A receiver detects a signal with a power level of -30 dBm. What is the RMS voltage of this detected signal? Assume a load resistance of 60 Ω.
To find the RMS voltage of the detected signal, we need to convert the power level from decibel-milliwatts (dBm) to milliwatts (mW), and then calculate the voltage using Ohm's Law.
1. Convert from dBm to mW:
- The formula to convert from dBm to mW is: P (mW) = 10^(P(dBm)/10)
- Plugging in the given power level of -30 dBm: P (mW) = 10^(-30/10)
- Calculating: P (mW) = 0.001 mW
2. Calculate the voltage:
- The formula relating power (P), voltage (V), and resistance (R) is: P = V^2/R
- Rearranging the formula, we have: V = sqrt(P * R)
- Plugging in the calculated power level of 0.001 mW and the given resistance of 60 Ω: V = sqrt(0.001 * 60)
- Calculating: V ≈ 0.2449 V
Therefore, the RMS voltage of the detected signal is approximately 0.2449 V.