m -m signal phasor: noise phasor: s(t)s(t) phase deviation due to noise: n (t) noise performance...

m

-m

Signal Phasor: Noise Phasor:

s(t)

( )s s sV t V t

Phase Deviation due to noise:

n(t)

Noise Performance for Phase Modulation

For sinusoidal modulation, let a(t) = sin(mt)Then s(t) = m[sin(mt)]

( ) s

n

RMSSNR v

RMS

2s RMS m

Coherent Phase Detector

kp

s(t) + n(t)

vout kps(t) + kpn(t)

Signal Noise

hmmm…

RMS Noise Radius

The Noise Phasor

( ) ( ) ( )

2

N

s s

N t N t t

N t N t

N t t N t t

N t

N t

22

0

1( )

T

N RMS N t dtT

2 2 2

22

2

N RMS N RMS N RMS

N RMS

N RMS N RMS

S t

S t N t n t

1tan

2

n

n

N t N tt

S t S t

N RMS N RMSRMS

S RMS S RMS

2( )

2

s

n

out in

RMS S RMSmSNR v m

RMS N RMSN RMS

S RMS

SNR m SNR

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 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.

Pre-emphasis/De-Emphasis

Vm(t) Phase Demodulator

DifferentiatorLow Pass

Filter

vPM(t) vFM(t) vD(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:

sinn n nv t V t cosn n n nv t V t

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-emphasisIn 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)

ch

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