
Principles of Analog Electronics
16
In the rst of the two equations we substitute
x = ωt + φ
getting cos ωϕ
ωϕ
tRee
jt
+
()
=
+
, so multiplying both sides by
F
we have
FtFRee
jt
cos ωϕ
ωϕ
+
()
=
+
F
of the right-hand side can be inserted inside the real part.
The study of the vector
Fe
jt
+
provides the necessary information (through
the real/imaginary part) about the trend over time on the periodic wave.
In conclusion a general periodic wave
vt
0
cos
can be considered the real part of a complex quantity such as
vt Ve Ve eVe
jt
jj
t
()
===
+
ωϕ
ϕω ω
where VVe
j
=
ϕ
is a constant complex number, with magnitude V
and phase φ,
whil ...