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## Units of Measure and Physical Constants

### Units of Measure

Phased Array System Toolbox™ software almost exclusively uses SI base and derived units to measure physical quantities. The software does not provide any utilities for converting SI base or derived units to other systems of measurement.

#### Angles

Angles are an exception to the use of SI base and derived units. All angles in Phased Array System Toolbox software are specified in degrees. See Spherical Coordinates for an explanation of the angles used in the software. There are two utility functions for converting angles from radians to degrees and degrees to radians: `rad2deg` and `deg2rad`.

#### Decibels

To accurately model and simulate phased array systems, it is necessary to account for gains and losses in power incurred at various stages of processing. In Phased Array System Toolbox software, gains and losses are specified in decibels (dB). Signal to noise ratios (SNRs) and the receiver noise figure are also expressed in dB. Power in dB is related to power in watts, P, by:

`$10{\mathrm{log}}_{10}\left(P\right)$`

There are two utility functions for converting between dB and power: `db2pow` and `pow2db`, and two utility functions for converting between magnitude and dB: `db2mag` and `mag2db`.

### Physical Constants

Modeling and simulating phased array systems requires that you specify values for several physical constants. For example, the distribution of thermal noise power per unit bandwidth depends on the Boltzmann constant. To measure Doppler shift and range in radar, you have to specify a value for the speed of light. The following table summarizes the three physical constants used in the toolbox. See `physconst` for additional information.

ConstantDescriptionValue
`'LightSpeed'`Speed of light in vacuum299,792,458 m/s. Most commonly denoted by c.
`'Boltzmann'`Boltzmann constant relating kinetic energy to temperature$1.\text{3806504}×{10}^{-23}$ J/K. 2006 NIST value, most commonly denoted by k.
`'EarthRadius'`Mean radius of the Earth6,371,000 m

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