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Signal Phasor:

Noise Performance for Phase Modulation. Phase Deviation due to noise:. RMS Noise Radius. f s ( t ) + Dq n ( t ). Noise Phasor:. Signal Phasor:. Coherent Phase Detector k p. m. f s ( t ). Dq n ( t ). v out = k p f s ( t ) + k p Dq n ( t ). Signal Noise. -m. hmmm….

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Signal Phasor:

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  1. Noise Performance for Phase Modulation Phase Deviation due to noise: RMS Noise Radius fs(t) + Dqn(t) Noise Phasor: Signal Phasor: Coherent Phase Detector kp m fs(t) Dqn(t) vout=kpfs(t) + kpDqn(t) Signal Noise -m hmmm… For sinusoidal modulation, let a(t) = sin(wmt) Then fs(t) = m[sin(wmt)]

  2. The Noise Phasor Random Amplitudes When Dqn is “small”

  3. FM/PM SNR Improvement SNR(out) 20 log(m) SNR(in) 10 dB Power SNR to noise ratio is equal to voltage SNR2, so Power SNR improvement ratio is equal to m2. Since occupied bandwidth increases in proportion to m, so does kTB noise power, so overall system power SNR improvement ratio is just m.

  4. Pre-emphasis/De-Emphasis vD(t) vFM(t) vPM(t) Low Pass Filter Phase Demodulator Vm(t) Differentiator The output of the differentiator will be: The RMS noise amplitude is independent of frequency, therefore its demodulated spectrum is flat. The noise spectrum exiting the low pass filter will be: Let the noise voltage at some frequency wn be: The noise amplitude for FM is proportional to frequency: The Low Pass Filter De-emphasizes the high frequency content, resulting in a flat noise spectrum above wc.

  5. 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/ wc. The filter flattens out at some frequency wh , above the normal audio range. For fixed deviation FM, m = Dw/wm, so modulation index decreases as wm increases. Pre-emphasis increases the deviation for high frequencies to keep m fairly constant above wc . Pre-emphasis/de-emphasis filters are characterized by t = 1/wc H(w) 20 log(m) w wh wc

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