Aperture, Horn, Reflector and Lens Antennas

Introduction and Context

Aperture antennas radiate through an opening or an equivalent opening in a conducting or dielectric structure. Slots, horns, reflectors, and lenses are especially important at microwave and millimetre-wave frequencies because their dimensions can be made several wavelengths large, allowing narrow beams, high directivity, and controlled polarization. They are used in radar, satellite communication, radio astronomy, remote sensing, electronic warfare, automotive radar, and high-capacity point-to-point links.

The central analytical idea is aperture equivalence: the electromagnetic fields over an aperture can be replaced by equivalent electric and magnetic surface currents radiating in free space. When the aperture is electrically large, its far field is closely related to the spatial Fourier transform of the aperture field distribution. This provides a unified method for analysing slots, horns, reflectors, and lenses.

Reflector and lens antennas differ in how they produce a planar or nearly planar phase front. A reflector redirects a feed wave by reflection from a shaped conducting surface, whereas a lens modifies the phase velocity through a dielectric or artificial medium. In both cases, gain depends not only on physical aperture area but also on illumination, phase errors, polarization, spillover, blockage, losses, and manufacturing tolerances.

Learning Objectives

After studying this chapter, the reader should be able to:

1. Explain aperture equivalence and derive the far field of an aperture from its field distribution.

2. Relate aperture dimensions and illumination to beamwidth, sidelobes, directivity, and gain.

3. Analyse slot antennas and distinguish their complementary relationships.

4. Explain the geometry, operation, modes, and design trade-offs of pyramidal and conical horns.

5. Evaluate parabolic reflector geometries, feed arrangements, efficiency factors, and surface-error effects.

6. Explain lens focusing, dielectric and delay-lens principles, and practical limitations.

7. Select an appropriate aperture antenna for a high-gain microwave application.

1. Aperture Equivalence and Radiation from an Opening

Consider an aperture cut in an infinite perfectly conducting plane. The actual fields in the aperture may be replaced, according to the equivalence principle, by equivalent surface currents on a closed or open replacement surface. For a plane aperture with outward normal \(\hat{n}\), the commonly used equivalent currents are

\[

\mathbf{J}_s=\hat{n}\times\mathbf{H}, \qquad \mathbf{M}_s=-\hat{n}\times\mathbf{E},

\]

where \(\mathbf{E}\) and \(\mathbf{H}\) are the tangential electric and magnetic fields over the aperture. The signs follow the convention that the equivalent sources radiate into the selected observation region. These currents are mathematical sources; they do not imply that both electric and magnetic conductors physically exist.

For a planar aperture in the \(xy\)-plane, the far field can be written in terms of the spatial spectrum of the aperture field. In a common formulation, if the aperture electric field is \(\mathbf{E}_a(x,y)\), the angular dependence is governed by integrals of the form

\[

\mathcal{F}(k_x,k_y)=\iint_A \mathbf{E}_a(x,y) e^{j(k_xx+k_yy)}\,dx\,dy,

\]

where \(k_x=k\sin\theta\cos\phi\), \(k_y=k\sin\theta\sin\phi\), and \(k=2\pi/\lambda\). The exact vector field includes polarization-dependent factors and a multiplicative factor proportional to \(e^{-jkr}/r\). Thus, the far-field pattern is not generally the transform of a scalar field alone; vector orientation and boundary conditions must also be considered.

For a separable aperture distribution,

\[

E_a(x,y)=E_x(x)E_y(y),

\]

the pattern factor separates into two one-dimensional transforms. This is particularly useful for rectangular apertures and pyramidal horns.

Uniform Rectangular Aperture

For a uniformly illuminated rectangular aperture of dimensions \(a\) along \(x\) and \(b\) along \(y\), the normalized pattern factor is

\[

F(\theta,\phi)=\operatorname{sinc}\left(\frac{ka}{2}\sin\theta\cos\phi\right)

\operatorname{sinc}\left(\frac{kb}{2}\sin\theta\sin\phi\right),

\]

where \(\operatorname{sinc}(u)=\sin u/u\). The first null in a principal plane occurs approximately at

\[

\sin\theta_{FN}\approx \frac{\lambda}{a}

\]

for the plane associated with dimension \(a\), and similarly \(\sin\theta_{FN}\approx\lambda/b\) for dimension \(b\). For an electrically large aperture, the half-power beamwidth in degrees is approximately

\[

\text{HPBW}\approx 50.8\frac{\lambda}{D},

\]

where \(D\) is the aperture dimension in the relevant principal plane. The coefficient applies to a uniformly illuminated rectangular aperture and is an approximation near broadside; taper changes it.

The maximum directivity of an aperture is often estimated by

\[

D_0\approx \frac{4\pi A_e}{\lambda^2},

\]

where \(A_e\) is effective aperture area. If \(A\) is the physical aperture area and \(\eta_A\) is aperture efficiency,

\[

A_e=\eta_A A, \qquad D_0\approx \eta_A\frac{4\pi A}{\lambda^2}.

\]

The efficiency must include relevant reductions such as nonuniform amplitude and phase, spillover, blockage, conductor or dielectric loss, and polarization mismatch. Directivity is dimensionless; gain is \(G=\eta_rD\), where \(\eta_r\) represents radiation and other defined efficiency factors according to the adopted convention.

Illumination and Fourier-Transform Trade-offs

A uniform aperture produces the narrowest main beam for a given physical extent but has relatively high sidelobes; the first sidelobe of an ideal one-dimensional uniform aperture is approximately \(-13.2\) dB relative to the main beam. Tapering the amplitude toward the aperture edge lowers sidelobes but broadens the beam and reduces directivity. Common tapers include cosine, cosine-squared, Taylor, Chebyshev, and Gaussian distributions.

This trade-off is a design decision rather than a universal optimization. A radar requiring low false alarms may prefer low sidelobes, while a communication antenna may prioritize maximum gain and compactness. Fourier methods make the trade-off explicit: sharper truncation in space produces slower spectral decay and higher sidelobes, whereas smoother edge transitions generally reduce sidelobes.

2. Slot Antennas and Complementarity

A slot antenna is an aperture cut into a conducting sheet. Its radiation is governed by the electric field across the slot and by the associated equivalent magnetic current. For a narrow slot of length approximately \(\lambda/2\), the field distribution resembles that of a complementary dipole, although the actual impedance and current distribution depend on the surrounding conductor and feeding arrangement.

The Babinet principle states, in idealized electromagnetic form, that the fields from a conducting screen and its complementary aperture are related. The more specific Booker relation for complementary antennas gives an approximate impedance relationship

\[

Z_s Z_d=\frac{\eta_0^2}{4},

\]

where \(Z_s\) is the impedance of a slot antenna, \(Z_d\) is the impedance of its complementary dipole, and \(\eta_0\) is the intrinsic impedance of free space. The relation assumes a thin, perfectly conducting screen in a homogeneous medium and compatible definitions of terminal impedance. It is not exact for finite substrates, thick conductors, nearby objects, or practical feeds.

Slots may be fed directly by a coaxial probe, microstrip line, coplanar waveguide, or waveguide. Arrays of slots cut in waveguide walls are widely used because the waveguide both feeds the elements and provides mechanical support. Slot position, inclination, offset, and length control coupling, phase, polarization, and impedance.

Important advantages include low profile, integration with metallic structures, and suitability for arrays. Limitations include narrow bandwidth for resonant slots, sensitivity to substrate or enclosure effects, and fabrication tolerances at high frequency.

3. Horn Antennas

A horn is a flared waveguide whose aperture radiates into space. Flaring reduces abrupt discontinuity at the waveguide termination and transforms the guided wave into a beam. Horns are mechanically robust, have moderate-to-high gain, low loss, and comparatively broad bandwidth. They are also commonly used as standard-gain calibration antennas and as feeds for reflector antennas.

Modes and Aperture Field

A rectangular waveguide horn is generally excited in the dominant \(\mathrm{TE}_{10}\) mode. A pyramidal horn flares in both transverse dimensions, while an E-plane or H-plane sectoral horn flares in only one plane. A conical horn is formed from a circular waveguide and is commonly operated in a mode related to \(\mathrm{TE}_{11}\).

The aperture field of a horn is not exactly uniform. It contains amplitude variation due to the guided mode and phase variation due to the different path lengths from the throat to the aperture. The phase error is often described by the maximum difference between the shortest and longest aperture paths. Excessive phase error reduces aperture efficiency and broadens or distorts the beam.

A useful geometrical approximation for a rectangular horn is that the path-length difference in a flared plane is related to the aperture width and flare geometry. If the aperture has width \(D\) and the axial distance from the aperture plane to the phase centre is \(R\), the edge-to-centre path difference is approximately

\[

\Delta l\approx \sqrt{R^2+(D/2)^2}-R.

\]

For \(D\ll R\),

\[

\Delta l\approx \frac{D^2}{8R}.

\]

The corresponding phase error is

\[

\Delta\psi\approx k\Delta l=\frac{2\pi}{\lambda}\Delta l.

\]

These expressions are geometrical approximations and should be used with the actual horn mode and design charts or full-wave simulation for precision design.

Horn Gain and Beamwidth

The gain of a horn is commonly estimated from its effective aperture:

\[

G\approx \eta_A\frac{4\pi A}{\lambda^2},

\]

where \(A\) is the physical aperture area. The aperture efficiency depends on phase error, amplitude taper, conductor loss, mismatch, and cross-polarization. Increasing aperture size usually increases gain and narrows the beam, but excessive flare can increase phase error, while insufficient flare can increase mismatch and diffraction.

The design therefore involves a compromise between throat dimensions, flare angle, aperture dimensions, length, bandwidth, phase centre, and mechanical constraints. Horns are attractive where calibration traceability, moderate power handling, and predictable polarization are required.

4. Reflector Antennas

A reflector antenna uses a conducting surface to redirect energy from a feed into a desired beam. The most common form is the parabolic reflector. A paraboloid has the property that rays originating at its focus reflect into rays parallel to its axis. Conversely, a plane wave incident parallel to the axis is focused at the feed location.

Paraboloid Geometry

For a rotationally symmetric paraboloid with focal length \(f\), the surface can be represented in cylindrical coordinates by

\[

z=\frac{\rho^2}{4f},

\]

where \(\rho\) is radial distance from the axis and \(z=0\) is the vertex plane. If the reflector has diameter \(D\), its depth (sagitta) is

\[

d=\frac{D^2}{16f}.

\]

The ratio \(f/D\), called the focal ratio, controls reflector depth, feed viewing angle, blockage, and illumination requirements. A small focal ratio gives a deep reflector and a large subtended angle at the feed. A large focal ratio gives a shallow reflector but may require a feed with a narrow beam.

The far-field beamwidth is approximately inversely proportional to diameter. For a circular aperture, practical beamwidth formulas depend on illumination and the definition used; a commonly used engineering estimate for half-power beamwidth is

\[

\text{HPBW}\approx 58\frac{\lambda}{D}\quad \text{degrees},

\]

for a typical circular aperture. This coefficient is not universal: edge taper and phase distribution can change it significantly.

The ideal directivity of a circular aperture is

\[

D_0\approx \eta_A\left(\frac{\pi D}{\lambda}\right)^2,

\]

since \(A=\pi D^2/4\). This expression assumes an electrically large aperture and incorporates practical effects through \(\eta_A\).

Reflector Efficiency Budget

A useful engineering model is

\[

\eta_A=\eta_i\eta_s\eta_b\eta_p\eta_x\eta_l,

\]

where the factors may represent illumination, spillover, blockage, phase-error, polarization, and loss efficiencies. The exact factorization varies among authors because some effects overlap; therefore factors must not be multiplied twice.

Illumination efficiency measures how uniformly the reflector aperture is excited. Strong edge taper reduces spillover and sidelobes but wastes aperture area. Weak taper improves directivity but increases spillover and sidelobes.

Spillover efficiency is the fraction of feed power intercepted by the reflector rather than radiated past its edge. Spillover can increase system noise temperature when the feed sees the warm ground or other unwanted sources.

Blockage efficiency accounts for shadowing by a subreflector, feed, support struts, and associated scattering. It is particularly important for front-fed reflectors. Offset reflectors reduce blockage by moving the feed and support structure away from the main beam path, although they are more complex to manufacture and align.

Phase-error efficiency accounts for departures from a constant phase aperture. It is affected by feed displacement, reflector deformation, manufacturing errors, and defocus. A small random phase error with root-mean-square value \(\sigma_\phi\) radians is often approximated by

\[

\eta_{\phi}\approx e^{-\sigma_\phi^2},

\]

provided the errors are statistically characterized, sufficiently small, and approximately independent. This is a statistical approximation, not a universal exact law.

Polarization efficiency accounts for mismatch between the desired and actual polarization. Cross-polarization may arise from feed imperfections, reflector asymmetry, offset geometry, and surface irregularities.

Feeds and Reflector Configurations

The feed must illuminate the reflector with suitable amplitude taper, phase centre, polarization, bandwidth, and impedance match. Common feeds include waveguide horns, corrugated horns, open-ended waveguides, helix antennas, and small reflector subassemblies.

A prime-focus reflector places the feed at the main focus. It is simple but suffers from feed and support blockage. A Cassegrain reflector uses a convex hyperbolic subreflector and a main parabolic reflector. The feed is near the vertex, simplifying equipment access and reducing transmission-line length. A Gregorian reflector uses a concave ellipsoidal subreflector and can provide useful packaging and beam-control properties, but its subreflector geometry and blockage differ from those of a Cassegrain system.

An offset reflector is a section of a parent paraboloid arranged so that the feed does not block the aperture. It generally offers low sidelobes and low blockage but demands careful alignment and may introduce asymmetric mechanical loading.

Surface Accuracy and Ruze-Type Loss

Reflector surface errors cause phase errors. If the root-mean-square surface deviation is \(\sigma\), the approximate efficiency reduction due to random errors is described by the Ruze relation

\[

\eta_s\approx \exp\left[-\left(\frac{4\pi\sigma}{\lambda}\right)^2\right].

\]

The assumptions include random, statistically distributed surface errors, a suitable definition of RMS deviation, and a reflector operating near the intended pointing and polarization conditions. The factor \(4\pi\sigma/\lambda\) results because a surface displacement produces approximately twice that path change on reflection. This formula shows why a reflector accurate at 10 GHz may be inadequate at 100 GHz.

For example, if \(\sigma=0.5\) mm and \(\lambda=30\) mm,

\[

\eta_s\approx \exp[-(4\pi(0.5/30))^2]

=\exp[-0.0439]\approx 0.957.

\]

Thus the surface-error loss is about \(10\log_{10}(0.957)\approx -0.19\) dB. At \(\lambda=3\) mm with the same surface accuracy, the exponent is approximately 4.39 and efficiency falls to about 0.0125, illustrating the severe millimetre-wave sensitivity.

5. Lens Antennas

A lens antenna uses refraction, phase delay, or both to transform a spherical wave from a feed into a plane wave. In reception, it focuses an incident plane wave onto the feed. Lenses are especially useful at millimetre-wave frequencies, where large reflectors may be mechanically inconvenient and where dielectric or metamaterial fabrication can be integrated with packaging.

Phase Compensation

For a point feed, rays reaching different parts of a lens have different free-space path lengths. A lens is shaped or structured so that the total phase from the feed to the output aperture is approximately constant. For a homogeneous dielectric lens, the phase delay depends on refractive index \(n\), where approximately

\[

n\approx \sqrt{\varepsilon_r}

\]

for a low-loss, nonmagnetic, nondispersive dielectric. In real materials, \(n\) is frequency-dependent and loss may be significant.

A dielectric lens may be shaped as a hyperbolic or elliptical surface, depending on the feed and desired ray transformation. A delay lens may use stepped dielectric sections or artificial transmission-line paths. A zone plate or Fresnel lens reduces thickness by using phase zones, but quantization introduces loss and sidelobes.

Lens Types and Limitations

Common types include dielectric lenses, metal-plate lenses, dielectric-loaded lenses, zoned lenses, and gradient-index lenses. Metal-plate lenses use parallel conducting plates to control phase velocity and can reduce dielectric loss at some frequencies.

The main limitations are material loss, dispersion, reflection at lens surfaces, frequency-dependent beam squint, manufacturing tolerances, weight, and blockage by the feed. Antireflection layers or matching geometries reduce interface reflections. Gradient-index and metasurface lenses can provide thinner profiles and electronic beam steering, but their bandwidth, efficiency, calibration, and power-handling capabilities require careful assessment.

6. Worked Design Example: A Parabolic Reflector at 12 GHz

An earth-station or point-to-point communication terminal requires a reflector with diameter \(D=1.2\) m at \(f_0=12\) GHz. Assume an aperture efficiency of 0.65, neglect atmospheric loss, and use the speed of light \(c\approx3\times10^8\) m/s.

The wavelength is

\[

\lambda=\frac{c}{f_0}=\frac{3\times10^8}{12\times10^9}=0.025\text{ m}.

\]

The physical aperture area is

\[

A=\frac{\pi D^2}{4}=\frac{\pi(1.2)^2}{4}\approx1.131\text{ m}^2.

\]

The estimated directivity is

\[

D_0\approx0.65\left(\frac{\pi(1.2)}{0.025}\right)^2

\approx0.65(150.8)^2\approx1.48\times10^4.

\]

In decibels relative to isotropic radiation,

\[

D_{0,\mathrm{dBi}}=10\log_{10}(1.48\times10^4)\approx41.7\text{ dBi}.

\]

Using the practical circular-aperture estimate,

\[

\text{HPBW}\approx58\frac{0.025}{1.2}\approx1.21^\circ.

\]

If the focal ratio is \(f/D=0.4\), the focal length is \(0.48\) m and the depth is

\[

d=\frac{D^2}{16f}=\frac{1.2^2}{16(0.48)}=0.1875\text{ m}.

\]

These values are first-order design estimates. A final design must evaluate feed pattern, edge taper, spillover, blockage, polarization, radome effects, pointing accuracy, and structural deformation.

7. Applied Case: Millimetre-Wave Radar Aperture Selection

Background

Consider an illustrative 77-GHz automotive radar requiring a narrow azimuth beam, low sidelobes, compact packaging, and operation under vibration and temperature variation.

Problem

A conventional metallic reflector could provide high gain, but feed blockage, mechanical alignment, and enclosure integration are concerns. A dielectric lens could be compact, but material dispersion and manufacturing tolerances may affect beam pointing. A planar phased aperture offers electronic steering but increases RF-channel count and calibration complexity.

Analysis

At 77 GHz, \(\lambda\approx3.90\) mm. Surface errors of only a fraction of a millimetre can create substantial phase loss. A reflector therefore requires a highly stable and accurately manufactured surface. A lens avoids a metallic reflector support structure but must maintain refractive-index uniformity and low loss. A planar array provides beam steering and multiple beams but requires phase and amplitude calibration over temperature.

Approach and Solution

For a fixed forward-looking radar, an offset reflector or integrated dielectric lens may be selected when the required field of view is modest and low RF-channel count is important. The feed pattern is designed with controlled edge taper to limit spillover and sidelobes. Electromagnetic simulation is combined with thermal-mechanical analysis to predict phase errors. If wide-angle electronic scanning is mandatory, a calibrated phased aperture becomes more appropriate despite its greater cost and power consumption.

Outcome

The selection is determined not simply by peak gain. A lens may provide the best packaging and low blockage; a reflector may provide superior efficiency per unit cost; and a phased aperture may provide the best adaptability. Verification must include measured radiation patterns, gain, sidelobes, polarization, beam pointing, temperature cycling, and vibration testing.

Learning Points

1. Physical aperture area is only one contributor to gain.

2. Millimetre-wave surface and material tolerances are system-level constraints.

3. Feed selection affects spillover, noise, sidelobes, and blockage.

4. Architecture should be selected from requirements for scanning, bandwidth, cost, packaging, and reliability rather than gain alone.

8. Design Practice, Limitations, and Contemporary Developments

A reliable aperture-antenna design normally follows a sequence: define frequency, bandwidth, polarization, gain, beamwidth, sidelobe, scanning, power, environmental, and regulatory requirements; select the aperture architecture; estimate dimensions using aperture theory; design the feed and illumination; calculate efficiency losses; perform full-wave and physical-optics analysis; fabricate and measure a prototype; and iterate using tolerance and environmental analysis.

Physical optics is effective for electrically large smooth reflectors, while geometrical optics is useful for ray paths and lens or reflector shaping. Neither method fully captures all edge diffraction, multiple scattering, feed coupling, and finite-structure effects. Physical-optics, geometrical-theory-of-diffraction, uniform-theory-of-diffraction, method-of-moments, finite-element, and finite-difference methods may therefore be combined according to frequency and geometry.

Modern developments include metasurface lenses, transmitarrays, reflectarrays, additive-manufactured horns, 3D-printed dielectric lenses, sparse aperture arrays, reconfigurable intelligent surfaces, and hybrid reflector–array systems. Machine learning can assist surrogate modelling, feed optimization, tolerance analysis, and inverse design. It does not remove the need for Maxwell-equation-based validation, measurement, physical interpretability, or uncertainty analysis.

Regulatory and professional responsibilities include electromagnetic compatibility, exposure compliance, spectrum authorization, interference control, aviation or automotive safety requirements, and transparent reporting of measured rather than merely simulated performance. High-gain antennas can create hazardous power densities near feeds and can cause interference if improperly pointed or operated.

Chapter Summary

Aperture antennas are best understood through equivalence principles and Fourier-transform relationships. The aperture field determines the far-field pattern: aperture size controls beamwidth, while amplitude and phase distributions control sidelobes, gain, and efficiency. Slots use complementary aperture radiation and are convenient for low-profile arrays. Horns transform guided waves into free-space beams and provide robust, broadband microwave performance, but their flare and aperture dimensions must balance phase error and mismatch.

Parabolic reflectors convert spherical waves from a feed into plane waves. Their performance depends on illumination, spillover, blockage, phase error, polarization, losses, and surface accuracy. The Ruze relation demonstrates the severe effect of surface errors at short wavelengths. Lens antennas achieve focusing through dielectric, metallic, or engineered phase delay and are valuable at millimetre-wave frequencies, although loss, dispersion, reflection, and fabrication tolerances are important.

In practical design, aperture area is only the starting point. A successful antenna results from coordinated selection of geometry, feed, material, manufacturing process, mechanical structure, thermal environment, measurement method, and regulatory constraints.

Key Terms

Aperture equivalence: Replacement of fields at an opening by equivalent electric and magnetic surface currents.

Aperture efficiency: Ratio of effective aperture area to physical aperture area.

Babinet principle: Relation between electromagnetic fields of complementary conducting and aperture structures.

Blockage efficiency: Efficiency reduction caused by feed, subreflector, or support structures obstructing the aperture.

Cassegrain reflector: Dual-reflector system using a parabolic main reflector and convex hyperbolic subreflector.

Directivity: Ratio of radiation intensity in a specified direction to the average radiation intensity.

Edge taper: Reduction in feed illumination at the reflector edge relative to its centre.

Effective aperture: Area defined by the relation between received power and incident power density.

Focal ratio: Ratio of reflector focal length to reflector diameter.

Fourier-transform aperture theory: Method relating the aperture field distribution to the far-field angular spectrum.

Horn antenna: Flared waveguide used to radiate a guided electromagnetic mode.

Illumination efficiency: Efficiency associated with nonuniform amplitude excitation across an aperture.

Lens antenna: Antenna using refraction or engineered phase delay to focus or collimate electromagnetic waves.

Phase-centre: Location from which a radiated wavefront approximately appears to originate.

Phase-error efficiency: Efficiency reduction caused by nonuniform aperture phase.

Reflector antenna: Antenna using a conducting surface to redirect electromagnetic energy.

Ruze relation: Approximate expression for gain loss caused by random reflector surface errors.

Spillover: Feed radiation that misses the reflector aperture.

Surface current: Equivalent electric or magnetic current used to represent electromagnetic fields on a surface.

Zone plate: Stepped or zoned lens that approximates a required phase transformation.

Review Questions

Short Answer Questions

1. What is meant by aperture equivalence?

2. Why does tapering an aperture reduce sidelobes but broaden the main beam?

3. What is the function of a horn flare?

4. Define reflector spillover efficiency.

5. State the principal assumptions of the Ruze relation.

Long Answer Questions

1. Derive the Fourier-transform relationship for the far field of a rectangular aperture and discuss its principal-plane pattern.

2. Explain the operating principles, modes, advantages, and limitations of pyramidal and conical horn antennas.

3. Discuss the geometry and efficiency budget of a parabolic reflector antenna.

4. Explain how a dielectric lens produces phase compensation and compare it with a zone plate lens.

5. Describe the effects of illumination, blockage, phase error, polarization, and surface accuracy on reflector gain.

Analytical / Application Questions

1. A uniformly illuminated rectangular aperture is 0.30 m wide and operates at 10 GHz. Estimate its first-null angle and principal-plane half-power beamwidth.

2. A circular reflector has diameter 2 m, operates at 6 GHz, and has aperture efficiency 0.60. Estimate its directivity in dBi and discuss the assumptions behind the result.

3. Compare a horn, offset reflector, dielectric lens, and phased array for a high-gain 80-GHz sensing system requiring low sidelobes, compact packaging, and moderate electronic steering. Justify a recommended architecture.

Multiple Choice Questions with Answers

Question 1

Which mathematical operation most directly relates a planar aperture field to its far-field angular pattern?

A. Spatial Fourier transform

B. Temporal integration only

C. DC resistance calculation

D. Scalar multiplication by aperture perimeter

Correct Answer: A. Spatial Fourier transform

Question 2

For a physical aperture area A and aperture efficiency ηA, which expression estimates directivity?

A. ηA λ²/(4πA)

B. ηA 4πA/λ²

C. 4πλ²/(ηA A)

D. ηA Aλ²

Correct Answer: B. ηA 4πA/λ²

Question 3

What is the principal purpose of flaring a waveguide to form a horn?

A. To eliminate electromagnetic fields

B. To transform the guided wave into a more suitable radiating aperture field

C. To force operation only at zero frequency

D. To create a closed conducting cavity with no radiation

Correct Answer: B. To transform the guided wave into a more suitable radiating aperture field

Question 4

Which reflector loss is primarily associated with feed and support structures shadowing the aperture?

A. Polarization loss

B. Spillover loss

C. Blockage loss

D. Dielectric dispersion loss

Correct Answer: C. Blockage loss

Question 5

The Ruze relation predicts gain reduction mainly due to which effect?

A. Random reflector surface errors

B. Low antenna input resistance only

C. Incorrect cable colour

D. Excessive waveguide cutoff wavelength

Correct Answer: A. Random reflector surface errors

Question 6

For a uniformly illuminated one-dimensional aperture, the first sidelobe is approximately

A. −3 dB

B. −13.2 dB

C. −40 dB

D. +13.2 dB

Correct Answer: B. −13.2 dB

Question 7

A paraboloid converts radiation from a feed at its focus approximately into

A. A spherical wave with random phase

B. A plane wave parallel to its axis

C. A static electric field

D. A wave confined permanently to the feed cable

Correct Answer: B. A plane wave parallel to its axis

Question 8

If a circular reflector has D = 1 m, λ = 0.1 m, and ηA = 0.5, its approximate directivity is

A. 49.3

B. 493

C. 4.93

D. 0.493

Correct Answer: B. 493

Question 9

Which efficiency accounts for radiation from a feed that misses the reflector?

A. Spillover efficiency

B. Phase-centre efficiency

C. Conductor-thickness efficiency

D. Babinet efficiency

Correct Answer: A. Spillover efficiency

Question 10

A major advantage of an offset reflector is

A. It necessarily has zero surface error

B. Reduced blockage of the main aperture

C. Operation without any feed

D. Independence from frequency

Correct Answer: B. Reduced blockage of the main aperture