Radio Frequency Integrated Circuit Design - Webs

Mixers
Figure 7.24 RC networks to produce phase shift.
where � o = 1/CR.
vo1
v 1
vo2
v 2
=
=
sCR
1 + sCR =
1
1 + sCR =
j� /�o
1 + j� /� o
1
1 + j� /� o
221
(7.25)
It can be seen that at the center frequency, where � = �o , the output of
the lowpass filter is at vo1 /v 1 = 1/√2 ∠ 45° and the output of the highpass
filter is at vo2 /v 2 = 1/√2 ∠−45°. Thus, if v 1 = v 2, then vo1 and vo2 are 90°
out of phase. In a real circuit, the amplitude or phase may be shifted from their
ideal value. Such mismatch between the amplitude or phase can come from a
variety of sources. For example, R and C can be poorly matched, and the time
constant could be off by a large percentage. As shown in Figure 7.24, such an
error will cause an amplitude error, but the phase difference between the two
signals will remain at approximately 90°. If the phase-shifted signals are large
and fed into the switching quad of a mixer, amplitude mismatch is less important.
However, in any configuration requiring a phase shifter in the signal path, such
as those shown in Figures 7.21 and 7.22, the sideband cancellation or image
rejection will be sensitive to amplitude and phase mismatch. Even if the phase
shifter is perfect at the center frequency, there will be errors at other frequencies
and this will be important in broadband designs.