Radio Frequency Integrated Circuit Design - Webs

234 Radio Frequency Integrated Circuit Design
7.12.6 Matching, Bias Resistors, and Gain
If the base of the RF transistors were biased using a voltage divider with an
equivalent resistance of 50�, the input would be matched over a broad band.
However, the gain would have dropped by about 6 dB compared to the gain
achievable when matching the input reactively with an LC network or with a
transformer. For a resistively degenerated mixer, the RF input impedance (at
the base of the input transistors) will be fairly high; for example, with R E =
100�, Z in can be of the order of a kilohm. In such a case, a few hundred ohms
can make it easier to match the input; however, there will be some signal
attenuation and noise implications.
At the output, if matched, the load resistor R o is equal to the collector
resistor R C , and the voltage gain is modified by a factor of 0.5. Furthermore,
to convert from voltage gain A v to power gain Po /Pi , one must consider the
input resistance R i and load resistance R o = R C as follows:
Po
Pi
=
v 2 o
R o
v 2 i
R i
= v 2 o
v 2 i
Example 7.5 High-Linearity Mixer
R i
R o
= A 2 v
R i
R o
≈� 2 R C /2
� R � E 2 R i
R C
(7.43)
Design a mixer to downconvert a 2-GHz RF signal to a 50-MHz IF. Use a
low-side-injected LO at 1.95 GHz. Design the mixer to have an IIP3 of 8 dBm
at 15 dB of voltage gain. The mixer must operate from a 3.3-V supply and
draw no more than 12 mA of current. Determine the noise figure of the design
as well. Determine what aspects of the design dominate the noise figure. Do
not use any inductors in the design and match the input to 100� differentially.
Solution
Since inductors are not allowed in the design, the linearity must be achieved
with resistor degeneration. Since current sources require at least 0.7V and the
differential pair and quad will both require 1V, this would leave only 0.6V for
the load resistors. A design that stacks the entire circuit is unlikely, therefore,
to fit into the 3.3-V supply requirement; thus, it will have to be folded. Also,
since we are using resistive degeneration, we can probably match the input with
a simple resistor. Thus, the mixer topology shown in Figure 7.34 will probably
be adequate for this design.
We can now begin sizing components and determining bias currents. First,
we are told that we can use 12 mA in this design. There are two sources of
nonlinearity of concern, one is the exponential nonlinearity of the differential
pair and the other is the exponential nonlinearity of the quad. We note that