Chapter 7 Angle Modulation – PM, FM
Why? Improve fidelity and S/N
When? 1930-44
How? VCO
Where? FM radio, TV sound, cordless, mobile, and digital systems
v(t) = V cos ( 2 π f t + θ ) or Ve j(ωt+θ)
V:
f:
θ:
AM
FM
PM
ASK
FSK
PSK
Relation between phase and frequency
ωt is a time-varying phase.
θ(t) can also be a time-varying phase.
dθ/dt has the same significance as ω!
Instantaneous angular frequency: ω+ dθ/dt
Angular frequency deviation: ∆ω = dθ / dt
Phase change due to FM: θ = ∫ ∆ωdt - see Fig. 7.4
This implies the same formula can be applied to FM and PM.
FM deviation sensitivity: kf=∆f/em (Hz/V)
Peak frequency deviation: δ
δ
FM modulation index: m f =
fm
PM deviation sensitivity: kf=∆θ/em (radian/V)
PM modulation index: m p - peak phase deviation
PM Signal: vt = A sin(ω c t + m p sin ω m t )
Instantaneous angular frequency: ω c + m pω m cos ω m t
f c + m p f m cos ω m t = f c + δ cos ω m t
Spectrum of PM or FM signal:
v ( t ) = A{ J 0 ( m ) sin ω c t − J 1 ( m )[sin( ω c − ω m ) t − sin( ω c + ω m ) t
+ J 2 ( m )[ ω c ± 2ω m ] − J 3 ( m )[ ω c ± 3ω m ] + J 4 ( m )[ ω c ± 4ω m ]...}
Spectral Power ∝ J 02 , J 12 , J 22 , J 32 ,...
Question: Which component is the largest? Depending on m!
Bandwidth - Depending on the modulation index
Carson’s rule: B=2(δ+fm)
Narrow Band or Wide Band? m<0.5 or m>0.5
FM Noise – Very Important; similar considerations apply to lasers used in optical
communications systems.
Components of noise – Amplitude and Phase
Amplitude Noise – Limiter eliminates completely the amplitude noise.
Limiter – Clipped amplifier
Phase Noise – the vector picture
S/N Ratio – power ∝ voltage2 or 2x in dB unit
Signal frequency deviation, fS: 5 kHz
Noise frequency deviation, fN: 1 kHz
Signal amplitude, ES: 10
Noise amplitude, EN: 1
(S/N)V: 10
Frequency deviation caused by noise: 1 kHz x 0.1 rad = 100 Hz
(S/N)F: 5 kHz/100 Hz=50
(S/N)P-in: 20 dB
(S/N)F-in: 34 dB
Capture effect – When the S/N is below threshold, the receiver
might not lock on to the transmitter, therefore,
the performance deteriorates.
Noise in the FM system – Phase noise is white.
The frequency noise is linearly proportional to fm.
Larger signal is needed at higher frequency.
Pre-emphasis and de-emphasis - High pass and low pass filters
(preem.ewb and deem.ewb)
FM Stereo – L+R signal, 19 kHz pilot, 38 kHz sub-carrier, DSBSC L-R signal
Homework: 7-38