One of the advantages of using the base 10 logarithm ratio of two powers is that when dealing with multiple amplifier, filter or attenuator stages cascaded together, we can simply add or subtract their decibel values instead of multiplying or dividing their linear values. So the result is 100mW as declared in example No1. So if we use the logarithmic ratio of two quantities, P 1 and P 2 we end up with a new quantity or level which can be presented using Decibels. When analysing circuits in the frequency domain, it is more convenient to compare the amplitude ratio of the output to input values on a logarithmic scale rather than on a linear scale. Remembering of course that if a circuits output is positive, then it produces amplification or gain, and if its output is negative, then it produces attenuation or loss. Likewise if we cascaded together to first-order RC filter circuits with attenuations of 0.7071 each, the the total attenuation would be 0.5 (0.7071*0.7071). For example, if we cascade two amplifier stages together with power or voltage gains of say 20 and 36, respectively, then the total gain would be 720 (20*36). When designing or working with amplifier and filter circuits, some of the numbers used in the calculations can be very large or very small. Generally, decibels is a measure of loudness.
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