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?
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Asphere
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Brectangle
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Csquare
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Dellipse
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Ecylinder
Answer
Correct Answer: sphere
Explanation
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:
1) Choose a large radius r so all observations lie in the far field.2) Use a spherical surface area element dA = r^2 sinθ dθ dφ.3) Integrate the radial Poynting component over the sphere to obtain total radiated power.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