Key Concepts of Antennas

Why This Matters

Antennas sit at the heart of electromagnetic wave theory—they're the physical bridge between guided waves in circuits and free-space radiation. When you study antennas in Electromagnetism II, you're really being tested on how Maxwell's equations manifest in real devices: boundary conditions, radiation patterns, polarization, impedance matching, and the reciprocity principle. Every antenna type demonstrates specific electromagnetic principles, from the oscillating dipole moment to aperture diffraction.

Don't just memorize antenna names and applications. For exams, you need to understand why each design produces its particular radiation pattern, how wavelength relationships determine antenna dimensions, and what trade-offs exist between gain, bandwidth, and directivity. When an FRQ asks you to compare antenna types or explain a radiation mechanism, you'll need to connect physical structure to electromagnetic behavior.

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Resonant Element Antennas

These antennas rely on standing wave patterns in conductive elements, where the physical length directly relates to the operating wavelength. The current distribution along the element determines the radiation pattern through the superposition of infinitesimal dipole contributions.

Dipole Antennas

• Half-wavelength resonance—the total length equals $\lambda/2$ at the design frequency, creating a standing wave with current maximum at the center and voltage maxima at the ends
• Omnidirectional radiation pattern in the plane perpendicular to the antenna axis, with nulls along the axis direction due to symmetric current distribution
• Input impedance of approximately $73 \, \Omega$ at resonance makes impedance matching straightforward for standard transmission lines

Monopole Antennas

• Quarter-wavelength design—functions as half of a dipole with the ground plane providing an electrical mirror through image theory
• Vertical polarization is standard, with radiation concentrated in the horizontal plane above the ground surface
• Lower input impedance (approximately $36.5 \, \Omega$) compared to dipoles, requiring different matching network considerations

Loop Antennas

• Magnetic dipole behavior—small loops (circumference $\ll \lambda$) act as magnetic dipoles with radiation resistance proportional to $(A/\lambda^2)^2$
• Figure-eight pattern with nulls along the loop axis, making them valuable for direction finding applications
• Resonant loops with circumference equal to $\lambda$ exhibit higher radiation resistance and modified patterns compared to small loops

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Directional Array Antennas

These designs use multiple elements or geometric arrangements to achieve high gain and narrow beamwidths. Constructive and destructive interference between elements shapes the radiation pattern, concentrating energy in preferred directions.

Yagi-Uda Antennas

• Parasitic element array—a driven dipole element works with a slightly longer reflector behind it and shorter directors in front to create directional gain
• End-fire radiation pattern with typical gains of 7–15 dBi depending on the number of director elements
• Narrow bandwidth (typically 2–3% of center frequency) due to the resonant nature of parasitic elements—a key trade-off for high directivity

Log-Periodic Antennas

• Frequency-independent design—element lengths and spacings follow a geometric ratio $\tau$, so the active region shifts along the structure with frequency
• Wideband operation spanning multiple octaves while maintaining consistent gain and radiation pattern across the band
• Lower gain than Yagi-Uda at any single frequency—the bandwidth-gain trade-off is fundamental in antenna design

Phased Array Antennas

• Electronic beam steering—individual elements receive phase-shifted signals, allowing the main beam direction to change without mechanical movement
• Array factor multiplies the element pattern; the total pattern equals $F_{total}(\theta) = F_{element}(\theta) \times AF(\theta)$
• Grating lobes appear when element spacing exceeds $\lambda/2$, limiting the scan range and requiring careful design

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Aperture Antennas

Aperture antennas radiate through an opening or surface rather than discrete elements. The far-field pattern is the Fourier transform of the aperture field distribution—larger apertures yield narrower beams.

Parabolic Dish Antennas

• Geometric focusing—the parabolic reflector converts a spherical wave from the feed into a plane wave, achieving gains exceeding 30–40 dBi for large dishes
• Beamwidth inversely proportional to diameter: $\theta_{3dB} \approx 70\lambda/D$ degrees, where $D$ is the dish diameter
• Aperture efficiency (typically 50–70%) accounts for feed spillover, blockage, and surface errors—a common exam calculation topic

Horn Antennas

• Waveguide transition—the flared structure provides impedance matching between the waveguide and free space while controlling the aperture phase distribution
• Predictable gain makes horns standard reference antennas for calibration; gain depends on aperture area and flare angle
• Low side lobes achievable through proper design, with optimum dimensions balancing phase error across the aperture

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Specialized Geometry Antennas

These antennas use unique physical structures to achieve specific polarization or form-factor requirements. The geometry directly determines polarization state and radiation characteristics.

Patch Antennas

• Resonant cavity model—the patch and ground plane form a leaky cavity with fringing fields at the edges responsible for radiation
• Low profile (height typically $\lambda/20$ to $\lambda/100$) enables integration into surfaces, circuit boards, and mobile devices
• Narrow bandwidth (1–5% typical) due to high Q-factor, though techniques like stacking or slots can extend bandwidth

Helical Antennas

• Axial mode operation—when circumference $\approx \lambda$ and pitch $\approx \lambda/4$, the antenna produces circular polarization with end-fire radiation
• Normal mode for small helices (circumference $\ll \lambda$) produces omnidirectional patterns similar to short dipoles
• Polarization purity makes axial-mode helices ideal for satellite links where Faraday rotation in the ionosphere affects linear polarization

Log-Periodic Antennas

• Self-similar structure—the antenna looks electrically identical at frequencies related by the scaling factor $\tau$
• Frequency-independent impedance simplifies matching across the entire operating band
• Moderate directivity (typically 7–12 dBi) with consistent front-to-back ratio across the bandwidth

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Quick Reference Table

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Self-Check Questions

1. Both dipole and small loop antennas are resonant structures, but they behave as different types of elementary radiators. What electromagnetic principle explains why their radiation patterns are oriented 90° apart?

2. A Yagi-Uda antenna achieves 12 dBi gain at 150 MHz but only 3% bandwidth. A log-periodic antenna covers 100–500 MHz with 8 dBi gain. Explain the fundamental trade-off these designs illustrate and identify which antenna parameter is being exchanged.

3. Compare the mechanisms by which a parabolic dish and a phased array achieve high directivity. How does each antenna create constructive interference in the desired direction?

4. An FRQ describes a satellite communication link experiencing signal fading as the satellite moves across the sky. Which two antenna types from this guide could address this problem, and what different approaches do they represent?

5. Both patch antennas and monopole antennas use ground planes, but for different electromagnetic purposes. Explain what role the ground plane plays in each design and how this affects their radiation patterns.