Radio Frequency Integrated Circuit Design - Webs

206 Radio Frequency Integrated Circuit Design
where v RF is the output voltage obtained without the switching (i.e., for a
differential amplifier). This means that because of the frequency translation,
the amplitude of each mixed frequency component is
vo = 2
� v RF = v RFdB
− 3.9 dB (7.18)
As a result of mixing, gain is modified by a factor of 1/2 or −6 dB, but
a square wave has a fundamental larger by 2.1 dB, for a net change of −3.9
dB. Third harmonic terms are down by 1/3 or −9.5 dB, while fifth harmonics
are 1/5 or −14 dB. Intermodulation (other than mixing between RF and LO)
is often due to the RF input and its nonlinearity. Thus, the analysis of the
differential pair may be used here. From Chapter 6, the gain for the differential
amplifier with load resistors of R C and emitter degeneration resistors of R E per
side was given by:
v RF =
R C
re + R E v in
(7.19)
Thus, a final useful estimate of gain in a mixer such as the one shown in
Figure 7.4 (at one output frequency component) is the following:
vo = 2
�
R C
re + R E
v in
(7.20)
We note that this is voltage gain from the base of the input transistors
to the collector of the switching quads. In an actual implementation with
matching circuits, these also have to be taken into account.
In Figures 7.6 and 7.7, the LO frequency is much greater than the RF
frequency (it is easier to draw the time domain waveform). This is upconversion,
since the output signal is at a higher frequency than the input signal. Downconversion
is shown in Figure 7.8. This is downconversion because the output
signal of interest is at a lower frequency than the input signal. The other output
component which appears at higher frequency will be removed by the IF filter.
Note also that any signals close to the LO or its multiples can mix into
the IF. These signals can be other signals at the input, intermodulation between
input signals (this tells us we need linear RF inputs), noise in the inputs, or
noise in the mixer itself.
7.7 Mixer Noise
Mixer noise figure is somewhat more complicated to define compared to that
of an LNA, because of the frequency translation involved. Therefore, for mixers,