11.3 Antenna Principles & Electromagnetic Wave Propagation

PRC Electronics Engineering Licensure Examination Study Guide Exam

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7 Chapter 7: Electronics Engineering - Circuits & Semiconductor Diodes

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8 Chapter 8: Electronics Engineering - Transistors & Analog Circuits

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10 Chapter 10: EST - Communications Fundamentals & Transmission Lines

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11 Chapter 11: EST - Digital Communications, Wireless & Optical Systems

11.1 Pulse & Digital Modulation Systems 11.2 Data Communications, OSI Model & Protocols 11.3 Antenna Principles & Electromagnetic Wave Propagation 11.4 Optical Fiber, Microwave, Satellite & Philippine NTC Regulations

11.3 Antenna Principles & Electromagnetic Wave Propagation

Key Takeaways Explain This Topic AI

An ideal isotropic radiator emits electromagnetic energy uniformly in all directions with a baseline gain of 0 dBi (equivalent to -2.15 dBd relative to a half-wave dipole).

The physical resonant length of a half-wave dipole in free space is L = 143 / f_MHz meters (accounting for a 5% end-effect velocity factor).

The Friis Free-Space Transmission Equation calculates received signal power Pr = Pt * Gt * Gr * (lambda / (4 * pi * d))^2, demonstrating inverse-square distance loss.

Ionospheric Maximum Usable Frequency is defined by the Secant Law: MUF = fc / cos(theta) = fc * sec(theta), where fc is critical frequency.

EM wave propagation mechanisms encompass Surface/Ground Waves (<2 MHz), Ionospheric Skywaves (2-30 MHz), and Line-of-Sight Space Waves (>30 MHz).

Last updated: July 2026

11.3 Antenna Principles & Electromagnetic Wave Propagation

Quick Answer: Antennas couple guided electromagnetic energy to unguided space waves. Key PRC licensure formulas include resonant half-wave dipole length ( L = 143 / f MHz L = 143 / f_{\text{MHz}} L = 143/ f MHz ​ meters), antenna gain conversion ( G dBi = G dBd + 2.15 G_{\text{dBi}} = G_{\text{dBd}} + 2.15 G dBi ​ = G dBd ​ + 2.15 ), radio horizon distance ( d km = 3.57 [ h t + h r ] d_{\text{km}} = 3.57 [\sqrt{h_t} + \sqrt{h_r}] d km ​ = 3.57 [ h t ​ ​ + h r ​ ​ ] ), ionospheric Maximum Usable Frequency ( M U F = f c ⋅ sec ⁡ θ MUF = f_c \cdot \sec \theta M U F = f c ​ ⋅ sec θ ), and Free-Space Path Loss ( F S P L dB = 32.44 + 20 log ⁡ 10 f MHz + 20 log ⁡ 10 d km FSPL_{\text{dB}} = 32.44 + 20 \log_{10} f_{\text{MHz}} + 20 \log_{10} d_{\text{km}} FSP L dB ​ = 32.44 + 20 lo g 10 ​ f MHz ​ + 20 lo g 10 ​ d km ​ ).

Antenna Fundamentals & Radiation Mechanism

An antenna (or aerial) is a metallic conductor or structure that acts as a transducer between a guided electrical wave traveling along a transmission line and an unguided electromagnetic (EM) wave propagating in free space. Radiation occurs when alternating electric currents accelerate along a conductor, detaching electric ( E ⃗ \vec{E} E ) and magnetic ( H ⃗ \vec{H} H ) fields that propagate orthogonally to each other and to the direction of propagation.

Key Antenna Performance Parameters

Isotropic Radiator: A theoretical point-source antenna that radiates energy equally in all directions, producing a spherical wavefront. Serves as the fundamental reference ( 0 dBi 0 \text{ dBi} 0 dBi ).

Half-Wave Dipole ( λ / 2 \,\lambda / 2 λ /2 Dipole): The standard physical reference antenna. Radiates a doughnut-shaped omnidirectional pattern in its azimuth plane, possessing a directivity gain of 2.15 dBi 2.15 \text{ dBi} 2.15 dBi ( 1.64 1.64 1.64 linear gain) and a radiation resistance of 73 Ω 73 \ \Omega 73 Ω at resonance. G dBi = G dBd + 2.15 G_{\text{dBi}} = G_{\text{dBd}} + 2.15 G dBi ​ = G dBd ​ + 2.15

Directive Gain ( G G G ) & Directivity ( D D D ): Directivity is the ratio of radiation intensity in a specific direction to the average radiation intensity in all directions. Gain incorporates antenna efficiency η \eta η ( 0 ≤ η ≤ 1 0 \le \eta \le 1 0 ≤ η ≤ 1 ): G = η ⋅ D G = \eta \cdot D G = η ⋅ D

Half-Power Beamwidth (HPBW): The angular width of the main lobe measured between the two points where radiated power density drops to half ( − 3 dB -3 \text{ dB} − 3 dB ) of its maximum peak.

Polarization: The spatial orientation of the electric field vector ( E ⃗ \vec{E} E ) radiated by the antenna (Vertical, Horizontal, Circular, or Elliptical).

Practical Antenna Sizing Formulas

Due to the finite thickness of antenna conductors and capacitive end-effect , EM waves travel approximately 5 % 5\% 5% slower along metallic conductors than in free space (velocity factor v f ≈ 0.95 v_f \approx 0.95 v f ​ ≈ 0.95 ). ◄────────────── Length L ──────────────►

• ┌──────────────────┐┌──────────────────┐
• │ Dipole Arm 1 ││ Dipole Arm 2 │
• └────────┬─────────┘└─────────┬────────┘
• │ Feedline 73Ω │
• └─────────┐ ┌───────┘
• │ │
• Resonant Half-Wave Dipole Antenna

For a center-fed half-wave dipole, the physical length L L L is: L meters = 0.95 ⋅ c 2 f = 143 f MHz ( or L feet = 468 f MHz ) L_{\text{meters}} = \frac{0.95 \cdot c}{2 f} = \frac{143}{f_{\text{MHz}}} \quad \left(\text{or } L_{\text{feet}} = \frac{468}{f_{\text{MHz}}}\right) L meters ​ = 2 f 0.95 ⋅ c ​ = f MHz ​ 143 ​ ( or L feet ​ = f MHz ​ 468 ​ )

Quarter-Wave Vertical Monopole Antenna

A quarter-wave monopole mounted over a perfectly conducting ground plane utilizes image theory to form a virtual half-wave dipole, exhibiting a 36.5 Ω 36.5 \ \Omega 36.5 Ω radiation resistance: L monopole, meters = 71.5 f MHz ( or L feet = 234 f MHz ) L_{\text{monopole, meters}} = \frac{71.5}{f_{\text{MHz}}} \quad \left(\text{or } L_{\text{feet}} = \frac{234}{f_{\text{MHz}}}\right) L monopole, meters ​ = f MHz ​ 71.5 ​ ( or L feet ​ = f MHz ​ 234 ​ )

Common Antenna Configurations

Yagi-Uda Array: End-fire directional array comprising a driven element (half-wave dipole), a slightly longer reflector placed behind ( + 5 % +5\% + 5% length), and one or more shorter directors ( − 5 % -5\% − 5% length) placed in front.

Parabolic Reflector Dish: High-gain aperture antenna used for microwave and satellite links. Parabolic surface reflects rays into a parallel beam. Gain equation: G = η ( π D λ ) 2 G = \eta \left(\frac{\pi D}{\lambda}\right)^2 G = η ( λ π D ​ ) 2 where D D D is dish diameter, λ \lambda λ is wavelength, and η \eta η is aperture efficiency (typically 55 % − 70 % 55\% - 70\% 55% − 70% ).

Electromagnetic Wave Propagation Modes

EM waves travel from transmitter to receiver via three primary modes: Ionosphere Layer (Skywave Refraction: 2 - 30 MHz)

• ─────────────────────────────────────────────────────────────
• ▲ │
• │ Skywave │ Refracted Skywave
• │ ▼
• ┌───┴───┐ ┌───┴───┐
• │ TX │=== Direct Line-of-Sight =====>│ RX │ (Space Wave: > 30 MHz)
• └───┬───┘ (Space Wave: > 30 MHz) └───┬───┘
• ─────┴────────────────────────────────────────┴─────────────
• Ground/Surface Wave Diffraction (< 2 MHz)

Ground Wave (Surface Wave) Propagation ( < 2 MHz < 2 \text{ MHz} < 2 MHz ): Waves tilt and follow the curvature of the Earth due to ground diffraction and induced surface currents. Used for VLF/LF/MF broadcast radio (AM radio 535 − 1705 kHz 535 - 1705 \text{ kHz} 535 − 1705 kHz ). Severely attenuated over land; travels best over saltwater.

Skywave Propagation ( 2 MHz − 30 MHz 2 \text{ MHz} - 30 \text{ MHz} 2 MHz − 30 MHz ): High Frequency (HF) waves hit the ionized upper atmosphere ( Ionosphere ) and refract (bend) back to Earth, enabling transoceanic long-distance communications beyond the horizon.

Space Wave (Direct & Ground-Reflected) Line-of-Sight ( > 30 MHz > 30 \text{ MHz} > 30 MHz ): VHF, UHF, and microwave signals penetrate the ionosphere into space without bending back. Propagation is restricted to direct Line-of-Sight (LOS) .

Radio Horizon Calculation

Due to atmospheric refraction ( 4 / 3 4/3 4/3 effective Earth radius factor), the radio horizon extends slightly beyond the optical horizon: d LOS, km = 3.57 ( h t + h r ) d_{\text{LOS, km}} = 3.57 \left(\sqrt{h_t} + \sqrt{h_r}\right) d LOS, km ​ = 3.57 ( h t ​ ​ + h r ​ ​ )

where h t h_t h t ​ and h r h_r h r ​ are transmitter and receiver antenna heights above ground in meters.

Ionospheric Skywave Propagation & Formulas

The ionosphere contains ionized atmospheric layers ( D , E , F 1 , F 2 D, E, F_1, F_2 D , E , F 1 ​ , F 2 ​ ) formed by solar ultraviolet radiation.

D Layer (60-90 km): Exists only during daytime; absorbs HF waves ( < 3 MHz < 3 \text{ MHz} < 3 MHz ).

E Layer (90-130 km): Refracts upper MF and lower HF waves during the day.

F Layer (150-400 km): Splices into F 1 F_1 F 1 ​ and F 2 F_2 F 2 ​ layers by day and merges into a single F F F layer by night. Primary ionospheric layer for long-distance HF skip communications.

Critical Frequency ( f c f_c f c ​ )

The highest frequency that returns to Earth when transmitted straight up vertically ( 90 ∘ 90^\circ 9 0 ∘ incidence): f c = 9 N m a x f_c = 9 \sqrt{N_{max}} f c ​ = 9 N ma x ​ ​

where N m a x N_{max} N ma x ​ is maximum electron density in electrons/m 3 \text{electrons/m}^3 electrons/m 3 .

Maximum Usable Frequency (MUF)

The highest frequency that can be used for skywave communication between two specific points at an angle of incidence θ \theta θ (Secant Law): M U F = f c cos ⁡ θ = f c ⋅ sec ⁡ θ MUF = \frac{f_c}{\cos \theta} = f_c \cdot \sec \theta M U F = cos θ f c ​ ​ = f c ​ ⋅ sec θ

Optimum Working Frequency (OWF / FOT)

To protect against ionospheric diurnal variations, the operational frequency is chosen as 85 % 85\% 85% of MUF: O W F = 0.85 × M U F OWF = 0.85 \times MUF O W F = 0.85 × M U F

Free-Space Path Loss & Friis Link Equation

In an ideal unobstructed free space, power density decreases with the square of distance.

Friis Transmission Equation P r = P t ⋅ G t ⋅ G r ( λ 4 π d ) 2 P_r = P_t \cdot G_t \cdot G_r \left(\frac{\lambda}{4 \pi d}\right)^2 P r ​ = P t ​ ⋅ G t ​ ⋅ G r ​ ( 4 π d λ ​ ) 2

where P r P_r P r ​ is received power, P t P_t P t ​ is transmit power, G t , G r G_t, G_r G t ​ , G r ​ are antenna linear gains, and d d d is path distance.

Free-Space Path Loss (FSPL) Formula in Decibels

Converting the loss factor ( 4 π d / λ ) 2 (4\pi d / \lambda)^2 ( 4 π d / λ ) 2 into logarithmic decibel form yields the mandatory board exam formula: F S P L dB = 32.44 + 20 log ⁡ 10 ( f MHz ) + 20 log ⁡ 10 ( d km ) FSPL_{\text{dB}} = 32.44 + 20 \log_{10}(f_{\text{MHz}}) + 20 \log_{10}(d_{\text{km}}) FSP L dB ​ = 32.44 + 20 lo g 10 ​ ( f MHz ​ ) + 20 lo g 10 ​ ( d km ​ )

(Alternatively, if frequency is in GHz: F S P L dB = 92.45 + 20 log ⁡ 10 ( f GHz ) + 20 log ⁡ 10 ( d km ) FSPL_{\text{dB}} = 92.45 + 20 \log_{10}(f_{\text{GHz}}) + 20 \log_{10}(d_{\text{km}}) FSP L dB ​ = 92.45 + 20 lo g 10 ​ ( f GHz ​ ) + 20 lo g 10 ​ ( d km ​ ) ).

Step-by-Step Path Loss Calculation Example

Problem: A line-of-sight wireless telemetry link operates at 2.4 GHz 2.4 \text{ GHz} 2.4 GHz ( 2400 MHz 2400 \text{ MHz} 2400 MHz ) across a distance of 10 km 10 \text{ km} 10 km . Calculate the Free-Space Path Loss ( F S P L FSPL FSP L ) in decibels.

Solution:

Identify Given Values: f = 2400 MHz f = 2400 \text{ MHz} f = 2400 MHz , d = 10 km d = 10 \text{ km} d = 10 km .

Apply FSPL Equation: F S P L dB = 32.44 + 20 log ⁡ 10 ( 2400 ) + 20 log ⁡ 10 ( 10 ) FSPL_{\text{dB}} = 32.44 + 20 \log_{10}(2400) + 20 \log_{10}(10) FSP L dB ​ = 32.44 + 20 lo g 10 ​ ( 2400 ) + 20 lo g 10 ​ ( 10 )

Calculate Logarithms: log ⁡ 10 ( 2400 ) ≈ 3.3802 → 20 × 3.3802 = 67.60 dB \log_{10}(2400) \approx 3.3802 \rightarrow 20 \times 3.3802 = 67.60 \text{ dB} lo g 10 ​ ( 2400 ) ≈ 3.3802 → 20 × 3.3802 = 67.60 dB log ⁡ 10 ( 10 ) = 1.0000 → 20 × 1.0000 = 20.00 dB \log_{10}(10) = 1.0000 \rightarrow 20 \times 1.0000 = 20.00 \text{ dB} lo g 10 ​ ( 10 ) = 1.0000 → 20 × 1.0000 = 20.00 dB

Sum Components: F S P L dB = 32.44 + 67.60 + 20.00 = 120.04 dB FSPL_{\text{dB}} = 32.44 + 67.60 + 20.00 = 120.04 \text{ dB} FSP L dB ​ = 32.44 + 67.60 + 20.00 = 120.04 dB