A 1-mW signal is attenuated at the rate of 5 dB/1,000ft. What is the power

level into a receiver that is 6,000 feet from the signal source?

The decibel (db) is the unit used to measure levels in telecommunications. It is based onthe base 10 logarithm of a ratio (Reference Sheet). The ratio can be the ratio of input to output for indicating relative gains and losses in a system. The ratio can also be the ratio of a level relative to an absolute value. This question considers both types of decibels.To determine the power level at the input to the receiver, convert the 1 mW (milliwatt) to dBm (decibels relative to a 1 mW reference) as follows:

10 * log(value/reference value) = 10 * log(1mW/1mW) = 0 dBm

Since the output level equals the reference level, the value of 1 mW is 0 dBm. The totalloss of the link is:

5 dB/1000ft * 6 = 30 dB loss.

The level into the receiver = 0 dBm – 30 dB = -30 dBm.

The decibel (db) is the unit used to measure levels in telecommunications. It is based onthe base 10 logarithm of a ratio (Reference Sheet). The ratio can be the ratio of input to output for indicating relative gains and losses in a system. The ratio can also be the ratio of a level relative to an absolute value. This question considers both types of decibels.To determine the power level at the input to the receiver, convert the 1 mW (milliwatt) to dBm (decibels relative to a 1 mW reference) as follows:

10 * log(value/reference value) = 10 * log(1mW/1mW) = 0 dBm

Since the output level equals the reference level, the value of 1 mW is 0 dBm. The totalloss of the link is:

5 dB/1000ft * 6 = 30 dB loss.

The level into the receiver = 0 dBm – 30 dB = -30 dBm.