Mobile and satellite communications

Introduction to mobile and satellite systems

Objective

Define parameters/quantities usually employed to evaluate antenna systems for ICTS.

Coordinate systems

Antenna systems are often studied in terms of their spatial properties. To represent such properties, the usual choice is to use spherical coordinates.

Cartesian = x, y, z

Spherical = r, θ, φ

r = √^{x² + y² + z²}

θ = arccos(_z/_r)

φ = arccos(_x/_senθ)

Note - θ, φ are angles, usually measured in [rad], [deg]

Radiation pattern

A radiation pattern is a function or a graphical representation of the spatial properties of an antenna F(θ, φ). The function can be:

• Radiated Power Density
• Directivity
• Gain
• Polarization

How do we plot them?

Introduction to mobile and satellite systems

Objective

Define parameters/quantities usually employed to evaluate antenna systems for NTSC.

Coordinate systems

Antenna systems are often studied in terms of their spatial properties. To represent such properties, the usual choice is to use spherical coordinates.

Cartesian = x, y, z

Spherical = r, θ, φ

r = √(x² + y² + z²)

θ = arccos (z/r)

φ = arccos (x/senθ)

Note - θ, φ are angles, usually measured in [rad], [deg]

Radiation pattern

A radiation pattern is a function or a graphical representation of the spatial properties of an antenna F(θ, φ). The function can be:

• Radiated Power Density
• Directivity
• Gain
• Polarization

How do we plot them?

3D polar pattern

Idea: For each (θ, φ) I draw a dot in the position (F(θ, φ), θ, φ).

Note: Since F(θ, φ) usually has a huge dynamic range → dB scale.

2D polar pattern

Idea: We set a φ value (φ=φ₀) and plot the "slice" of F(θ, φ) in that plane. Example: φ=0.

Cartesian 2D pattern

Example: Typical Mobile Antenna vs. Typical Satellite Antenna.

Pattern lobes

Consider a 2D Cartesian pattern:

• Lobe: Angular region of radiation pattern delimited by nulls
• Main lobe: Lobe which contains the maximum of F(θ,φ)
• Secondary/side lobes: All other lobes
• Peak side lobe: Secondary lobe with maximum of F(θ,φ)
• Peak Sidelobe Level (PSL): ^{max F(θ,φ) | _{main lobe}} / _{max F(θ,φ) | _{side lobes}}

Typical Values:

• Communications (BTS): PSL > 15 dB (~ 40 Linear)
• Radar (Automotive): PSL > 40 dB (10,000)

Once identified, it is useful to measure the antenna beams (main beams) F(θ,φ).

Antenna classification

Classification of antennas can be done in many ways. Let us just consider radiation pattern.

• Isotropic Antenna: F(θ, φ) = constant ∀θ, φ (→ Ideal, does not exist)
• Omnidirectional Antenna: F(θ, φ) = constant in a plane - Example: Dipole
• Directional: All others

28/09/24

When introducing "radiation pattern" we referred to power/polarization/...

EM field clarification

To clarify their meaning, let us recall what is an EM field. The EM field is defined by four vectorial fields.

To clarify:

e(r,t) = _x(r,t) ̂ + _y(r,t) ̂ + _z(r,t) ̂ (in Cartesian coordinates)

where , are position and time. In our course, we are interested in the field propagating in air/free-space. In such cases, we can use the constituting equations of these materials to simplify descriptions.

(r,t) = ₀ (r,t) (r,t) = ₀ (r,t)

₀ = electric permittivity of free space

₀ = magnetic permeability of free space

➡ We can describe radiation only using (r,t) and (r,t).