Mobile and satellite communications

Introduction To Mobile And Satellite Systems

Objective - Define parameters/quantities usually employed to evaluate antenna systems for Msc.

(1) Coordinate Systems

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

Cartesian = x, y, zSpherical = r, θ, φ

r = √(x² + y² + z²)θ = arccos(z/r)φ = arccos(x/(r sinθ))

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

(2) 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?

2.1 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 huge dynamic range → dB scale

2.2 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

2.3 CARTESIAN 2D PATTERN

F(θ, φ)

Example = Typical Mobile Antenna vs Typical Satellite Antenna

≈ Constant

The phasors are COMPLEX QUANTITIES, only depending on the position z.

The use of E(z) and H(z) simplifies solutions of EM problems significantly.

Most solvers/can simulators operate in phasor domain (HFSS is like that)

NOTE: E(z) may be counter-intuitive to use because

• E(z) = Ex(z)x̂ + Ey(z)ŷ + Ez(z)ẑ =
• = Ex(z) x̂ + j Ex(z) x̂ + ...
• = E*_T(z) + j E*_L(z)

L every point is described by two 3D vectors.

Can we further simplify?

Under the assumption of "FAR FIELD REGION" the field radiated by any antenna simplifies

E(z) ≅ E_o(θ,ϕ) e^-j5π / π

H(z) ≅ 1 / η ẑ x E(z)

(by solving MAXWELL EQ.)

where E_o(θ,ϕ) = E_oθ(θ,ϕ)θ̂ + E_oφ(θ,ϕ)φ̂

Observations:

• Field can be described just by E(z)
• Any antenna radiates a SPHERICAL WAVE
• The field magnitude decreases as 1/π
• The field has just 2 components, E_oθ and E_oφ, while E_L ≈ 0 for every antenna.

So it turns out that we do not need to plot e_x(z,t), e_y(z,t), e_z(z,t), e_L(z,t), d_L(z,t), V_L(z,t).

It is sufficient to provide E_oθ(θ,ϕ), E_oφ(θ,ϕ) (➝two 2D plots)

30/09/21

The power distribution by any antenna is described by U(θ, φ) [w/sterad].

We have seen that a more suitable description of antenna properties requires to normalize U(θ, φ):

D(θ, φ) = _{U(θ, φ)}/^U₀ = 4π^{U(θ, φ)}/_Prad      [NO DIMENSION]

According to definition D(θ, φ) ≥ 0      ∀θ, φ

The maximum of D(θ, φ) is D_max = max_{θ, φ} D(θ, φ)

What ranges can D_max have?

D_max ∈ [1, ∞)

D_max in practical antennas has a very wide range of variations

1 ∼ 4      ANTENNA FOR HANDHELD SYSTEMS

D_max ≥ 10,000      SATELLITE SYSTEMS

For this reason, D_max is often represented in dB → D_max|_dB = 10 log₁₀ [D_max]

In dB: D_max|_dB ∈ [0, +∞)      (or dBi: → normalized respect to an isotropic antenna)

NOTE: D(θ, φ) and D_max are difficult to measure accurately

D(θ, φ) = 4π^{U(θ, φ)}/_Prad      where      P_rad = ∫₀^2π ∫₀^π U(θ, φ) sinθ dθ dφ

The GAIN is much easier to measure

G(θ, φ) ≜ 4π^{U(θ, φ)}/_Pin

to measure the input power → just 1 circuit probe

05/10/21

We have seen that in a given point r₀, the field E(r₀) can have a polarization (linear, circular, elliptical) which is associated to the time-domain evolution of

e(r₀,t) = Re {E(r₀)e^jωt}

How we determine polarization from E(r₁)? (Phasor)

NOTE - E(r₁) = E_R(r₁) + j E_I(r₁)

E(r₁) = ẑ          linear

E(r₁) = ẑ (1+ȳ)          linear (E_R=ẑ, E_I=ȳ)

E(r₁) = ẑ + jȳ          circular (E_R=ẑ, E_I=ȳ)

E(r₁) = ẑ + ȳ          linear (E_R=ẑ+ȳ, E_I=0) on slant 45°

One possibility to compute e(r₁,t) evolution, alternatively, is (simple rule):

• linear          E_R, E_I are linearly dependent
• circular          E_R, E_I are ⊥ and |E_R| = |E_I|
• elliptical          all other cases

The polarization of radiated fields in far field has a simple expression:

E(r₁) = e^-jkr₁/r₁ [ E_θ(θ,φ) θ̂ + E_φ(θ,φ) φ̂ ]

We notice that:

• Polarization does not depend on r but it depends on θ and φ
• It is usual to define polarization unit vector: ρ̂(θ,φ) =          E(r₁) / |E(r₁)|          ∈

Usually it is sufficient to state the polarization type in θ,φ corresponding to G_max.

Configurations for Microstrip Antennas

Usually possible to define 4 classes

1. Microstrip Patch Antennas
2. Printed Dipole Antennas
3. Printed Slot Antennas
4. Microstrip Traveling-Wave Antennas

Technologically similar, but design and performance are very different.

A) Microstrip Patches

They are based on basic prototype seen before.

In principle the patch can have any shape.

However, canonical shapes exist which are used in basic applications.

• Square
• Rectangular
• Circular
• Elliptical
• Triangle
• Ring

More complex shape enable more flexibility in performance tuning (especially Γ(f)).

Of course this also means more difficult design.

Typical examples:

• Inset-Based Patch
• L-Shaped
• T-Shaped
• H-Shaped
• C-Shaped
• U-Shaped (Wideband)
• Bowtie (Ultra Wideband)
• Hourglass (UWB)
• Dog-Bone (UWB)