C.1 INTRODUCTION

The decibel (dB) is one of the most widely used—but also one of the most frequently misunderstood—units in communications engineering. Despite its reputation for complexity, the decibel is simply a logarithmic way of expressing a ratio of two powers, P₁ and P₂(commonly the output and input powers of a device or system) The definition is.

d B = 10 \log_{10} (\frac{P_{2}}{P_{1}})

(C.1)

If the ratio of output power to input power is 15 W to 2 W (a linear ratio of 7.5), the gain in decibels is:

d B = 10 \log_{10} (\frac{15}{2}) d B = 8.75 d B

(C.2)

Thus, a gain ratio of 7.5 corresponds to a gain of 8.751 dB. Conversely, a system may exhibit loss if the output power is smaller than the input power. In that case, the ratio is inverted, yielding a negative value:

d B = 10 \log_{10} (\frac{2}{15}) d B = - 8.75 d B

(C.3)

Hence, we may equivalently describe the system as having a gain of –8.751 dB or a loss of 8.751 dB.