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Sec. 4–11 Mixers, Up Converters, and Down Converters 269
v in (t)
+
+
Nonlinear
device
v 1 (t)
Filter
v out (t)
v LO (t)=A 0 cos( 0 t)
Local
oscillator
Figure 4–9
Nonlinear device used as a mixer.
v 1 (t) = K 2 (v in + v LO ) 2 + other terms
= K 2 1v 2 in + 2v in v LO + v 2 LO 2 + other terms
(4–63)
The cross-product term gives the desired multiplier action:
2K 2 v in v LO = 2K 2 A 0 v in (t) cos v 0 t
(4–64)
If we assume that v in (t) is a bandpass signal, the filter can be used to pass either the up- or
down-conversion terms. However, some distortion products may also fall within the output
passband if v c and v 0 are not chosen carefully.
In the third method, a linear device with time-varying gain is used to obtain multiplier
action. This is demonstrated in Fig. 4–10, in which the time-varying device is an analog
switch (such as a CMOS 4016 integrated circuit) that is activated by a square-wave oscillator
signal v 0 (t). The gain of the switch is either unity or zero. The waveform at the output of the
analog switch is
v 1 (t) = v in (t)s(t)
(4–65)
Analog switch
(a linear time-varying device)
v in (t)
v 1 (t)
Filter
v out (t)
s(t)
t
Multivibrator
(a square-wave oscillator)
Figure 4–10
Linear time-varying device used as a mixer.