phy 712 electrodynamics 11-11:50 am mwf olin 107 plan for...
TRANSCRIPT
04/24/2013 PHY 712 Spring 2013 -- Lecture 35 1
PHY 712 Electrodynamics11-11:50 AM MWF Olin 107
Plan for Lecture 35:
Read about antennas in Chap. 9
1. Power distribution of linear antenna
2. Interference effects
04/24/2013 PHY 712 Spring 2013 -- Lecture 35 2
04/24/2013 PHY 712 Spring 2013 -- Lecture 35 3
Signup for presentations:Schedule for PHY712 presentations -- please enter your own name replacing “presenter” and also list your presentation title replacing “title”. Of course, please do not change other student entries without their permission.
Monday April 29, 201311:00 - 11:15 -- Pete Diemer Magnetrons and Microwaves11:15 - 11:30 -- (Jiajie Xiao) (title)11:30 - 11:45 -- (Chaochao Dun) (Antireflection Thin Film)
Wednesday May 1, 201311:00 - 11:15 -- Katelyn Goetz Space Charge Limited Current Measurements11:15 - 11:30 -- Zach Lamport Dielectric properties of monolayer11:30 - 11:45 -- Xiaohua Liu Electron paramagnetic resonance
Thursday May 2, 20139:00 - 9:15 -- (David Montgomery) (Auroras)9:15 - 9:30 -- Ryan Godwin Drude Oscillator Model9:30 - 9:45 -- David Harrison Charges on a sphere9:45 - 10:00 -- (Evan Welchman) (Ewald Summation)
04/24/2013 PHY 712 Spring 2013 -- Lecture 35 4
04/24/2013 PHY 712 Spring 2013 -- Lecture 35 5
Review from Lecture 23:Maxwell’s equations in terms of vector and scalar potentials (Lorentz gauge)
41
:formequation General
1
/1
01:conditionLorentz
2
2
22
02
2
22
02
2
22
2
ftc
tc
tc
tc
LL
LL
LL
JAA
A
04/24/2013 PHY 712 Spring 2013 -- Lecture 35 6
Solution of Maxwell’s equations in the Lorentz gauge -- continued
cttttG /'''
1',';, rrrr
rr
',''1''
1''
,,:,fieldfor Solution
3
0
tfc
ttdtrd
ttt
f
rrrrr
rrr
04/24/2013 PHY 712 Spring 2013 -- Lecture 35 7
Electromagnetic waves from time harmonic sources
0,~,~0,,:conditioncontinuity that theNote
,~,:densityCurrent
,~,:densityCharge
rJrrJr
rJrJ
rr
ittt
et
etti
ti
,~4
,~or
,~4
1,~For
,~,:sourceGeneral
0
0
rr
rr
rr
i
ti
Jf
f
eftf
04/24/2013 PHY 712 Spring 2013 -- Lecture 35 8
,'~'
',~
,'~'1''
1''
,~,~
',''1''
1''
,,
'3
0
'3
0
3
0
tii
tif
ti
tif
ti
f
eferde
efc
ttdtrd
ee
tfc
ttdtrd
tt
c
rrr
r
rrrrr
rr
rrrrr
rr
rr
Electromagnetic waves from time harmonic sources –continued:
04/24/2013 PHY 712 Spring 2013 -- Lecture 35 9
Electromagnetic waves from time harmonic sources –continued:
,'~'
'4
1,~,~
)gauge,(Lorentzpotentialscalar For
'3
00
rrr
rrrr
ikerd
ck
,'~'
'4
,~,~
)gauge,(LorentzpotentialFor vector
'30
0
rJrr
rArArr
ikerd
ck
04/24/2013 PHY 712 Spring 2013 -- Lecture 35 10
Consider antenna source
x
y
zr
q
f
d
d
ck
dzdyxzdkI
for sinˆ,~ zrJ
04/24/2013 PHY 712 Spring 2013 -- Lecture 35 11
....3,2,1;
for sinˆ,~
ndn
ck
dzdyxzdkI
zrJ
Consider antenna source -- continued
n=1
n=3
n=2
04/24/2013 PHY 712 Spring 2013 -- Lecture 35 12
Consider antenna source -- continued
....3,2,1;
for sinˆ,~
ndn
ck
dzdyxzdkI
zrJ
zdkedzIre
erdredr
erd
d
d
ikzikr
ikikr
ik
sin4
ˆ,~
,'~'4
,~For
,'~'
'4
,~
:sourcefrompotentialVector
cos0
ˆ30
'30
q
zrA
rJrA
rJrr
rA
r'r
rr
04/24/2013 PHY 712 Spring 2013 -- Lecture 35 13
Consider antenna source -- continued
20
cos0
sincoscoscos2
4ˆ
sin4
ˆ,~
kdkdIkre
zdkedzIr
e
ikr
d
d
ikzikr
z
zrA
22
20
222
0
2*2
0
sincoscoscos
8
,~ˆ,~2
,~,~ˆ2
1,~ˆˆ,~
,~ˆ,~,~:zoneradiation In the
kdkdIcddP
rckrddP
ikc
ik
rArrArBrEr
rArrrE
rArrArB
04/24/2013 PHY 712 Spring 2013 -- Lecture 35 14
Consider antenna source -- continued
22
20
sincoscoscos
8
kdkdIc
ddP
n=1
n=3
n=2
04/24/2013 PHY 712 Spring 2013 -- Lecture 35 15
Consider antenna source -- continued
22
20
sincoscoscos
8
kdkdIc
ddP
n=1 n=3n=2
04/24/2013 PHY 712 Spring 2013 -- Lecture 35 16
Radiation from antenna arrays
z y
x2d
a
f
....3,2,1;
for 1sinˆ,~ 12
1
nd
nc
k
dzdyajNxzdkIN
j
zrJ
04/24/2013 PHY 712 Spring 2013 -- Lecture 35 17
Radiation from antenna arrays -- continued
f
f
f
f
cossinsincossin12sin
sin4
ˆ,~
for 1sinˆ,~
,'~'4
,'~'
'4
,~
:sourcearray frompotentialVector
21
21
cossin
coscossin0
12
1
ˆ30'
30
kaNkae
zdkedz Ier
e
dzdyajNxzdkI
erdr
eerd
N
Nj
ikaj
d
d
ikzN
Nj
ikajikr
N
j
ikikrik
zrA
zrJ
rJrJrr
rA r'rrr
04/24/2013 PHY 712 Spring 2013 -- Lecture 35 18
Radiation from antenna arrays -- continued
2
21
212
22
0
22
0
22*2
0
cossinsincossin12sin
sincoscoscos
8
,~ˆ,~2
,~,~ˆ2
1,~ˆˆ,~
,~ˆ,~,~:zoneradiation In the
ff
kaNkakdkdIc
ddP
crkrddP
ikc
ik
rArrArBrEr
rArrrE
rArrArB
N=2;a=d/2; f0
N=0
N=2;a=d; f0