Radar is an object detection system that uses electromagnetic waves to identify the range, altitude, direction, or speed of both moving and fixed objects. Radar and Radio are using similar formulas and they share some of them with telecommunications like the ones we presented in our Top 10 Telecommunications Formulas post.

1. Radar Range

To calculate the range of a radar you need to know, the transmitted pulse peak power, the maximum power gain of antenna, the Radar cross section area, the antenna aperture, the minimum detectable signal of receiver, and… pi (spoiler alert, it's 3,14).

2. Radiant Exitance (real surface)

In radiometry, radiant exitance is the radiant flux emitted by a surface per unit area, and spectral exitance is the radiant exitance of a surface per unit frequency or wavelength, depending on whether the spectrum is taken as a function of frequency or of wavelength. This is the emitted component of radiosity.

3. Ratiometric Correction of Transducer Output

Piezoresistive transducers configured as Wheatstone bridges. often exhibit ratiometric behavior with respect not only to the measured pressure, but also the transducer supply voltage. P is the actual measured pressure, K the nominal transducer scale factor and V is for the transducer supply voltage.

4. Fraunhofer diffraction (Diffraction by a double slit)

In optics, the Fraunhofer diffraction equation is used to model the diffraction of waves when the diffraction pattern is viewed at a long distance from the diffracting object, and also when it is viewed at the focal plane of an imaging lens. In contrast, the diffraction pattern created near the object, in the near field region, is given by the Fresnel diffraction equation.
In a diffraction by a double slit, (Double slit fringes with sodium light illumination) the two slits are illuminated by a single light beam.

5. Fractional bandwidth (RLC circuits)

The bandwidth as a fraction of the resonance frequency. It is the difference between the upper and lower frequencies in a continuous set of frequencies.  The bandwidth is measured between the frequencies at which the power passed through the circuit has fallen to half the value passed at resonance. There are two of these half-power frequencies, one above, and one below the resonance frequency.

6. Guided ray (acceptance angle)

A guided ray (also bound ray or trapped ray) is a ray of light in a multi-mode optical fiber ( type of optical fiber mostly used for communication over short distances), which is confined by the core.

7. Hemispherical attenuation coefficient

Attenuation coefficient or narrow beam attenuation coefficient of the volume of a material characterizes how easily it can be penetrated by a beam of light, sound, particles, or other energy or matter. A large attenuation coefficient means that the beam is quickly “attenuated” (weakened) as it passes through the medium, and a small attenuation coefficient means that the medium is relatively transparent to the beam.

8. Planck's law (by the wavelength)

Planck’s law describes the electromagnetic radiation emitted from a black body at a certain temperature. Radiance and spectral radiance are measures of the quantity of radiation that passes through or is emitted from a surface and falls within a given solid angle in a specified direction. Planckian spectral radiance can be measured by the wavelength of the radiation.

9. Q factor (RLC circuits)

The Q factor in an RLC circuit is the peak energy stored in the circuit divided by the average energy dissipated in it per cycle at resonance, and is the inverse of fractional bandwidth which is dimensionless. Simple as that!

10. Spectral Exitance (real surface)

The spectral exitance of a real surface around a given frequency or wavelength, according to the Lambert’s cosine law and the Planck’s law, is equal to the formula shown above, where h is the Planck constant, c the speed of light, λ the wavelength, k the Boltzmann constant and T the temperature of the surface. π is pi, and e is e (duh!).

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