Total Radiated Power and the Radiation Sphere Concept To compute the total power radiated by an antenna, one conceptually encloses it with a very large closed surface and integrates the outward power flow. What is this surface taken to be in standard antenna theory?

Introduction / Context:
Total radiated power is found by integrating the time-average Poynting vector over a closed surface enclosing the source in the far field. The choice of surface simplifies calculation and interpretation of radiation intensity and directivity.

Given Data / Assumptions:

• Far-field region such that fields locally approximate outward spherical waves.
• Steady-state sinusoidal excitation.
• Lossless surrounding space for the conceptual integration.

Concept / Approach:

In the far field, radiation from any antenna approximates a spherical wave with power density decreasing as 1/r^2. Because of this, a sphere centered on the antenna is the natural Gaussian surface for integration. The radiation intensity U(θ, φ) relates to total power Prad via Prad = ∮ S · dA over the sphere, commonly expressed as Prad = ∫∫ U(θ, φ) dΩ.

Step-by-Step Solution:

Verification / Alternative check:

Directivity, gain, and effective aperture are all derived using spherical integration, reinforcing the standard choice.

Why Other Options Are Wrong:

Rectangles, squares, ellipses, or cylinders complicate integration and are not aligned with the spherical symmetry of far-field radiation.

Common Pitfalls:

Confusing near-field reactive energy with radiated power; only the far-field outward flux contributes to total radiated power.

Final Answer:

sphere