Chippmann Omega-PhiCS-8 Series, Руководство пользователя

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CS-8 Series Omega-Phi Rev1.04, Oct. 2015
-30-
' ∙
Φ
ൌ ' ∙ బ
೘
and
ϕ
F
,
ϕ
P,
ϕ
C
can be chosen that PM(t) and FM(t)
becomes equal.
Well! We computed, respectively written the wave-functions for FM(t) and
PM(t), with sinus-functions for carrier and modulator. But the phase
modulation generates also frequency shifts as the FM. For FM the frequency
was the starting point (we computed the current phase as a function of time
by integration of the frequency as function of time). To obtain the momentary
frequency
ω
PM
(t) for the PM, the term in the round bracket behind the sinus of
PM(t), namely the phase as a function of time
φφφφ
ൌ ࣓ ∙
Φ
Φ Φ
Φ
∙
࡯
is to derivate with respect to time (inversion of integration):
࣓ ൌ
∅
ൌ ࣓ ∙
Φ Φ Φ Φ
∙
And with M(t)=sin(
ω
m
t+
ϕ
P
) we finally obtain
࣓ ൌ ࣓ ∙
Φ Φ Φ Φ
∙ ࣓ ∙ !"࣓ )
and for FM(t) with M(t)=sin(
ω
m
t+
ϕ
F
) it is already written above
࣓ ൌ ࣓ ∙ ࣓ ∙ ࣓
Because the extremes of sinus and cosine are ±1, for the maximum/minimum
momentary frequencies we obtain:
࣓
,/
ൌ ࣓ ∙
Φ Φ Φ Φ
∙ ࣓
࣓
,/
ൌ ࣓ ∙ ࣓
As one can see for the PM
ω
m
is a constant of proportionality in
ω
PM
(t); that
means that the index (modulation depth) increases with the modulation
frequency
ω
m
, whereas the index for FM is constant, the modulation frequency
ω
m
doesn't appear, only the constant index m
FM
and the constant
ω
0
.