is their ratio in units of dBs. will be negative if the output amplitude is smaller than the input amplitude. Using this formula, if Aout at some frequency is 1/1000 of Ain at that frequency, then =-60 dB.The decibel (dB) is a way of expressing the gain of a filter as a function of frequency. The gain at a particular frequency is expressed as a ratio of the output signal amplitude divided by the input signal amplitude at that frequency. The reason dBs are used rather than simple ratios is that very large and very small ratios can be described with numbers of reasonable size. Another reason is that two ratios can be multiplied or divided by adding or subtracting their values in dBs, thus simplifying calculations.
Figure 13 is the mathematical definition of gain in dBs. In this formula, Aout is the output amplitude, Ain is the input amplitude, and is their ratio in units of dBs. will be negative if the output amplitude is smaller than the input amplitude. Using this formula, if Aout at some frequency is 1/1000 of Ain at that frequency, then =-60 dB.
Some other examples: A gain of -1 dB decreases the output amplitude to 0.89 times the input amplitude and -6 dB decreases the output amplitude to 0.50 times the input amplitude. A gain of +6 dB multiplies the input amplitude by 2.0.
-- J.L.
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