Decibels and Radars

dBm measures power relative to 1 milliwatt, while dBW measures power relative to 1 watt.

So to convert between the two, you have these equations:

dBm = dBW + 30

or

dBW = dBm - 30

dBW = 10 x log₁₀(Power_Watts)

dBW: Transmitter power output in decibels.
Power_Watts: Transmitter power output in watts.

EXAMPLE: What is the dBW of a 1 megawatt radar?

10 x log₁₀(1,000,000) = 60 dB

Power_Watts = 10^{(Decibels/10)}

Power_Watts: Transmitter power output in watts.
Decibels: Transmitter power output in decibels.

EXAMPLE: What is the power in watts of a 100 dBw radar?

10^(100/10) = 10,000,000,000 watts.

dBsm = 10 x log₁₀(RCS/1m²)

dBsm: Radar Cross Section of target in decibels.
RCS: Radar Cross Section of target in square meters.

EXAMPLE: What is the dBsm of a stealth fighter with a RCS of 0.01 m²?

10 x log₁₀(0.01/1m²) = -20 dBsm

RCS = 10^{(Decibels/10)}

RCS: Radar Cross Section of target in square meters.
Decibels: Radar Cross Section of target in decibels.

EXAMPLE: What is the RCS in square meters of an aircraft with a RCS of 5 dB?

10^(5/10) = 3.16 m2

dBi = 10 x log₁₀(Gain/1)