How much does increasing a receiver’s bandwidth from 50 Hz to 1,000 Hz increase the receiver’s noise floor?

To find the increase in a receiver's noise floor when bandwidth changes, you must calculate the decibel difference using the power ratio of the two bandwidths. The formula is 10 * log10(BW2 / BW1). In this case, the new bandwidth is 1,000 Hz and the old bandwidth is 50 Hz. The ratio of the bandwidths is 1,000 / 50 = 20. Because noise power is directly proportional to bandwidth, the noise power increases by a factor of 20. Plugging this ratio into the formula yields 10 * log10(20). Since the log10 of 20 is approximately 1.30, multiplying by 10 gives 13 dB. Therefore, increasing the bandwidth from 50 Hz to 1,000 Hz raises the noise floor by exactly 13 dB.