What is the power gain in dB when a transmitter's power increases from 5 watts to 50 watts?

To determine the power gain in decibels (dB) when a transmitter's power increases from 5 watts to 50 watts, you can use the formula for power gain in dB, which is:

[ \text{Gain (dB)} = 10 \times \log_{10}\left(\frac{P2}{P1}\right) ]

In this case, (P1) is 5 watts and (P2) is 50 watts. Plugging the values into the formula gives:

[ \text{Gain (dB)} = 10 \times \log_{10}\left(\frac{50}{5}\right) ]

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

[ = 10 \times 1 ]

[ = 10 , \text{dB} ]

This calculation shows that the power gain achieved when the transmitter's power increases from 5 watts to 50 watts is 10 dB. The logarithmic scale used for measuring gain allows for a simpler understanding of changes in power levels, as each 10 dB increase represents a tenfold increase in power level. Thus, a gain of 10 d