
84-11Modulation
Equation 84.15 was derived using the trigonometric identities cos(a)cos(b) = 0.5 × [cos(a + b) +
cos(a − b)] and cos(a)sin(b) = 0.5 × [sin(a + b) − sin(a − b)]. Passing
f t
I
( )
and
f t
Q
( )
th
rough
lo
w-pass
fi
lters
ha
ving
cu
toff
fr
equencies
we
ll
be
low
ω
c
removes all but the dc components from the outputs
f
I
(t) and f
Q
(t). The dc components are
f
AA
f
AA
I
s
Q
s
= = −
π
θ
π
θ
cos( ) sin( )
(84.16)
e
a
mplitude
a
nd
p
hase
o
f
t
he
m
odulated
si
gnal
a
re
f
ound
b
y
t
he
f
ollowing
e
quation:
A
A
f f
f
f
s I Q
Q
I
= + =
−
−
π
θ
2 2 1
tan
(84.17a,b)
Figure
84.11 il
lustrates
ex
ample
wa
veforms
in th
e
PS
D
of Fi
gure
84.10. In th
is
ca
se,
th
e
ga
in
of th
e
am
plier
A =