In electrical, RF, and optical engineering, power levels often span many orders of magnitude, ranging from Picowatts (pW) at a receiver to Watts (W) at a transmitter. Working with this vast range using linear units is cumbersome, making system calculations prone to error.The Decibel (dB) system solves this problem by using a logarithmic scale, converting complex multiplication and division operations into simple addition and subtraction.
Relative (dB) vs. Absolute (dBm) Power
The fundamental distinction is the reference point.
Decibel (dB): The Relative Ratio
The dB is a dimensionless unit used to express the ratio between two power levels (\(P_1\)and \(P_2\)) or voltage levels (\(V_1\) and \(V_2\)). It is used to quantify gain (amplification) or loss (attenuation).
Convenience: Signal chain calculations become additive. If a source has a 10 dB gain and then passes through a 3 dB cable loss, the net change is simply \(10 - 3 = 7 dB\).
Power Ratio (Gain/Loss):
Voltage Ratio (Gain/Loss):
Note on Voltage (\(20 \cdot\log\)): The \(20 \cdot\log\) formula is only valid if the measurement is taken across points with identical impedance (e.g., \(50 \Omega\) or \(75 \Omega\)). If the impedances differ, the direct power formula (\(10 \cdot\log\)) must be used.
Decibel-Milliwatt (dBm): The Absolute Level
The \(\text{dBm}\) is an absolute unit of power, where the reference power (\(P_{ref}\)) is always 1 milliwatt (\(\text{1 mW}\)). It is the standard unit for expressing transmitter output power and receiver sensitivity in both \(\text{RF}\) and optical power systems.
$$P (\text{dBm}) = 10 \cdot \log_{10} \left( \frac{P (\text{mW})}{1 \text{ mW}} \right)$$Conversion: You can convert directly between \(\text{dBm}\) and Watts:
$$\text{Power} (\text{mW}) = 10^{\frac{P (\text{dBm})}{10}}$$