Radio Frequency Integrated Circuit Design - Webs

236 Radio Frequency Integrated Circuit Design
Since this formula is an approximation and we have one other nonlinearity
to worry about, we will choose R E = 70� for this design.
Next, we can find the load resistor, noting that we want 15 dB of voltage
gain or 5.6 volts per volt (V/V). Using (7.20) (omitting output matching),
R C = �
2 A v� re + R E
2 �
�
= 5.6(8.3� + 35�) = 380�
2
Note that there will be losses due to the ro of the quad transistors and
some loss of current between the stages, but we will start with an R C value of
400�. We also include capacitors C C in parallel with the resistors R C to filter
out high-frequency signals coming out of the mixer. We will choose the filter
to have a corner frequency of 100 MHz; therefore, the capacitors should be
sized to be
C C =
1
2�fc R C
=
1
= 4pF
2�(100 MHz)(400�)
Now the coupling network needs to be designed. The current sources
I bias will need about 0.7V across them to work properly, and the differential
pair should have roughly 1.5V to avoid nonlinearity. This leaves the resistors R cc
with about 0.8V; thus, a value between 200� and 400� would be appropriate for
these resistors. We choose 300�.
The quad transistors will each have an re of 16.7�. This is less than
1/10th of the value of R cc, and if they are placed in series with a 3-pF capacitor,
they still have an impedance with a magnitude of 31.5� or about 1/10th that
of R cc. Thus, little current will be lost through the resistors R cc.
The quad transistors themselves were sized so that when operated at 1.5
mA each, they were at the current for peak f T . For minimum noise, the
differential pair transistors were sized somewhat larger than the quad transistors.
However, since the noise will be dominated by R E , exact sizing for minimum
noise was not critical.
The circuit also needs to be matched. Since inductors have not been
allowed, we do this in a crude manner by placing a 100� resistor across the
input.
Next, we can estimate the noise figure of this design. The biggest noise
contributors will be R E , R Match, and the source resistance. The noise spectral
density produced by both the matching resistor and the source vn(source) will
be
vn(source) = √ 4kTR Match = 1.29 nV
√ Hz