## Example 4.1

#### A radio receiver is limited in performance by thermal noise in the receiver 'front-end'. It is designed to provide an S/N ratio of better than 10 dB to the demodulator input. The channel bandwidth for the receiver is 25 kHz. What is the minimum received signal level that can be used to achieve this performance target, assuming the receiver is operating at a temperature of 280oK?

### Solution

#### The average power of thermal noise for this case is given by:
Nav = kTB = 1.38 x 10–23 x 280 x 25000 = 9.66 x 10–17 W or –130 dBm (dB relative to 1 mW.)
To achieve an S/N ratio of 10 dB, the received signal power must therefore be in excess of (–130 + 10) = –120 dBm.