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Bandpass Signaling Principles and Circuits Chap. 4
This is called down conversion with low-side injection, because the LO frequency is below
that of the incoming signal (i.e., f 0 6 f c ). Here the output modulation is the same as that of the
input, except for the A 0 2 scale factor. The other possibility is f d = f 0 - f c 7 0, where f 0 7 f c ,
which produces the output complex envelope
g 2 = A 0
2 g * in (t)
(4–61c)
This is down conversion with high-side injection, because f 0 7 f c . Here the sidebands on the
down-converted output signal are reversed from those on the input (e.g., an LSSB input signal
becomes a USSB output signal).
Ideal mixers act as linear time-varying circuit elements, since
v 1 (t) = (A cos v 0 t)v in (t)
where A cos v 0 t is the time-varying gain of the linear circuit. It should also be recognized that
mixers used in communication circuits are essentially mathematical multipliers. They should
not be confused with the audio mixers that are used in radio and TV broadcasting studios. An
audio mixer is a summing amplifier with multiple inputs so that several inputs from several
sources—such as microphones, tape decks, and CD decks—can be “mixed” (added) to
produce one output signal. Unfortunately, the term mixer means entirely different things,
depending on the context used. As used in transmitters and receivers, it means a multiplying
operation that produces a frequency translation of the input signal. In audio systems, it means
a summing operation to combine several inputs into one output signal.
In practice, the multiplying operation needed for mixers may be realized by using one
of the following:
1. A continuously variable transconductance device, such as a dual-gate FET.
2. A nonlinear device.
3. A linear device with a time-varying discrete gain.
In the first method, when a dual-gate FET is used to obtain multiplication, v in (t) is usually
connected to gate 1 and the local oscillator is connected to gate 2. The resulting output is
v 1 (t) = Ky in (t)v LO (t)
(4–62)
over the operative region, where v LO (t) is the local oscillator voltage. The multiplier is
said to be of a single-quadrant type if the multiplier action of Eq. (4–62) is obtained only
when both input waveforms, v in and v LO (t), have either nonnegative or nonpositive values
[i.e., a plot of the values of v in (t) versus v LO (t) falls within a single quadrant]. The multiplier
is of the two-quadrant type if multiplier action is obtained when either v in (t) or
v LO (t) is nonnegative or nonpositive and the other is arbitrary. The multiplier is said to be
of the four-quadrant type when multiplier action is obtained regardless of the signs of
v in (t) and v LO (t).
In the second technique, a nonlinear device can be used to obtain multiplication by
summing the two inputs as illustrated in Fig. 4–9. Looking at the square-law component at the
output, we have