more important metrics in communications, used to categorize the qual- ity of transmission. That metric is known as the signal-to-noise ratio. The bel represents the first in a series of power ratios developed to quan- tify the proportion of power between two points. As you might sur- mise, the bel owes its name to Alexander Graham Bell, the inventor of the telephone. The bel uses logarithms to the base 10 to express the ratio Chapter Two of power transmitted to power received. The resulting gain or loss for a circuit is given by the following formula: B = log 11 where B is the power ratio in bels, P is the power output or received, and P1 is the input or transmitted power. The bel used logarithms to measure power because humans hear logarithmically and the first series of power measurements were applied to telephone circuits that carried audio. In other words, the human ear perceives sound or loudness on a logarithmic scale. For example, if we estimate the loudness of a signal to have doubled, the transmission power will have actually increased by a factor of approximately 10. Another reason for the use of logarithms in power measurements is that signal boosts (gain) due to amplification or signal loss due to resistance are additive. The ability to add and subtract when performing power measurements based on a log (logarithmic) scale simplifies computations. For example, a 10-B signal that encounters a 5-B loss and is then passed through a 15-B amplifier results in a signal strength of 10 -5 +15, or 20 B. For those of you who are a bit rusty when it comes to logarithms, note that the logarithm to the base 10 (log lo) of a number is equivalent to how many times 10 is raised to a power equal to that number. For example, log 100 is 2, log log 1000 is 3, and SO on. Because output or received power is normally less than input or transmitted power, the denominator in the preceding equation is normally larger than the numerator. To simplify computations, we can note a second important property of logarithms: As an exam