Friis Transformation and Radiation from Dipole

Week 3

Equivalent Circuit of Antenna

Z_A = R_A + j X_A

R_A = R_R + R_L

• R_R - Radiation resistance

• R_L - Loss resistance

• X_A - Antenna reactance

Radiation Efficiency

𝜂_r = power radiated / (power radiated + power lost) = R_R / (R_R + R_L)

Power dissipated (as heat) by antenna

P_A = ½ * |𝐼|² * (𝑅_𝐿+𝑅_𝑅)

Reflection coefficient

Γ = (𝑍_𝐴 − 𝑍_𝑂 ) / (𝑍_𝐴 + 𝑍_𝑂)

where 𝑍_𝑂 is the characteristic impedance of transmission line

when 𝑍_𝐴 = 𝑍_𝑂 → Γ = 0 = perfect match

VSWR

VSWR = Voltage Standing Wave Ratio = (1 + | Γ |) / (1 − | Γ |)

How well an antenna is matched or how much power it will accept from a source

VSWR of 1 indicates a perfect match

Impedance of Free Space

377

Antenna Effective Area

A measure of the ability of an antenna to capture energy

A_e = Power delivered to load / Incident power density = 𝐺𝜆² / 4𝜋

Aperture Efficiency

𝜂_Ae = effective area / physical area

Antenna Bandwidth

Band of frequencies within which antenna performance characteristics are acceptable

Characteristics:

• Input impedance

• Beamwidth

• Gain

• Sidelobes

• VSWR

• Axial ratio

Antenna Effective Collecting Area

The effective absorption area (A_e), presented by an antenna, gives an indication of the power collected/absorbed (P_R) as in response to an incident plane wave.

P_R = P_AA_e

Dipole Antennas

• Common antenna at low frequencies < 1GHz

• A linear conductor driven at its centre

• Simplest dipole to analyse is a short (Herzian) dipole

Dipole Antennas Pattern