Editing Radar cross section (section)

==Formulation==

Informally, the RCS of an object is the cross-sectional area of a perfectly reflecting sphere that would produce the same strength reflection as would the object in question. (Bigger sizes of this imaginary sphere would produce stronger reflections.) Thus, RCS is an abstraction: the radar cross-sectional area of an object does not necessarily bear a direct relationship with the physical cross-sectional area of that object but depends upon other factors.<ref name="Balanis 12">C. A. Balanis, "Advanced Engineering Electromagnetics", 2nd ed. New York, NY, USA: Wiley, 2012.</ref>

Somewhat less informally, the RCS of a radar target is an effective area that intercepts the transmitted radar power and then scatters that power [[isotropic radiator|isotropically]] back to the radar receiver.

More precisely, the RCS of a radar target is the hypothetical area required to intercept the transmitted power density at the target such that if the total intercepted power were re-radiated isotropically, the power density actually observed at the receiver is produced.<ref>Skolnick, M.I., Introduction to Radar Systems, McGraw-Hill, 1980.</ref> This statement can be understood by examining the monostatic (radar transmitter and receiver co-located) [[Radar#Radar range equation|radar equation]] one term at a time:

:<math>P_r = {{P_t G_t}\over{4 \pi r^2}} \sigma {{1}\over{4 \pi r^2}} A_\mathrm{eff}</math>

where
*<math>P_t</math> = transmitter's input power (watts)
*<math>G_t</math> = [[Gain (electronics)|gain]] of the radar transmit antenna (dimensionless)
*<math>r</math> = distance from the radar to the target (meters)
*<math>\sigma</math> = radar cross-section of the target (meters squared)
*<math>A_\mathrm{eff}</math> = [[Antenna aperture|effective area]] of the radar receiving antenna (meters squared)
*<math>P_r</math> = power received back from the target by the radar (watts)

The
<math display=inline>{{P_t G_t}\over{4 \pi r^2}}</math>
term in the radar equation represents the power density (watts per meter squared) that the radar transmitter produces at the target. This power density is intercepted by the target with radar cross-section <math display=inline>\sigma</math>, which has units of area (meters squared). Thus, the product
<math display=inline>{{P_t G_t}\over{4 \pi r^2}} \sigma</math>
has the dimensions of power (watts), and represents a hypothetical total power intercepted by the radar target. The second <math display=inline>{{1}\over{4 \pi r^2}}</math> term represents isotropic spreading of this intercepted power from the target back to the radar receiver.  Thus, the product
<math display=inline>{{P_t G_t}\over{4 \pi r^2}} \sigma {{1}\over{4 \pi r^2}}</math>
represents the reflected power density at the radar receiver (again watts per meter squared). The receiver antenna then collects this power density with effective area <math display=inline>A_\mathrm{eff}</math>, yielding the power received by the radar (watts) as given by the radar equation above.

The scattering of incident radar power by a radar target is never isotropic (even for a spherical target), and the RCS is a hypothetical area. In this light, RCS can be viewed as a correction factor that makes the radar equation "work out right" for the experimentally observed ratio of <math display=inline>P_r/P_t</math>. However, RCS is a property of the target alone and may be measured or calculated. Thus, RCS allows the performance of a radar system with a given target to be analysed independent of the radar and engagement parameters. In general, RCS is a function of the orientation of the radar and target. A target's RCS depends on its size, ''[[Fresnel reflectivity|reflectivity]]'' of its surface, and the ''[[directivity]]'' of the radar return caused by the target's geometric shape.