Download Dipole Antenna

Antennas/Radiation
Six 22 m antennas comprising the Australia Telescope
Compact Array (ATCA)
Why do moving charges radiate?
http://www.cco.caltech.edu/~phys1/java/
phys1/MovingCharge/MovingCharge.html
Hertzian Dipole
Static
charge
Uniform
velocity
Sudden
acceleration
Uniform
acceleration
p = I0l/w
Eq = m0 d2p/dt2 x sinqq/4pr = (qm0/4p)a(t)sinqq/r
•
•
•
•
Need accelerating charges a(t)
Transverse field components are the ones to notice Eq
1/r dependence (radiation fields propagate far away)
Angle dependence (radiate perp. to oscillation)  sinq
(Remember Brewster angle. Also watch kinks)
Shortening  Cerenkov Radiation
1/[1-vcosq/c]
Source outruns wave
Front falls behind,
like the wake of
a boat
v < c/n
v > c/n
Why do moving charges radiate?
Rest position of charge
at t=0
Charge stops
accelerating here
at t=Dt
Present position of
charge uniformly moving
at time t
First (larger) sphere launched at t=0 (left red dot)
Second (smaller) launched at t=Dt (middle one)
Both have evolved to their current sizes at t when charge is at the rt. dot
Why do moving charges radiate?
Inside smaller sphere:
see present uniformly moving
charge and its radial field
Outside larger sphere:
See original static charge
and its radial field
Shaded area: created during acceleration
0 < t < Dt
Here fields bend to connect the two other radial fields
Why do moving charges radiate?
The kinks in this “sphere of influence” propagate
as radiation fields. Note that they are angle-dependent
and don’t decrease as fast with radius.
Why do moving charges radiate?
Optical “Shock Front”
Kink
Propagates outwards
at speed of light
Eq q
q
vt
Er = q/4pe0r2
r=ct
v=aDt
Eq = Er (vtsinq/cDt)
= (q/4pe0c2)(vsinq/Dt)(1/ct)
Eq q
q
vt
Er = q/4pe0r2
r=ct
v=aDt
Eq = (qm0/4p)asinq/r
Transverse E is radiated
Eq(t) = (qm0/4p)[a(t’)]sin(q)/r
Hf(t) = Eq/Z0 = (q/4pc)[a(t’)]sin(q)/r
S = EqHf  a2sin2(q)/r2
P ~ S.r2dW ~ constant (Larmor formula)
t’ = t – r/c
Electrostatics, ∫E.dA independent of r
(Flux field conserved)
EM Radiation, ∫S.dA independent of r
(Flux power conserved)
What about oscillating charges
Kinks turn into loops
http://www.falstad.com/emwave1/
http://www-antenna.ee.titech.ac.jp/~hira/hobby/edu/em/smalldipole/smalldipole.html
Disconnect between outside and inside
Kinks/loops
Eq ~ m0qasinq/4pr
Hj ~ Eq/Z0
Hertzian Dipole (far field)
Delay effect
A ~ m0Idej(wt-bR)/4pR
^
= [m0wjpej(wt-bR)/4pR]z
^
^
= [m0wjpej(wt-bR)/4pR](Rcosq-qsinq)
Assume v << c so we ignore
Doppler ‘shortening’
From A to B
^
R^
Rq
B =  x A = ∂/∂R ∂/∂q
AR
RAq
^
Rsinqj
2sinq
/R
∂/∂j
RsinqAj
2
^
= m0p0jwej(wt-bR)sinqj(1+jbR)/4pR
From B to E
^
^
R
Rq
m0e0jwE =  x B = ∂/∂R ∂/∂q
BR
RBq
^
Rsinqj
2sinq
/R
∂/∂j
RsinqBj
E has two parts
^
3
^
E1 = p0ej(wt-bR)(1+jbR)(2Rcosq+qsinq)/4pe
R
0
Oscillatory dipolar field
^
E2 = (m0sinq/4pR)(d2p/dt2)q
Transverse radiation field
Hertzian Dipole
p = I0l/w
E = E1 + E2
E1 = p0[sin(wt-br) + br.cos(wt-br)]
x [2cosqr + sinqq]/4pe0r3
Usual dipolar field, with oscillations
E2 = m0w2p0sin(wt-br)sinqq/4pr
= m0 d2p/dt2 x sinqq/4pr
= (qm0/4p)asinqq/r
Transverse radiation field
Radiation Patterns
Transverse
radiation field
completes loops
Dipole field
Flipped
Dipole field
from
oscillation
term
cos(wt-bR)
Oscillatory
term has a
node
Half-wave antenna
I = I0ejwtsin(2pz/l) = I0ejwtsin(bz)
L = l/2
Half-wave antenna
Many small dipoles, for each of which
dEq ~ m0wI(z)dzsinqej(wt-bR’)/4pR’
dz
z q
R
Far field:
Eq ~ jI0c2ej(wt-bR) F(q)/4pe0R
F(q) = cos[(p/2)cosq]/sinq
Half-wave antenna
Far field:
Eq ~ jI0c2ej(wt-bR) F(q)/4pe0R
F(q) = cos[(p/2)cosq]/sinq
Slightly tighter than
point dipole
L=l
L = 1.5 l
Parabolic Reflector
(Dish Antenna)
http://www.antenna-theory.com/antennas/dipole.php