m -m Signal Phasor: Noise Phasor: s(t)s(t) Phase Deviation due to noise:  n (t) Noise Performance for Phase Modulation For sinusoidal modulation, let a(t) = sin(  m t) Then  s (t) = m[sin(  m t)] Coherent Phase Detector k p  s (t) +  n (t) v out  k p  s (t) + k p  n (t) Signal Noise hmmm… RMS Noise Radius

The Noise Phasor Random Amplitudes When  n is “small”

FM/PM SNR Improvement 20 log(m) SNR(in) SNR(out) 10 dB Power SNR to noise ratio is equal to voltage SNR 2, so Power SNR improvement ratio is equal to m 2. Since occupied bandwidth increases in proportion to m, so does kTB noise power, so overall system power SNR improvement ratio is just m.

Pre-emphasis/De-Emphasis V m (t) Phase Demodulator Differentiator Low Pass Filter v PM (t) v FM (t) v D (t) The RMS noise amplitude is independent of frequency, therefore its demodulated spectrum is flat. Let the noise voltage at some frequency  n be: The output of the differentiator will be: The noise amplitude for FM is proportional to frequency: The noise spectrum exiting the low pass filter will be: The Low Pass Filter De-emphasizes the high frequency content, resulting in a flat noise spectrum above  c.

Pre-emphasis In order to reproduce the source spectrum accurately, the source information must have its high frequencies “pre-emphasized “ by a pre-emphasis filter having time constant equal to 1/  c. The filter flattens out at some frequency  h, above the normal audio range. 20 log(m) cc hh   For fixed deviation FM, m =  /  m, so modulation index decreases as  m increases. Pre-emphasis increases the deviation for high frequencies to keep m fairly constant above  c. Pre-emphasis/de-emphasis filters are characterized by  = 1/  c