A 10W signal is received at 5 W. This is a _____ dB loss:

To determine the dB loss in this scenario, we can use the formula that relates power levels in decibels:

[ \text{dB loss} = 10 \times \log_{10}\left(\frac{P_{\text{input}}}{P_{\text{output}}}\right) ]

In this case, the input power is 10 W, and the output power is 5 W. Plugging these values into the formula gives us:

[ \text{dB loss} = 10 \times \log_{10}\left(\frac{10\text{ W}}{5\text{ W}}\right) ]

[ = 10 \times \log_{10}(2) ]

The logarithm of 2 is approximately 0.301, so:

[ \text{dB loss} \approx 10 \times 0.301 = 3.01 \text{ dB} ]

When rounding to the nearest whole number, this results in a loss of approximately 3 dB.

Understanding a 3 dB loss is crucial as it corresponds to halving the power. In this scenario, receiving a 5 W signal when the transmitted signal was