Comprehensive study notes covering fundamental concepts, radiation parameters, antenna types, and array theory for undergraduate electrical engineering students.
| Band | Frequency Range | Wavelength | Applications |
|---|---|---|---|
| L-Band | 1 - 2 GHz | 30 - 15 cm | GPS, GSM, Radio Astronomy |
| S-Band | 2 - 4 GHz | 15 - 7.5 cm | Bluetooth, WiFi (2.4 GHz), Radar |
| C-Band | 4 - 8 GHz | 7.5 - 3.75 cm | Satellite Communications, WiFi (5 GHz) |
| X-Band | 8 - 12 GHz | 3.75 - 2.5 cm | Weather Radar, Military, Satellite |
| Ku-Band | 12 - 18 GHz | 2.5 - 1.67 cm | Direct Broadcast Satellite (DBS) |
| K-Band | 18 - 27 GHz | 1.67 - 1.11 cm | Automotive Radar, 5G Backhaul |
| Ka-Band | 27 - 40 GHz | 1.11 - 0.75 cm | High-speed Satellite Internet, 5G |
An antenna is a transducer that converts guided electromagnetic waves in a transmission line to radiated waves in free space (transmitting mode), or vice versa (receiving mode). At microwave frequencies, antennas are critical for efficient power transfer and directive radiation.
Key Principle:
Time-varying currents → Radiated EM fields
Microwaves typically span frequencies from 300 MHz to 300 GHz (wavelengths 1 m to 1 mm). At these frequencies, antennas exhibit unique characteristics including high directivity, compact size, and significant atmospheric absorption effects.
Wavelength-Frequency Relation:
λ = c / f = v / f
where c = 3 × 10⁸ m/s (speed of light)
Only time-varying or accelerated charges radiate. Static charges produce only near-field components.
Radiation pattern determined by current distribution on the antenna structure.
Fields must satisfy Maxwell's equations and boundary conditions at conductor surfaces.
A mathematical function or graphical representation of the radiation properties of the antenna as a function of space coordinates. In microwave antennas, we typically plot field strength or power density versus angle.
Pattern in the plane containing the electric field vector and the direction of maximum radiation
Pattern in the plane containing the magnetic field vector and the direction of maximum radiation
Main lobe contains direction of max radiation; side lobes represent unwanted radiation in other directions
Pattern Multiplication for Arrays:
E(total) = E(single element) × Array Factor
Typical Half-Wave Dipole Radiation Pattern (E-plane)
Ratio of radiation intensity in a given direction to the average radiation intensity over all directions. Measures focusing capability.
D = U / U₀ = 4πU / P_rad
U = radiation intensity, P_rad = total radiated power
For isotropic radiator: D = 1 (0 dBi)
Ratio of radiation intensity in a given direction to that of an isotropic radiator fed with the same input power. Accounts for losses.
G = η × D
η = radiation efficiency (0 ≤ η ≤ 1)
Typically expressed in dBi (relative to isotropic)
Angular separation between two points on the main lobe where the radiation intensity is half the maximum value (3 dB down).
Approximation for Uniform Line Source:
HPBW ≈ 50.8° × (λ/L)
L = length of antenna, λ = wavelength
Range of frequencies over which antenna parameters (impedance, pattern, gain) remain within specified limits.
Fractional Bandwidth:
BW = (f_high - f_low) / f_center × 100%
Ratio of voltage to current at the antenna terminals. Consists of real (radiation resistance + loss resistance) and imaginary (reactive) parts.
Z_in = R_rad + R_loss + jX
For max power transfer: Z_in = Z₀ (conjugate match)
VSWR: Voltage Standing Wave Ratio indicates impedance matching quality. VSWR = 1 indicates perfect match.
Orientation of the electric field vector as a function of time. Critical for minimizing polarization mismatch loss.
Polarization Loss Factor:
PLF = |ρ̂_w · ρ̂_a|²
Length ≈ λ/2. Most fundamental resonant antenna.
Input Z: 73 + j42.5 Ω
Directivity: 2.15 dBi
Pattern: Figure-8
Vertical λ/4 radiator over ground plane.
Input Z: 36.5 + j21.25 Ω
Directivity: 5.15 dBi
Image theory applies
Circular or square loop. Small loops act as magnetic dipoles.
Circumference << λ: Magnetic dipole
Circumference ≈ λ: High gain
Used in RFID, AM radio
Flared waveguide providing smooth transition from waveguide mode to free space. High power handling, pure polarization.
Pyramidal Horn
Flared in both E and H planes. Most common type.
Sectoral Horn
Flared in one plane only (E-plane or H-plane).
Conical Horn
Circular cross-section, used with circular waveguides.
Gain ≈ 4πA_e/λ² where A_e = effective aperture
Dish antennas using parabolic reflector to focus parallel rays to a focal point (feed). Very high gain, narrow beam.
Key Properties:
Beamwidth Approximation:
HPBW ≈ 70° × (λ/D)
D = dish diameter
Low-profile antennas consisting of a metallic patch on a dielectric substrate with ground plane. Popular in mobile and satellite applications due to conformal properties.
Length L ≈ λ/2√ε_r, Width W controls input impedance
Radius a determined by resonance condition
Rectangular Microstrip Patch Geometry
Substrate thickness h << λ
Advantages: Low profile, lightweight, conformal, easy fabrication | Disadvantages: Narrow bandwidth (~1-5%), low power handling
Narrow slots cut in conducting surfaces, complementary to dipoles (Babinet's principle). Often fed by waveguides or microstrip lines.
End-fire array consisting of driven element, reflector, and directors. High gain with simple feed structure.
Multiple antenna elements arranged to enhance directivity and control radiation patterns.
The total field of an array is the product of the element pattern and the array factor (Pattern Multiplication). For N identical elements:
AF = Σ I_n e^{j(n-1)(kd cos θ + β)}
Maximum radiation perpendicular to array axis (θ = 90°). Requires β = 0.
Maximum radiation along array axis (θ = 0° or 180°). Requires β = -kd.
Electronic beam steering by adjusting phase β between elements.
Nulls occur when:
ψ = ±m(2π/N), m = 1,2,3...
where ψ = kd cos θ + β
Undesired maxima occurring when element spacing d > λ. Avoid by:
Array directivity increases with number of elements N and array length L. For uniform linear array:
D ≈ 2N(d/λ) (broadside)
Elements along a straight line. Simplest configuration, used in base stations.
2D arrangement allowing beam steering in both azimuth and elevation.
Conform to curved surfaces (aircraft, missiles). Maintain aerodynamic profile.
Interactive tool for quick microwave antenna calculations
Note: Patch calculations use approximate formulas. Actual dimensions require full-wave simulation or cavity model analysis accounting for fringing fields.
Antennas are reciprocal transducers; transmitting and receiving properties are identical (reciprocity theorem).
Directivity and gain measure focusing capability; gain includes efficiency losses (ohmic, mismatch).
Aperture antennas (horns, dishes) dominate microwave frequencies due to high gain and power handling.
Arrays enable electronic beam steering (phased arrays) and enhanced directivity through pattern multiplication.