During a test, a NATO surveillance radar system, operating at 12 GHz at 180 kW of power, attemp

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During a test, a NATO surveillance radar system, operating...

During a test, a NATO surveillance radar system, operating at $12 \mathrm{GHz}$ at $180 \mathrm{~kW}$ of power, attempts to detect an incoming stealth aircraft at $90 \mathrm{~km}$. Assume that the radar beam is emitted uniformly over a hemisphere. (a) What is the intensity of the beam when the beam reaches the aircraft's location? The aircraft reflects radar waves as though it has a cross-sectional area of only $0.22 \mathrm{~m}^{2} .$ (b) What is the power of the aircraft's reflection? Assume that the beam is reflected uniformly over a hemisphere. Back at the radar site, what are (c) the intensity, (d) the maximum value of the electric field vector, and (e) the rms value of the magnetic field of the reflected radar beam?

During a test, a NATO surveillance radar system, operating at $12 \mathrm{GHz}$ at $180 \mathrm{~kW}$ of power, attempts to detect an incoming stealth aircraft at $90 \mathrm{~km}$. Assume that the radar beam is emitted uniformly over a hemisphere. (a) What is the intensity of the beam when the beam reaches the aircraft's location? The aircraft reflects radar waves as though it has a cross-sectional area of only $0.22 \mathrm{~m}^{2} .$
(b) What is the power of the aircraft's reflection? Assume that the beam is reflected uniformly over a hemisphere. Back at the radar site, what are (c) the intensity, (d) the maximum value of the electric field vector, and (e) the rms value of the magnetic field of the reflected radar beam?

Key Concepts

Peak and RMS Values in Sinusoidal Waves

In the context of alternating current (AC) or sinusoidal electromagnetic waves, the peak value represents the maximum amplitude of the field variation, while the root mean square (rms) value gives an effective average amplitude over time. The rms value is derived by dividing the peak value by the square root of two for a sinusoidal wave. These concepts are essential for accurately characterizing the energy content and power levels in periodic electromagnetic signals such as those encountered in radar systems.

Relationship Between Electric and Magnetic Fields in Electromagnetic Waves

Electromagnetic waves consist of oscillating electric and magnetic fields that are intrinsically linked. The intensity of the wave can be expressed in terms of the amplitude of these fields through relationships involving the permittivity of free space and the speed of light. These relationships allow one to calculate the maximum (peak) value of the electric field from the intensity, and similarly relate the fields to the magnetic field, which is central to analyzing wave properties in radar applications.

Reflection and Scattered Power

This concept involves the process by which an incident electromagnetic wave is intercepted and reflected by a target. The reflective power of the target is a function of the incident intensity and the target's effective cross-sectional area (its radar cross section). After reflection, this power is spread out again over space, and understanding this scattering is key to determining how much of the original signal returns to the radar station.

Radar Cross Section

The radar cross section is a measure of how detectable an object is by radar, essentially representing the effective area that intercepts and reradiates the incident electromagnetic energy back to the radar receiver. It is a critical parameter in radar system analysis, especially when dealing with stealth objects; a smaller radar cross section indicates that less energy is reflected back, making the object harder to detect.

Geometric Spreading and Hemispherical Emission

Geometric spreading addresses how the energy from a source is spread over an ever-increasing area as the distance from the source grows. When a source emits uniformly over a hemisphere, as in many radar systems, the power is distributed over half the surface area of a sphere. This has significant implications on the intensity experienced at a given distance and is crucial when calculating how much energy reaches a target or returns to the transmitter after reflection.

Electromagnetic Wave Intensity

This concept refers to the power transmitted per unit area by an electromagnetic wave. As waves spread out from a source, their energy is distributed over an expanding surface, and the intensity decreases with distance according to the inverse square law. Calculations involving intensity take into account the total power of the source and the area over which it is spread, which is especially important when the emission is not isotropic but is restricted, for example, to a hemisphere.

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