The dBa is typically used to specify or quantify filter performance. The input signal power is a power unit, so 10log10 is used to convert from linear. The dBc is typically used in communication to denote signals of interest with respect to the carrier sinusoid.Ī relative power unit that references the power of an input signal. The carrier power is a power unit, so 10log10 is used to convert from linear. The W is a power unit, so 10log10 is used to convert from linear.Īn relative power unit that references the power of a carrier. The mW is a power unit, so 10log10 is used to convert from linear.Īn absolute power unit that references 1 W. While field or amplitude quantities relate to power through the square and use the equation:Īn absolute power unit that references 1 mW. The dB is the fundamental unit of logarithmic power ratios. On the other hand, the plot in dB clearly shows the relative amplitudes of both the sinusoids and their proximity to the noise floor. The linear plot shows the sinusoid at 18 MHz, but we can visualize nothing about the floor or any other signals in the spectrum. The following figures illustrate this point using a noise floor and two sinusoids.īoth plots are based on the same data. Adding small numbers is much easier than multiplying large numbers.Īnother advantage to using the dB scale is the ease of visualization of signals with large dynamic ranges. I could either multiply 1.4125e6 by 1.22 in linear scale, or add 0.5 dB to 61.5 dB for the same gain description. For example, what if I added another gain stage of 1.22 to the previous example. Logarithms can be added instead of multiplied, so it’s more manageable to understand gain stages in terms of dB than linear scales. It’s easier to say the the amplifier has 61.5 dB of gain. It can be difficult and cumbersome to talk about a receiver that has, for example, 1.4125 million times the amplification of the received input signal. Why Engineers Use dBĮngineers use the decibel (dB) system because it’s a convenient way of manipulating and visualizing large numbers and large dynamic ranges. The only assumption used is that the two resistances are the same for both voltages, which is a good assumption for well-designed circuits. This is demonstrated using the ratio of two voltages: The conversion to dB using 20log10 is required because squared field quantities (like voltage and current) are proportional to power. When the two ratio quantities are field quantities (or amplitudes) use the definition: When the two ratio quantities are already powers, the previous equation can be used (shown again here): Keep in mind that the decibel represents the ratio between to power quantities. These units are denoted with another letter after the dB, such as dBm, dBW, etc. The dB is used to describe relative powers, or ratios, but there are also many derived units that represent absolute quantities or reference specific quantities. The dB can be converted from the logarithmic scale back to linear using the following equation: The decibel (dB) is unitless, just like when we talk about ratios on a linear scale (e.g. The dB is positive when describing powers greater than the reference power and negative for powers less than the reference power. Where P_ref is the reference power and P is the power to be quantified. The decibel is a unit of measure that quantifies the ratio of two powers using the logarithmic scale.
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