 of input signal; (b) output signal due to interference (18.46) The output signal power, from Equation 18.43 is as in Equation 18.47. (18.47) Thus, the output signal to noise ratio is given by Equation 18.48. (18.48) The input signal power is as in Equation 18.49. fc-61 si=12 (18.49) Figure 18.13 Amplitude/frequency spectra of angle If wideband (high index) FM is used, the bandwidth is approxi- modulated waves: (a) B = 0.2; (b) B = 1.0; (c) B=5.0 mately 2A S, SO the input noise power is given by Equation 18.50 and the input signal to noise ratio by Equation 18.51. (18.45) (18.50) (18.51) The total output noise power, from Equation 18.42, is given by Equation 18.46. Therefore Equation 18.52 may be obtained. 18/12 Analogue modulation (18.52) Although the improvement in signal to noise ratio is proportional to B3 (i.e. to AF3, the input noise power is proportional to the bandwidth (2AF). Thus, the output signal to noise ratio is propor- tional to the square of the bandwidth used. An octave increase in the frequency deviation and bandwidth increases the output signal to noise ratio by 6dB. The bandwidth required is 6 times that for AM, so for equal noise power densities, the noise power at the input to the receiver is 6 times that for AM. Consequently, for fully modulated AM and the same carrier power, the improvement is given by Equation 18.53. (18.53) Output signal noise ratio for r FM = 3 B2 Output signal noise ratio for For example, FM broadcasting typically has a baseband of 15kHz and a maximum frequency deviation of 75kHz, i.e. B = 5. The improvement in signal to noise ratio compared with AM with 100% modulation is 3 X 25 = 75, i.e. 19dB. It has been shown above that the output noise spectrum for FM is parabolic. The output signal to noise ratio can therefore be improved INPUT SIGNAL/NOISE RATIO (dB) further by making the signal power also increase with frequency. It is common practice to insert in front of the modulator at the trans- Figure 18.15 Improvement in signal to noise ratio given mitter a pre-emphasis