Log base of decibel scale4/11/2024 ![]() Other helpful formulas and conversions can be found at the AH Systems website, AR EMC Formulas & Equations document and Sengpiel Audio website. dBuV referred to 1uV, dBm is referred to 1mW. If the ratio is referred to a specific quantity this is indicated by a suffix, i.e. Conversion between voltage in dBuV and power in dBm for a given impedance Z ohms is V(dBuV) = 90 + 10 log (Z) + P(dBm). A base-10 log scale is used for the Y axis of the bottom left graph, and the Y axis ranges from 0.1 to 1,000. A logarithmic scale is a nonlinear scale often used when analyzing a large range of quantities. Power is proportional to voltage squared, hence the ratio of voltages or currents across a constant impedance is given by dB = 20 log (V1/V2) or 20 log I1/I2). The utility of dB comes from two properties: The logarithmic scale applies conveniently to situations where you have a huge dynamic range. Originally the dB was conceived as a power ratio, given by dB = 10 log (p1/P2). A decibel is one tenth of a bel, a seldom-used unit named in honor of Alexander Graham Bell. The number of decibels is ten times the logarithm to base 10 of the ratio of the two power quantities. RatiodB 10log 10 ( P1 / P0) Amplitude ratio The ratio of quantities like voltage, current and sound pressure level are calculated as ratio of squares. The decibel is also commonly used as a measure of gain or attenuation, the ratio of input and output powers of a system, or of individual factors that contribute to such ratios. One of these quantities is often a reference value, and in this case the decibel (dB) can be used to express the absolute level of the physical quantity. ![]() The decibel (dB) is a logarithmic unit used to express the ratio between two values of a physical quantity, often power or intensity. ![]() ![]() Gains of amplifiers, attenuation of signals, and signal-to-noise ratios are often expressed in “dB”. The inverse of a logarithm is called an antilogarithm or antilog thus, is the antilog of in the base. The base is chosen to be a positive real number, and we normally only take logs of positive real numbers (although it is ok to say that the log of 0 is ). The decibel (dB) is used for a variety of measurements in science and engineering, most prominently in acoustics, electronics, and EMC / EMI. The term logarithm'' can be abbreviated as log''. ![]()
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