waves, Optics
• Applications such as Capacitive Sensors
• Noise
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Relationship with Circuit Theory
Many of these effects are more important at
High Frequency
Need to be considered when designing for High
Speed Applications
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HOWEVER
Current technology (with High Speed Computers) enables
accurate circuit simulation
Simulation Packages include:
a) SPICE (from UC Berkeley)
b) SABER (systems approach)
• Accurate simulation requires understanding of “ components”
and interactions
• Interactions also need to be described by Models
• Models are obtained by an understanding of EM Fields
Question: Why do companies spend resources on developing models?
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Why Study E&M?
Microwave energy scattering from missile antenna radome.
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(Taflove)
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Why Study E&M?
 The bedrock of introductory circuit analysis, Kirchoff’s current
and voltage laws, fail in most high-speed circuits. These must
be analyzed using E&M theory. Signal power flows are not
confined to the intended metal wires or circuit paths.
• Microwave circuits typically process bandpass signals at frequencies
above 3 GHz. Common circuit features include microstrip
transmission lines, directional couplers, circulators, filters, matching
networks, and individual transistors. Circuit operation is
fundamentally based upon electromagnetic wave phenomena.
• Digital circuits typically process low-pass pulses having clock rates
below 2 GHz. Typical circuits include densely packed, multiple
planes of metal traces providing flow paths for the signals, dc
power feeds, and ground returns. Via pins provide electrical
connections between the planes. Circuit operation is nominally not
based upon electromagnetic wave effects.
 The distinction between the design of these two classes is
blurring.
(Taflove)
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Why Study E&M?

False-color visualization (right) illustrating the coupling and
crosstalk of a high-speed logic pulse entering and leaving a
microchip embedded within a conventional dual in-line
integrated-circuit package (left). The fields associated with the
logic pulse are not confined to the metal circuit paths and, in fact,
smear out and couple to all adjacent circuit paths.
(Taflove)
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Review of 5 Experiments





Experiment
Experiment
Experiment
Experiment
Experiment
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1
2
3
4
5
–
–
–
–
–
Two-Wire Capacitor
Transformers
EMI Radiation
Motion Sensor
Transmission Lines
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Exp 1: Capacitor
Function
generator
input
Ground
rails
V out
Jumper
wires
R1
C1
50
Two Wires
8pF
V
V
V1
VOFF = 0
VAMPL = 10
FREQ = 30kHz
R2
10k
R3
10k
0
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Exp 1: Capacitor
200mV
OUTPUT
0V
-200mV
V(C1:2)
10V
INPUT
0V
SEL>>
-10V
0s
10us
20us
30us
40us
50us
60us
70us
80us
90us
100us
V(R1:2)
Time
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Exp 2: Transformers
 Combination should look like a transformer
 If acting as an ideal transformer, the voltage
ratio should be correct
 Transformers act more ideally at certain
frequencies
 Works better as a transformer when the
secondary is tightly wound on the primary
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Exp 3: EMI radiation and wave
propagation
Unshielded Wire
Coaxial Cable
Pomona 3788
•An unshielded wire can act like a simple antenna
•What frequencies are observed?
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Exp 4: Motion Sensor
Magnetic
Pickup
Coil
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Exp 4: Motion Sensor
0
100
80
60
40
20
0
-20
-40
-60
-80
-100
-120
0.
03
0.
05
0.
08
0.
1
0.
13
0.
15
0.
18
0.
2
0.
23
0.
25
Comparison of Position, Velocity and Acceleration
Acceleration
200 Times Velocity
15000 Times Position
Time
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The Analog Device Accelerometer
 The ADI
Accelerometer is an
excellent example of
a MEMS device in
which a large number
of very, very small
cantilever beams are
used to measure
acceleration. A
simplified view of a
beam is shown here.
http://www.flickr.com/photos/mitopencourseware/3362590885/
5/23/2017
ENGR-4300 Electronic
Instrumentation
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Exp 5: Transmission Lines
coax spool

Chan 1
~
Oscilloscope
function generator
Chan 2

terminator

The same signal passes through the short cable to channel 2 and the long cable (60100 meters) to channel 1.
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Exp 5: Transmission Lines
 What is observed?
• Phase shift between input and output
• Output signal is somewhat smaller than input on the long
cable
• When the terminating resistor is removed, the signal
changes
• The wires have finite resistance ( ~ 50 m meter)
 What can we conclude from this?
• Wire resistance is low so, for shorter cables, we can consider
transmission lines to be lossless
• What else?
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Transmission Lines
 Connect to circuit theory
 Demonstrate the need to understand R,
L, C, & G per unit length parameters
 Very useful devices (all EE, CSE, EPE
students will use them someday)
 Can be easily analyzed to find electric
and magnetic fields
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Information Card








Name
Major (s)
Class Year
Degree Concentration Area
Technical jobs, internships or co-op experiences
Other schools attended
Professional goals
Comments or questions
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Transmission Line
Fundamental Purpose of TL
Transfer signal/power
from A to B
EXAMPLES:
• Power Lines (60Hz)
• Coaxial Cables
• Twisted Pairs
• Interconnects (approximates a parallel plate capacitor)
• All have two conductors
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Transmission Line Effects
RELEVANT EFFECTS:
• Time Delays
• Reflections/Impedance Matching
TL effects more important at high f (or short t) and long lengths

E
and

H
effects are important for understanding
But, calculations use V and I for predicting effects
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Transmission Line Model
Cables have both L and C:
C between conductors
2 wire example:
I
L is a
series
effect
I
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Transmission Line Model
L
Model of SHORT SECTION:
C
L and C are distributed through the length of the cable
Model the full length as:
L
L
C
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L
L
C
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C
C
….etc.
27
Transmission Line Model
Does L -C combination behave like a cable?
How would you know?
Time Delay ~ same as cable delay
l  z
Each,
c  z
, represents a length of cable
l
c
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= inductance/length
= capacitance/length
28
Transmission Line Model
When is model of L - C combination valid?
• need z small
z  
• chosen z is a compromise
• works well at 600 kHz but not 6 MHz
At 6 MHz, the L - C model is a low pass filter but coax-cable is not
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Transmission Line Representation
As
z  0
limit
V ( z  z )
V( z )
I
V ( z  z )  V ( z )   L
I
t
l
I V V


t z
z
l  z
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Transmission Line Representation
Similarly,
I
V
 c 
z
t
 2V 
I
 I
 2V
 ( l  )  l  ( )  lc 2
2
z
t
t z
z
t
Obtain the following PDE:
 2V
 2V
 lc 2
2
z
t
z
Solutions are: f ( t  )
u
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These are functions
that move with
velocity u
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Transmission Line Representation
Functions that move with velocity u
Example:
At t=0,
cos( t 
cos( 

u

z)
u
z)
Wave
moving to
the right
t =1

At t =1 cos( 1 
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
u
u
z)
z
t =0
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Using PSpice
 We can use PSpice to do numerical
experiments that demonstrate how
transmission lines work
R1
VOFF = 0
V1
VAMPL = 10
FREQ = 1MegHz
50
V
T1
R2
50
0
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0
33
PSpice
R1
VOFF = 0
V1
VAMPL = 10
FREQ = 1MegHz
50
V
T1
V
R2
50
0
0
5.0V
OUTPUT
INPUT
0V
-5.0V
2.0us
V(R1:2)
2.5us
3.0us
3.5us
4.0us
4.5us
5.0us
V(T1:B+)
Time
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Sine Waves
 The form of the wave solution
 

A cos t  z  A cost  z

u 
 First check to see that these solutions have
the properties we expect by plotting them
using a tool like Matlab
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Sine Waves
 The positive wave
 
2f 


cos t  z  cos 2ft 
z


u 
u 
u
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Solutions to the Wave Equation
 Now we check to see that the sine waves are
indeed solutions to the wave equation

cost  z   sint  z
t

cost  z     sint  z
z
2
2
cos

t


z


cost  z


2
t
2
2
cos

t


z


cost  z


2
z
2
2 2
1 2
 

A cost  z  2 2 A cost  z  2 2 A cos t  z
2

u 
z
 t
u t
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Solutions to the Wave Equation
 Thus, our sine wave is a solution to the
voltage or current equation  2V
 2V
z
 if  

u
  lc
or
2
 lc
t 2
1
u
lc
 u = the speed of wave propagation
= the speed of light
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Velocity of Propagation
Hosfelt
 Check for RG58/U Cable
• Inductance per unit length is 0.25 micro Henries per
meter
• Capacitance per unit length is 100 pico Farads per
meter
1
1
109
1



 2 x108 m s
u
6
12
18
5
(
0
.
25
x
10
)(
100
x
10
)
25
x
10
lc
or 2/3 the speed of light
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From Digi-Key (Carol Cable)
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From Elpa (Lithuania)
Capacitance
Velocity ratio = .68
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Coaxial Cable Parameters
 Capacitance
 Inductance
o 
2 F
c
b m
ln
a
m bH
l
ln
2 a m
1
x10  9 F m
36
mo  4x10  7 H m
m  mr mo
  r o
23 May 2017
Ulaby
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For Next Time
 Download the Orcad PSpice Student
Version if you do not already have it.
 I will do some numerical experiments in
class using PSpice
 Do the reading
 Acquaint yourself with the course
webpages (open and WebCT)
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