A directional coupler with an attenuation of -30 dB indicates what power level at the line if a measurement shows 100 milliwatts?

A directional coupler with an attenuation of -30 dB means that for every 1,000 milliwatts (or 1 watt) of input power, only a portion is coupled through according to the specified attenuation. In this context, -30 dB indicates that the power is reduced by a factor related to the logarithmic scale of decibels, specifically that 1 watt will translate to 0.001 watts at the coupled output.

Given the measurement indicates 100 milliwatts at the line, we want to calculate the corresponding input power. Since -30 dB equates to a power reduction, we can find the input power using the formula for converting dB to linear scale:

[ P_{in} = P_{out} / 10^{(dB/10)} ]

Thus, if the output is 100 milliwatts (0.1 watts), we can rearrange the equation:

[ P_{in} = 0.1 / 10^{(-30/10)} = 0.1 / 10^{-3} = 0.1 \times 1000 = 100 \text{ watts} ]

This calculation indicates that the original power level at the line