Antenna Basics: How Antennas Radiate, Radiation Pattern, Gain, Directivity & Types (Solved Problems + MCQs)

Every wireless link — FM radio, mobile phone, Wi-Fi, GPS, satellite TV, radar — begins and ends at an antenna. Antenna fundamentals (radiation pattern, gain, directivity, beamwidth, dipole length, Friis equation) are regular questions in BCS (EEE/Telecom), BTCL, Teletalk, BTRC, Bangladesh Betar, BTV and university exams. This post shows how an antenna actually radiates with an animation, then explains every parameter and antenna type with solved problems and MCQs.

⚡ Key takeaways

• An antenna is a transducer that converts guided electrical energy (current on a line) into free-space electromagnetic waves, and vice versa (reciprocity).
• Radiation is produced by accelerating (time-varying) charges; a half-wave dipole (length λ/2) is the basic resonant antenna, with input impedance ≈ 73 Ω and gain 2.15 dBi.
• Gain = efficiency × directivity (G = ηD). Isotropic antenna: D = 1 (0 dBi).
• HPBW = angle between the −3 dB points of the main lobe.
• Friis: P_r = P_t G_t G_r (λ / 4πR)².

📑 Contents

1. What is an antenna?
2. How does an antenna radiate? (animation)
3. Radiation pattern and lobes
4. Key antenna parameters
5. Types of antennas
6. Friis transmission equation
7. Solved problems
8. Practice MCQs
9. বাংলায় দ্রুত রিভিশন

1. What Is an Antenna?

IEEE defines an antenna as “a means for radiating or receiving radio waves”. It is the transition structure between a guided wave (in a coaxial cable, waveguide or transmission line) and a free-space wave. The same antenna works for transmission and reception with identical pattern, gain and impedance — the principle of reciprocity.

An antenna radiates efficiently only when its size is comparable to the wavelength λ = c/f — which is why low-frequency signals must be modulated onto a high-frequency carrier before transmission.

2. How Does an Antenna Radiate? (Animation)

1. An RF source drives alternating current into the two arms of a dipole. Charges accelerate back and forth.
2. Accelerating charges create time-varying electric and magnetic fields. Near the antenna the fields mostly store energy (reactive near field).
3. Beyond about λ/2π, field lines detach and form closed loops that travel outward at the speed of light — the radiated far field, with E and H perpendicular to each other and to the direction of travel.
4. A half-wave dipole is resonant: the current is maximum at the centre and zero at the ends, forming a standing wave, so it presents a nearly resistive impedance (≈ 73 Ω).

Animation 1 – Left: waves spreading out from a vertical dipole (red/blue = opposite field polarity); note the weak field along the dipole axis. Right: its figure-8 elevation pattern compared with an isotropic source.

3. Radiation Pattern and Lobes

The radiation pattern is a graphical plot of radiated field or power versus direction, usually drawn in two principal planes: the E-plane (containing the electric field) and the H-plane (containing the magnetic field).

• Isotropic: radiates equally in all directions (theoretical reference).
• Omnidirectional: uniform in one plane (e.g. a vertical dipole is omnidirectional in the horizontal plane).
• Directional: concentrates power in one direction (Yagi, dish, horn).

Animation 2 – A directional pattern: main lobe, side lobes, back lobe and half-power beamwidth.

4. Key Antenna Parameters

Parameter	Meaning	Formula / typical value
Directivity (D)	Ratio of maximum radiation intensity to that of an isotropic source radiating the same total power	D = 4πUmax/Prad; short dipole 1.5; λ/2 dipole 1.64
Gain (G)	Directivity reduced by losses	G = η D; expressed in dBi (vs isotropic) or dBd (vs dipole); 0 dBd = 2.15 dBi
Radiation efficiency (η)	Fraction of input power actually radiated	η = Rr/(Rr + Rloss)
Radiation resistance (Rr)	Fictitious resistance that would dissipate the radiated power	Short dipole: 80π²(l/λ)² Ω; λ/2 dipole ≈ 73 Ω; λ/4 monopole ≈ 36.5 Ω
Input impedance	Impedance at the feed terminals; should match the line (50 or 75 Ω)	Mismatch measured by VSWR or return loss
Beamwidth (HPBW)	Angle between half-power (−3 dB) points of the main lobe	Dish ≈ 70λ/D degrees
Effective aperture (Ae)	Area that captures power from an incoming wave	Ae = G λ² / 4π
Bandwidth	Frequency range over which performance (VSWR, pattern) is acceptable	Often quoted for VSWR ≤ 2
Polarization	Orientation of the E-field: linear (vertical/horizontal), circular, elliptical	Mismatch causes polarization loss
Front-to-back ratio	Main-lobe power ÷ back-lobe power	In dB; high for Yagi and dishes

5. Types of Antennas

Category	Examples	Features	Typical use
Wire antennas	Half-wave dipole, quarter-wave monopole, loop, folded dipole	Simple, cheap; folded dipole ≈ 292 Ω	FM/TV, AM broadcast towers (monopole), receivers
Array antennas	Yagi-Uda, log-periodic, phased array	Directional; Yagi = driven dipole + reflector + directors	Rooftop TV reception, 5G base stations, radar
Aperture antennas	Horn, slot, waveguide aperture	Wideband, moderate–high gain	Microwave links, dish feeds, measurement
Reflector antennas	Parabolic dish, Cassegrain	Very high gain, very narrow beam	Satellite TV, earth stations, radio astronomy
Microstrip (patch)	Rectangular / circular patch on PCB	Low profile, light, low cost; narrow bandwidth	Mobile phones, GPS, Wi-Fi, RFID
Helical	Axial-mode helix	Circular polarization	Satellite telemetry, GPS
Lens	Dielectric / Luneburg lens	Focuses waves like optics	mm-wave radar, high-frequency links

See also why microwaves are used for satellite communication and the types of satellite orbits.

6. Friis Transmission Equation

P_r = P_t G_t G_r (λ / 4πR)²

In decibels: P_r(dBm) = P_t(dBm) + G_t(dBi) + G_r(dBi) − FSPL, where the free-space path loss FSPL (dB) = 20 log₁₀(4πR/λ) = 32.45 + 20 log₁₀ f(MHz) + 20 log₁₀ R(km). Received power falls with the square of distance (6 dB per doubling of distance).

7. Solved Problems

Problem 1. Find the length of a half-wave dipole for 100 MHz.

λ = 3 × 10⁸ / 100 × 10⁶ = 3 m ⇒ λ/2 = 1.5 m. In practice the dipole is cut about 5 % shorter (≈ 1.43 m) because of end effect.

Problem 2. A 3 m parabolic dish works at 10 GHz with aperture efficiency 55 %. Find its gain and beamwidth.

1. λ = 0.03 m; G = η(πD/λ)² = 0.55 × (π × 3/0.03)² = 0.55 × 98 696 ≈ 54 300 ⇒ ≈ 47.3 dBi
2. HPBW ≈ 70λ/D = 70 × 0.03/3 = 0.7° — a very narrow pencil beam.

Problem 3. Two Wi-Fi antennas of 20 dBi each are 1 km apart at 2.4 GHz. Transmit power is 1 W. Find the received power.

1. λ = 0.125 m; (λ/4πR)² = (0.125/12 566)² ≈ 9.9 × 10⁻¹¹
2. P_r = 1 × 100 × 100 × 9.9 × 10⁻¹¹ ≈ 0.99 µW ≈ −30 dBm

8. Practice MCQs (click to see answer)

1. Input impedance of a half-wave dipole is about: (a) 36.5 Ω (b) 50 Ω (c) 73 Ω (d) 300 Ω

✔ (c) 73 Ω.

2. Gain of a half-wave dipole relative to isotropic is: (a) 0 dBi (b) 1.76 dBi (c) 2.15 dBi (d) 3 dBi

✔ (c) 2.15 dBi (directivity 1.64).

3. An antenna that radiates equally in all directions is: (a) Omnidirectional (b) Isotropic (c) Directional (d) Broadside

✔ (b) Isotropic (theoretical).

4. Antenna gain is related to directivity by: (a) G = D/η (b) G = ηD (c) G = D² (d) G = η/D

✔ (b) G = ηD.

5. The angle between half-power points of the main lobe is called: (a) FNBW (b) HPBW (c) Polarization (d) Aperture

✔ (b) Half-power beamwidth.

6. Yagi-Uda antenna consists of: (a) Only a dipole (b) Driven element, reflector and directors (c) Parabolic dish and feed (d) Patch and ground plane

✔ (b) Driven element, reflector and directors.

7. Radiation resistance of a quarter-wave monopole is about: (a) 73 Ω (b) 36.5 Ω (c) 300 Ω (d) 600 Ω

✔ (b) 36.5 Ω.

8. Received power in free space varies with distance R as: (a) 1/R (b) 1/R² (c) 1/R³ (d) 1/R⁴

✔ (b) 1/R² (Friis).

9. Antennas used in mobile phones and GPS receivers are mostly: (a) Parabolic (b) Horn (c) Microstrip patch / PIFA (d) Rhombic

✔ (c) Microstrip patch / planar inverted-F types.

10. Half-wave dipole length at 300 MHz is: (a) 1 m (b) 0.5 m (c) 0.25 m (d) 2 m

✔ (b) 0.5 m (λ = 1 m).

11. The principle that an antenna has the same properties in transmit and receive modes is: (a) Superposition (b) Reciprocity (c) Duality (d) Huygens’ principle

✔ (b) Reciprocity.

9. বাংলায় দ্রুত রিভিশন

📝 পরীক্ষার আগে এক নজরে

• অ্যান্টেনা একটি ট্রান্সডিউসার যা তারের বৈদ্যুতিক শক্তিকে মুক্ত আকাশে তড়িৎচুম্বকীয় তরঙ্গে রূপান্তর করে এবং উল্টোটাও করে (রেসিপ্রোসিটি)।
• ত্বরিত চার্জ থেকে বিকিরণ হয়। অর্ধ-তরঙ্গ ডাইপোল: দৈর্ঘ্য λ/2, ইম্পিড্যান্স ≈ ৭৩ Ω, গেইন ২.১৫ dBi; λ/4 মনোপোল ≈ ৩৬.৫ Ω।
• গেইন = দক্ষতা × ডিরেক্টিভিটি; HPBW = প্রধান লোবের −3 dB বিন্দুর মধ্যবর্তী কোণ।
• Friis সমীকরণ: Pr = Pt·Gt·Gr·(λ/4πR)² — দূরত্ব দ্বিগুণ হলে শক্তি এক-চতুর্থাংশ হয়।
• প্রকার: ডাইপোল/মনোপোল (রেডিও), ইয়াগি (টিভি), প্যারাবোলিক ডিশ (স্যাটেলাইট), হর্ন (মাইক্রোওয়েভ), প্যাচ (মোবাইল, GPS)।

Related Posts

• Microwaves: Properties, Advantages & Disadvantages
• Why Microwaves Are Used for Satellite Communication
• Advantages of Optical Fiber Communication
• Why Is Modulation Needed?

References: Constantine A. Balanis, Antenna Theory: Analysis and Design; J. D. Kraus, Antennas; IEEE Std 145 (antenna terms). Images and animations: original work by Totalecer.