Radiation Pattern

The radiation pattern of an antenna is one of its most fundamental characteristics, describing how the antenna distributes radiated power in different directions in three-dimensional space. It forms the basis for computing directivity, gain, and beamwidth — all of which are central to antenna design and GATE examination questions.

Understanding the Radiation Pattern

The radiation pattern is a graphical representation of the radiated field strength (or power density) as a function of direction from the antenna, measured in the far field at a constant distance. Patterns can be plotted in terms of field intensity (E-field pattern), power density (power pattern), or normalized to their maximum value (normalized pattern). In GATE, the normalized power pattern is most commonly used.

A typical directional antenna pattern has a main lobeside lobes — smaller lobes at angles away from the main beam. Energy radiated into side lobes is wasted in most communication applications and can cause interference.

The back lobeside lobe level (SLL) or side lobe ratio, expressed in dB. A well-designed antenna has SLL below -20 dB.

Beamwidth

The half-power beamwidth (HPBW)first null beamwidth (FNBW) is the angular separation between the first nulls on either side of the main beam, and FNBW is approximately twice the HPBW for most practical antennas.

For a uniformly illuminated aperture of length L, the HPBW in radians is approximately 0.886 times λ/L. For a half-wave dipole, the HPBW in the elevation plane is 78 degrees. These values frequently appear in GATE numerical problems.

Mathematical Expression

The normalized power pattern F(θ,φ) is defined as the ratio of the power density U(θ,φ) at any direction to its maximum value U_max. Therefore F(θ,φ) = U(θ,φ) / U_max, and its value ranges from 0 to 1 (or 0 to 0 dB on a logarithmic scale). The front-to-back ratio (FBR) is defined as the ratio of the maximum main lobe power density to the power density at the back lobe direction, expressed in dB. FBR = 10 log₁₀ (U_max / U_back).

Practical Understanding

In wireless communication systems, high directivity (narrow HPBW) is desirable for point-to-point links because it concentrates energy in the desired direction and reduces interference to other users. In broadcasting applications, an omnidirectional pattern with uniform radiation in the azimuth plane is preferred. Radar systems require very low side lobes to prevent false target detection.

Pattern measurement is always performed in the far field, typically in anechoic chambers. The measured pattern at one polarization (co-polarization) and the orthogonal polarization (cross-polarization) together characterize the full polarization purity of the antenna beam.

Given:
Antenna aperture length L = 0.3 m, Operating frequency f = 10 GHz, λ = c/f = 3×10⁸ / 10×10⁹ = 0.03 m

Why this formula applies:
For a uniformly illuminated aperture, HPBW ≈ 0.886 × λ/L gives the half-power beamwidth in radians.

Formula:
HPBW = 0.886 × (λ / L)  [in radians]
HPBW (degrees) = HPBW (rad) × (180 / π)

Substitution:
HPBW = 0.886 × (0.03 / 0.3) = 0.886 × 0.1

Calculation:
HPBW = 0.0886 rad
HPBW = 0.0886 × 57.3°

Final Answer with units:
HPBW ≈ 5.08°
The antenna has a 5.08° half-power beamwidth, indicating a highly directive beam suitable for point-to-point links.

Exam Tip: GATE frequently asks to distinguish HPBW from FNBW. Remember FNBW ≈ 2 × HPBW for most antennas. Also, when the pattern is expressed in dB, the -3 dB points correspond to half-power — do not confuse -3 dB field level (which is -6 dB power) with -3 dB power level.

• The main lobe carries maximum radiation and points in the intended communication direction.
• Side lobes represent wasted power and potential interference — antenna design aims to minimize them.
• HPBW is the angular width at -3 dB power level of the main lobe; FNBW is approximately twice HPBW.
• Narrower HPBW means higher directivity — aperture antennas achieve this by increasing physical size.
• Front-to-back ratio (FBR) in dB quantifies how much the antenna discriminates between main and back lobe directions.

Quick Revision

• Radiation pattern: graphical representation of radiated power (or field) vs direction at constant far-field distance.
• Main lobe: direction of maximum radiation. Side lobes: smaller lobes adjacent to main lobe.
• HPBW = angular width between -3 dB (half-power) points of main lobe.
• FNBW ≈ 2 × HPBW for most practical antennas.
• For aperture antenna: HPBW ≈ 0.886 λ/L radians.
• Side lobe level (SLL) expressed in dB: a good antenna has SLL less than -20 dB.
• Trap: -3 dB power point is NOT the same as -3 dB field point (field amplitude at HPBW is 1/√2 of peak).