Antennas & EM Waves: Radiation Resistance, Half-Wave Dipole & Friis Formula
High-yield antenna theory and RF propagation principles used across satellite ground stations and missile guidance systems.
In-Depth Interview Questions & Model Solutions
Q1Derive and explain the Radiation Resistance (Rr) of a Half-Wave Dipole antenna (λ/2) and why it is ~73.13 Ohms.
For a center-fed half-wave dipole carrying sinusoidal current distribution `I(z) = I0 * cos(βz)` from -λ/4 to +λ/4, the total radiated power (Prad) is obtained by integrating the Poynting vector over a distant sphere. Equating `Prad = (1/2) * I0² * Rr`, integration yields `Rr = 73.13 Ω` with an inductive reactive component of `+j42.5 Ω`. By shortening the dipole slightly to ~0.48λ, the reactance cancels, producing a purely resistive 73 Ω input impedance matched to 75 Ω coaxial feed lines.
- Directivity of Half-Wave Dipole = 1.64 (2.15 dBi).
- Radiation pattern is doughnut-shaped (omni-directional in H-plane, figure-8 in E-plane).
- Effective Aperture Ae = (λ² / 4π) * D.
Q2State and interpret the Friis Free Space Transmission Equation for satellite communication links.
The Friis equation calculates received power (Pr) over line-of-sight free space: `Pr = Pt * Gt * Gr * (λ / (4π * d))²`, where Pt is transmitted power, Gt and Gr are antenna gains, λ is wavelength, and d is separation distance. The term `(4π * d / λ)²` is the Free Space Path Loss (FSPL), showing that received power attenuates inversely with the square of distance (1/d²) and square of carrier frequency (1/f²) for constant antenna gains.
- Path loss increases rapidly at higher microwave / millimeter-wave frequencies (Ku, Ka band).
- EIRP (Effective Isotropic Radiated Power) = Pt * Gt.
Technical Panel Interview Strategy Tips
- For ISRO telemetry interviews, know the standard frequency bands: L-band (1-2 GHz), S-band (2-4 GHz), C-band (4-8 GHz), X-band (8-12 GHz), Ku-band (12-18 GHz).