About Watts (W) to Decibel-Milliwatts (dBm) Conversion

What are Watts and dBm?

Watts (W) and decibel-milliwatts (dBm) are units used to measure power, but in different contexts:

• Watt (W): The SI unit of power, defined as one joule per second. It measures the rate of energy transfer.
• Decibel-milliwatt (dBm): A power ratio in decibels (dB) of the measured power referenced to one milliwatt (mW). It's commonly used in radio, microwave, and fiber-optic communication contexts.

Formula for Watts to dBm Conversion

The formula to convert watts to dBm is:

\[dBm = 10 \log_{10}(W \times 1000)\]

Where:

• \(dBm\) is the power ratio in decibels of the measured power referenced to one milliwatt
• \(W\) is the power in watts
• 1000 is the factor to convert watts to milliwatts

Calculation Steps

1. Identify the power in watts.
2. Multiply the watt value by 1000 to convert to milliwatts.
3. Take the base-10 logarithm of this value.
4. Multiply the result by 10.
5. The final result is the power in dBm.

Example

Let's convert 1 watt to dBm:

1. Given: \(W = 1\)
2. Apply the formula: \(dBm = 10 \log_{10}(1 \times 1000)\)
3. Calculate: \(dBm = 10 \log_{10}(1000) = 10 \times 3 = 30\)

Visual representation:

Therefore, 1 watt is equivalent to 30 dBm.