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# What is the conversion factor from dBm to dBv in a 50 ohm system?

Value in dBm - 13dB = Value in dBv

Equations and Sample Calculations:

Convert power in dBm (PdBm) to power in milliwatts (PmW) via the equation:

• PdBm = 10 ^ ( PmW / 10 )
• e.g. for PdBm = -20dBm, then PmW = 10 ^ (-20/10) = 0.01mW

Convert power in milliwatts (PmW) to power in watts (PW) via the equation:

• PW = PmW / 1000
• e.g. for PmW = 0.01mW, then PW = 0.01/1000 = 0.00001

Convert power in watts to voltage RMS (VRms) via the equation:

• VRms = Square Root (Power Watts * System Zo) where System Zo = 50 Ohms
• e.g. for PW = 0.00001W, then VRms = Square Root (0.00001 * 50) = 0.02236

Convert VRms to Power in dBv (PdBv) via the equation:

• PdBv = 20 * Log (VRms / 1)
• e.g. for VRms = 0.02236, then PdBv = 20 * Log (0.02236 / 1) = -33.01dBv

Therefore, in a 50 Ohm System, -20dBm = -33dBv, or equivalently PdBv = PdBm - 13 dB