Radio Frequency Integrated Circuit Design - Webs

High-Frequency Filter Circuits
can be tolerated. If the Colpitts negative resistance circuit is sized so that C 1
is large and C 2 small, then the linearity of this circuit will improve.
In the case of the −Gm resonator as shown in either Figure 9.7 or 9.11,
the amount of negative resistance generated is
R neg
=
R negss
−2
g m
−2
g mss
=� 1 + v in
vT
+ 1 v
2
2
in
v 2 + ...�
T
−1
337
(9.35)
The voltage across the resonator is twice that across either Q 3 or Q 4,so
(vres = 2v in):
R neg
=
R negss
−2
g m
−2
g mss
=� 1 + v res
2v T
+ 1 v
2
2
res
4v 2 + ...�
T
−1
(9.36)
Therefore, as a voltage of about 2vT is applied to the resonator, its effectiveness
will degrade. Note that if resistors were added to the circuit to degenerate
the transistors Q 3 and Q 4, then signal size could be increased and the linearity
would improve. Alternatively, if a transformer with turns ratio greater than 1
is employed, then the voltage on the resonator could be stepped down, reducing
the required signal handling requirement of these transistors.
9.7 Noise Added Due to the Filter Circuitry
As has already been discussed, there are three major sources of noise in an LNA:
base shot noise, collector shot noise, and base resistance of the driver transistor.
In a filter, there is the additional noise due to the active Q enhancement circuitry.
Noise due to the base resistance of Q 1 is in series with the input voltage,
so it sees the full amplifier gain. The output noise due to base resistance is
given by
vno,r b ≈ √ 4kTr b � R L
Z E
(9.37)
It is assumed that Z E is the impedance in the emitter and the LNA, and
the load at the collector is again assumed to be R L .
Collector shot noise is in parallel to collector signal current and is directly
sent to the output load resistor.