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How to Convert kW to dBmV

Electronic signals range in power from millions of watts for transmitters to tiny fractions of a watt for receivers. Engineers developed the decibel to create a small range of numerical references to describe a wide range of powers. A decibel represents a logarithm or exponent that basically expresses the number of times the referenced power gets multiplied by itself. A dBm measurement uses a milliwatt as a power reference and a dBmV uses a millivolt. To convert kW to dBmV, first convert to kW to dBm and then convert dBm to dBmV.

Things You'll Need

Scientific calculator with square root and logarithm functions

Instructions

- 1
  Change the kW level to watts by moving the decimal point three places to the right. For example, 5 kW = 5,000 W and 10.5 kW = 10,500 W.
- 2
  Calculate the dBm level using the formula: dBm = 10 x log10[1000 x P(W)]. Enter the watts into the calculator, multiply by 1,000, press "log" and then multiply by 10. For example, 5,000 watts x 1,000 = 5,000,000, the logarithm is 6.69897 multiplied by 10 = 66.9897 dBm. 10,500 watts times 1,000 = 10,500,500, the logarithm is 7.02119 x 10 = 70.2119 dBm. Record the dBm figure.
- 3
  Calculate the impedance factor in the brackets needed for the formula: dBmV = dBm + 30 + [20 x log (of the square root of system impedance)]. Enter the impedance of the circuit in the calculator, press the square root button, press the "log" button and then multiply by 20. For example, the square root of 50 ohms is 7.07106, the logarithm of that is 0.84948 and multiplied by 20 is 16.9896. For a 75 ohm circuit, the square root is 8.66025, the logarithm is 0.93753 and multiplied by 20 is 18.7506. Record the result.
- 4
  Calculate dBmV by inserting the impedance factor between the brackets in the formula: dBmV = dBm + 30 + [20 x log (of the square root of system impedance)]. Add 30 to the dBm level and then add the impedance factor. For example, for 5 kW at 50 ohms, 66.9897 dBm + 30 + 16.9896 = 113.9792 dBmV. At 75 ohms, 66.9897 + 30 + 18.7506 = 115.7406 dBmV. For 10.5 kW at 50 ohms, 70.2119 dBm + 30 + 16.9896 = 117.2015 dBmV. At 75 ohms, 70.2119 dBm + 30 + 18.7506 = 118.9625 dBmV.

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