Hertz Dipole
Hertz Dipole
Hertz Dipole
Antennas
What is an antenna
Types of antennas
Reciprocity
Hertzian dipole
near field
far field: radiation zone
radiation resistance
radiation efficiency
Antennas convert currents to waves
An antenna is a device that converts a time-varying
electrical current into a propagating electromagnetic wave.
Since current has to flow in the antenna, it has to be made
of a conductive material: a metal.
atoms:
240 120
210 150
180
N electrons/m3
or they are freely
flowing (like a
time-varying
area A
current in a wire):
distance vave t
Reciprocity
qa t sin
E r, t
4 0 rc 2
Note that the radiated electric field is proportional to the
acceleration of the charge.
z Since Maxwell’s equations are linear:
a small E, B a t
metal
when a charge acceleration gives rise
element to a field, the same field can induce the
containing
accelerating same acceleration:
charges
4 0 rc 2
y a t E r, t cause effect
q sin
x
Antenna reciprocity: a receiving antenna’s properties
are identical to the transmitting properties of the same
antenna when it is used as a transmitter.
Antenna reciprocity
Antenna reciprocity: a receiving antenna’s properties
are identical to the transmitting properties of the same
antenna when it is used as a transmitter.
Properties: this includes
everything about the
antenna
• antenna gain
• radiation pattern
• radiation resistance e.g. this antenna transmits mostly in
• polarization one particular direction. It also receives
mostly from that same direction.
• bandwidth
V(t)
The Hertzian dipole antenna
The Hertzian dipole is a linear d <<
antenna which is much shorter than
the free-space wavelength: V(t)
For our purposes, we can treat this as a
wire of infinitesimal length d, carrying a
current I(t) = I0 cos(t) → I0 ejt.
d
y unit vector is not shown in this diagram.)
s
co
First limiting case: very near the antenna. So: k0r << 1
In this case, the 1/r3 terms are the only ones that
matter in the E-field expression. Also, exp(jk0r) ~ 1.
I0d
E r , , t 2 cos ˆ
r sin ˆ e jt
j 0 4 r 3
4 r 2
which is the same result one
finds for the static magnetic field
of a current element I0d (again
except for the time dependence).
The near field is the quasi-static regime
Very close to the antenna, the electric and magnetic fields
are the same as what one finds in electrostatics, except
that they oscillate in magnitude according to ejt (just as the
current in the antenna does).
In this case, the 1/r terms are the only ones that matter.
Also, exp(jk0r) is no longer equal to 1.
0 I 0 d e jk0 r jt ˆ
E r , , t j sin
4 r
The E and B fields are:
0 I 0 d e jk0 r jt ˆ
B r , , t j sin
4 c0 r
1 2
Pave I R
2
2 0 d 2 2 d2
Rrad 2 Z0 2
3 0 3
Rrad
Rrad ROhmic