Basic Principles of Digital Modulation - Digital Video and Audio Broadcasting Technology - page 211

at the time t = 0 is shown. The vector is then at the zero-phase angle and its
length corresponds to the amplitude of the sinusoidal quantity.
Fig. 13.1. represents a sine signal in the time domain and in the form of
a vector. The rotating vector, whose length corresponds to the amplitude,
is shown at zero-phase angle Φ. The sine signal is obtained by projecting
the rotating vector on the vertical axis (Im) and recording the position of
the vector tip versus time. The corresponding cosine signal is obtained by
projecting the rotating vector on the horizontal axis (Re).
The vector can be split into its real part and its imaginary part, terms
which are derived from the theory of complex numbers in mathematics.
The real part corresponds to the projection onto the horizontal axis and is
calculated from Re = A • cos . The imaginary part corresponds to the
projection onto the vertical axis and can be calculated from Im = A • sin .
The length of the vector is related to the real part and the imaginary part
via Pythagoras' theorem
;

2 + 2

= A .
The real part can also be imagined to be the amplitude of a cosine signal
and the imaginary part as the amplitude of a sine signal.
Any desired sine or cosine signal can be obtained by the superposition
of a sine and a cosine signal of the same frequency and the desired ampli-
tudes.
The real part is also called the I, or in-phase, component and the imagi-
nary part is called the Q, or quadrature, component, where in-phase stands
for 0 0 phase angle to a reference carrier and quadrature stands for 90 0
phase angle. The terms real part, imaginary part, cosine and sine compo-
nent and I and Q component will appear time and again in the sections to
follow.

Re Im

13.2 Mixer

We will see that the mixer is one of the most important electronic compo-
nents that make up an IQ modulator. A mixer is basically a multiplier. The
modulation signal is usually converted to the IF by means of a carrier sig-
nal. As a result, two sidebands about the carrier are obtained. This type of
modulation is known as double-sideband amplitude modulation with sup-
pressed carrier. The mixer shown in Fig. 13.2. is basically a double switch
driven by the carrier. It reverses the polarity of the modulation signal at the
carrier frequency.
In the case of a purely sinusoidal modulation signal, two spectral lines
are obtained - one above and one below the carrier frequency - each