Antenas

Antennas

Antennas
Transmitter

I
Transmission Line

Transmitting Antenna

Electromagnetic Wave I

Receiver

I
Transmission Line

Receiving Antenna

Electromagnetic Wave I

Antennas are transducers that transfer electromagnetic energy between a transmission line and free space.
© Amanogawa, 2006 – Digital Maestro Series 1

Antennas

Here are a few examples of commonantennas:
Linear dipole fed by a two-wire line Linear monopole fed by a single wire over a ground plane Coaxial ground plane antenna

Ground plane

Linear elements connected to outer conductor of the coaxial cable simulate the ground plane

Loop antenna Uda-Yagi dipole array Loop dipole

Multiple loop antenna wound around a ferrite core

Parabolic (dish) antenna

Log−periodic arrayPassive elements © Amanogawa, 2006 – Digital Maestro Series 2

Antennas

From a circuit point of view, a transmitting antenna behaves like an equivalent impedance that dissipates the power transmitted
Transmitting Antenna

Transmitter

I
Transmission Line

Electromagnetic Wave I

Transmitter

Zg Vg
Transmission Line

I

1 P( t ) = Req I 2 2
Zeq
I

= Req + jXeq

Thetransmitter is equivalent to a generator.
© Amanogawa, 2006 – Digital Maestro Series 3

Antennas

A receiving antenna behaves like a generator with an internal impedance corresponding to the antenna equivalent impedance.
Receiver

I
Transmission Line

Receiving Antenna

Electromagnetic Wave I

I

Zeq Zin

1 P( t ) = Rin I 2 2
Veq

ZR

Transmission Line

I

The receiverrepresents the load impedance that dissipates the time average power generated by the receiving antenna.
© Amanogawa, 2006 – Digital Maestro Series 4

Antennas

Antennas are in general reciprocal devices, which can be used both as transmitting and as receiving elements. This is how the antennas on cellular phones and walkie−talkies operate. The basic principle of operation of an antenna is easilyunderstood starting from a two−wire transmission line, terminated by an open circuit. |I| Zg Vg ZR → ∞
Open circuit

|I|

Note: This is the return current on the second wire, not the reflected current already included in the standing wave pattern.

© Amanogawa, 2006 – Digital Maestro Series

5

Antennas

Imagine to bend the end of the transmission line, forming a dipole antenna.Because of the change in geometry, there is now an abrupt change in the characteristic impedance at the transition point, where the current is still continuous. The dipole leaks electromagnetic energy into the surrounding space, therefore it reflects less power than the original open circuit ⇒ the standing wave pattern on the transmission line is modified | I0 | Zg |I| Vg Z0 |I|

| I0 |
©Amanogawa, 2006 – Digital Maestro Series 6

Antennas

In the space surrounding the dipole we have an electric field. At zero frequency (d.c. bias), fixed electrostatic field lines connect the metal elements of the antenna, with circular symmetry.

E

E

© Amanogawa, 2006 – Digital Maestro Series

7

Antennas

At higher frequency, the current oscillates in the wires and the fieldemanating from the dipole changes periodically. The field lines propagate away from the dipole and form closed loops.

© Amanogawa, 2006 – Digital Maestro Series

8

Antennas

The electromagnetic field emitted by an antenna obeys Maxwell’s equations

∇ × E = − jω µ H

∇ × H = J + jω ε E
Under the assumption of uniform isotropic medium we have the wave equation:

∇ × ∇ × E = − j ω µ ∇ × H =− j ω µ J + ω 2µ ε E ∇ × ∇ × H = ∇ × J + jω ε ∇ × E = ∇ × J + ω 2µ ε H
Note that in the regions with electrical charges ρ

∇ × ∇ × E = ∇∇ ⋅ E − ∇ 2 E = ∇ ( ρ ε ) − ∇ 2 E
© Amanogawa, 2006 – Digital Maestro Series 9

Antennas

In general, these wave equations are difficult to solve, because of the presence of the terms with current and charge. It is easier to use the magnetic vector...