PHY 712 Electrodynamics 10-10:50 AM MWF Olin 107 Plan for Lecture 14:
PHY 712 Electrodynamics 10-10:50 AM MWF Olin 107 Plan for Lecture 34:
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Transcript of PHY 712 Electrodynamics 10-10:50 AM MWF Olin 107 Plan for Lecture 34:
![Page 1: PHY 712 Electrodynamics 10-10:50 AM MWF Olin 107 Plan for Lecture 34:](https://reader030.fdocuments.us/reader030/viewer/2022032612/5681317d550346895d97f6d6/html5/thumbnails/1.jpg)
PHY 712 Spring 2014 -- Lecture 34 1
PHY 712 Electrodynamics10-10:50 AM MWF Olin 107
Plan for Lecture 34:
Special Topics in Electrodynamics:
Review – Scattering and interference phenomena
Course assessment forms
04/23/2014
![Page 2: PHY 712 Electrodynamics 10-10:50 AM MWF Olin 107 Plan for Lecture 34:](https://reader030.fdocuments.us/reader030/viewer/2022032612/5681317d550346895d97f6d6/html5/thumbnails/2.jpg)
PHY 712 Spring 2014 -- Lecture 34 204/23/2014
![Page 3: PHY 712 Electrodynamics 10-10:50 AM MWF Olin 107 Plan for Lecture 34:](https://reader030.fdocuments.us/reader030/viewer/2022032612/5681317d550346895d97f6d6/html5/thumbnails/3.jpg)
PHY 712 Spring 2014 -- Lecture 34 304/23/2014
![Page 4: PHY 712 Electrodynamics 10-10:50 AM MWF Olin 107 Plan for Lecture 34:](https://reader030.fdocuments.us/reader030/viewer/2022032612/5681317d550346895d97f6d6/html5/thumbnails/4.jpg)
PHY 712 Spring 2014 -- Lecture 34 404/23/2014
![Page 5: PHY 712 Electrodynamics 10-10:50 AM MWF Olin 107 Plan for Lecture 34:](https://reader030.fdocuments.us/reader030/viewer/2022032612/5681317d550346895d97f6d6/html5/thumbnails/5.jpg)
PHY 712 Spring 2014 -- Lecture 34 504/23/2014
![Page 6: PHY 712 Electrodynamics 10-10:50 AM MWF Olin 107 Plan for Lecture 34:](https://reader030.fdocuments.us/reader030/viewer/2022032612/5681317d550346895d97f6d6/html5/thumbnails/6.jpg)
PHY 712 Spring 2014 -- Lecture 34 604/23/2014
Review of radiation from antenna
Linear center-fed antennaz
r
qd/2
ˆ3 '0
0
,
' ',4
',
ˆsin | | ( ) ( )2
ikrik
kdk
ed r e
r
z xI y
r r
A r
J r
r zJ
![Page 7: PHY 712 Electrodynamics 10-10:50 AM MWF Olin 107 Plan for Lecture 34:](https://reader030.fdocuments.us/reader030/viewer/2022032612/5681317d550346895d97f6d6/html5/thumbnails/7.jpg)
PHY 712 Spring 2014 -- Lecture 34 704/23/2014
Linear center-fed antenna continued
/1
cos( '0
/2
)0
02
0
, ' 4
cos cos cos2 2
=2 sin
ˆ
sin | ' |2
ˆ
dikrik
d
ikr
zI edz e
r
kd kdI e
r
kdk z
z
z
A r
00
2
22
0
Time averaged power:
cos cos cos1 2 2
= 8 sin
kd kddP
Id
![Page 8: PHY 712 Electrodynamics 10-10:50 AM MWF Olin 107 Plan for Lecture 34:](https://reader030.fdocuments.us/reader030/viewer/2022032612/5681317d550346895d97f6d6/html5/thumbnails/8.jpg)
PHY 712 Spring 2014 -- Lecture 34 804/23/2014
Linear center-fed antenna continued
00
2
22
0
Time averaged power:
cos cos cos1 2 2
= 8 sin
kd kddP
Id
2
2 00 2 2
0
00 2 2
0
4
2
cos cos1 2
for = 8 sin
cos cos4 2
for 2
:
= 8 sin
:
dPkd I
d
dPkd I
d
![Page 9: PHY 712 Electrodynamics 10-10:50 AM MWF Olin 107 Plan for Lecture 34:](https://reader030.fdocuments.us/reader030/viewer/2022032612/5681317d550346895d97f6d6/html5/thumbnails/9.jpg)
PHY 712 Spring 2014 -- Lecture 34 904/23/2014
00
2
22
0
Time averaged power:
cos cos cos1 2 2
= 8 sin
kd kddP
Id
Linear center-fed antenna continued
Radiation patterns kd=m :p m=1 m=2 m=3
![Page 10: PHY 712 Electrodynamics 10-10:50 AM MWF Olin 107 Plan for Lecture 34:](https://reader030.fdocuments.us/reader030/viewer/2022032612/5681317d550346895d97f6d6/html5/thumbnails/10.jpg)
PHY 712 Spring 2014 -- Lecture 34 1004/23/2014
00
2
22
0
Time averaged power:
cos cos cos1 2 2
= 8 sin
kd kddP
Id
Linear center-fed antenna continued
Radiation patterns kd=m :p m=4 m=5 m=6
![Page 11: PHY 712 Electrodynamics 10-10:50 AM MWF Olin 107 Plan for Lecture 34:](https://reader030.fdocuments.us/reader030/viewer/2022032612/5681317d550346895d97f6d6/html5/thumbnails/11.jpg)
PHY 712 Spring 2014 -- Lecture 34 1104/23/2014
Antenna arrays
http://www.tennadyne.com/company.htm
z
x
rf
a
![Page 12: PHY 712 Electrodynamics 10-10:50 AM MWF Olin 107 Plan for Lecture 34:](https://reader030.fdocuments.us/reader030/viewer/2022032612/5681317d550346895d97f6d6/html5/thumbnails/12.jpg)
PHY 712 Spring 2014 -- Lecture 34 1204/23/2014
Antenna arrays z
x
rf
a
z’’
4 4z
/4 1
cos( )0 0
0/4
( 1) cos( )/20 0
ˆ, cos( )4
sin( cos( ) / 2)ˆ
2 sin( cos( ) / 2
)=
ikr Nikma
m
ikri N ka
I er dz kz e
r
I e Nkae
kr ka
A z
z
1
00
2
ˆ
4 4
, , , cos ( ) ( )N
i t
m
x y z I kz y x ma e
k zc
J z
![Page 13: PHY 712 Electrodynamics 10-10:50 AM MWF Olin 107 Plan for Lecture 34:](https://reader030.fdocuments.us/reader030/viewer/2022032612/5681317d550346895d97f6d6/html5/thumbnails/13.jpg)
PHY 712 Spring 2014 -- Lecture 34 1304/23/2014
Antenna arrays ( 1) cos( )/20 0
220 0
2
=
Time averaged power in x-y plane
sin( cos( ) / 2)ˆ,
2 sin( cos( ) / 2)
sin( cos( ) / 2)
8 sin( cos( )
:
)
/ 2
ikri N kaI e Nka
r ekr ka
I Nka
ka
cdP
d
A z
f
N=3 N=12