Antenna theory

AN4190

12/29

Doc ID 023812 Rev 1

In Table 1 the ratio from the power received from a receiver antenna and the maximum

power transmitted from a transmit antenna as a function of the polarization is shown. If the

antennas are the same, all the transmitted power is received, if the antennas are opposite,

for instance vertical in TX and horizontal in RX, the power received is zero.

1.8

Input impedance

The ability of an antenna to accept power from a source is determined by the input

impedance the antenna presents. For maximum power transfer, the input impedance should

exactly match the output impedance of the source. Strictly speaking, for maximum power

transfer the input impedance of the antenna must be the complex conjugate of the source's

output impedance. Essentially, all the RF sources exhibit real output impedance, with the

vast majority having output impedance of 50

Ω. The 50 Ω system impedance level was

chosen as the standard coaxial cable impedance and represents a good compromise

between dissipative loss and power handling. On the other hand, over a broad bandwidth,

the complex input impedance of an antenna differs greatly from 50

Ω.

The complex reflection coefficient at the input of the antenna is:

Equation 2

where:

The power reflected is equal to the incident (forward) power multiplied by the square of the

magnitude of the complex input reflection coefficient. The reflected power is the fraction of

the total power provided to the antenna that returns to the load.

Table 1.

Ratio of power received to maximum power

Transmit antenna

polarization

Receive antenna

polarization

Ratio of power received to maximum

power

Ratio

Ratio [dB]

Vertical

Vertical

1

0

Vertical

45 or 135 degree

½

-3

Vertical

Horizontal

0

-

∞

Vertical

Circular (right or left)

½

-3

Horizontal

Horizontal

1

0

Horizontal

45 or 135 degree

½

-3

Horizontal

Circular (right or left)

½

-3

Circular (right-hand)

Circular (right-hand)

1

0

Circular (right-hand)

Circular (left-hand)

0

-

∞

Circular (right or left)

45 or 135 degree

½

-3

Γ

Z

input

Z

o

–

()

Z

input

Z

o

+

()

⁄

=