# dB Power

Supplying two of the three values for dB, P1, or P2, calculates the remaining value. If over specified, the value for dB and P1 will be used to determine P2.

The equation used to determine the values is:

The decibel (dB) is a unit less value that expresses the ratio between two quantities on a logarithmic scale. Positive dB values indicate gain (amplification) and negative values indicate loss (attenuation).

There are some rule of thumb values that are handy to know. A value of 0 dB means that the input and output power is the same. A value of 3 dB means the output power is ≈2 time the input power. A value of -3dB means the output power is ≈0.5 times the input power. Note the ±3 dB rule only apples to power level and not voltage levels.

Using values in dB means that you to add rather than multiply when finding system gain. For example, assume that a number of ‘black boxes’ shown in the figure above are connected in series (the output of one is connected to the input of the next). The total gain or attenuation for the series connected set can be found by adding the dB values for each individual black box together. If the gain of each black box was known as a ratio between the input and output, their values would need to be multiplied.

Remember that a dB value is based on a ratio so it is acceptable to say that the gain is 5 dB because gain is an expression that relates the input to the output, but it is unacceptable to say that the power measure 5 dB without providing a value that the 5 dB was referenced to. In these cases, It is common to see dB values expressed with a letter appended to ‘dB’ as in, “the measured value was +12 dBW”. The additional letter provides the reference value which in this case it is 1W. When using the solver in this way, the reference level is considered the input to the ‘black box’ meaning in this case that P1 is 1W.

Some commonly used reference values are:

dBm: reference power of 1mW

dBW: reference power of 1W

dBk: reference power of 1kW