About Milliwatts (mW) to Decibel-Milliwatts (dBm) Conversion

What are Milliwatts and Decibel-Milliwatts?

Milliwatts (mW) and decibel-milliwatts (dBm) are both units used to measure power, particularly in radio, microwave, and fiber-optic communication circuits:

• Milliwatt (mW): A unit of power equal to one-thousandth of a watt. It's a linear measure of power.
• Decibel-Milliwatt (dBm): A power ratio in decibels (dB) of the measured power referenced to one milliwatt (mW). It's a logarithmic measure of power.

Formula for Milliwatts to Decibel-Milliwatts Conversion

The formula to convert milliwatts to decibel-milliwatts is:

\[dBm = 10 \log_{10}(mW)\]

Where:

• \(dBm\) is the power in decibel-milliwatts
• \(mW\) is the power in milliwatts
• \(\log_{10}\) is the base-10 logarithm

Calculation Steps

1. Identify the power in milliwatts.
2. Take the base-10 logarithm of this value.
3. Multiply the result by 10.
4. The result is the equivalent power in dBm.

Example

Let's convert 100 milliwatts to decibel-milliwatts:

1. Given: \(mW = 100\)
2. Apply the formula: \(dBm = 10 \log_{10}(100)\)
3. Calculate: \(dBm = 10 \times 2 = 20\)

Visual representation:

Therefore, 100 milliwatts is equivalent to 20 decibel-milliwatts.