IEEE Solid-State Circuits Magazine - Spring 2015 - 46
Among the feed-forward solutions, one that is
very popular is the boosted common gate LNTA.
The only way to reduce the impact
of the noise of the input impedance below 1 is to insert a feedback
or a feed-forward path around the
transconductor. As will be shown in
the examples reported in the following, feedback and feed-forward can
reduce only the noise of the matching network, while the only way to
reduce noise of the transconductor
is to amplify the signal in front of
the transconductor itself.
The use of feedback is more complicated in current-mode approach
since no voltage gain is developed at
the output of the LNTA. This explains
why the use of feed-forward approach
has become so popular in currentmode receivers. In the following the
three example of LNTA reported in
Figure 12 will be discussed.
In particular, in the LNTA drawn
in Figure 12(b), the input matching
is realized by an inductive degeneration where the inductance L s is
transformed into a resistance equal
to ~t L s (where ~t = g m /C gs) [5].
This is possible since the current
injected by the transistor is in quadrature with the input current flowing through C gs . The network is
completed adding an inductance L g
at the gate of the transistor in order
to resonate the reactive part of the
input impedance given by C gs . The
obtained series resonance provides
also an amplification of the input
signal at the input of the transconductor proportional to the quality
factor (Q) of the resonance.
In first approximation the noise
factor of this amplifier is given by
Inductive Degenerated LnTA
One of the feedbacks techniques that
does not involve the output of the
transistor is source degeneration.
(11)
where for the transistor has been
assumed a noise source reported
Iout
Vin
Rs
(Antenna)
4kTRs
c
,
Q2 gm RS
nfLNTA = 1 +
4kT/gm
LNTA
gm
Iout
Lg
Vin
4kTRs
Rs
(LNTA)
gm
Iin
Cgs
jωCgs
Iin
Zin
Ls
at its gate equal to 4kTc/g m . Compared to (10), the term associated to
the input termination disappeared,
since R s is synthesized starting
from an inductor that is in theory noiseless. In addition to that,
the noise of the transconductor is
divided by Q 2, taking advantage of
the signal amplification produced
by the series resonance.
This LNTA is one of the less noisy
available in literature; however, there
are two drawbacks. The inductive
degenerated amplifier is intrinsically
narrowband since relies on a series
resonance whose implementation
requires two inductors (in the GHz
range generally L g is external).
Boosted Common gate LnTA
Among the feed-forward solutions, one
that is very popular is the boosted common gate LNTA reported in Figure 12(c)
(many variations of the theme are present in literature). In this case the input
signal is injected into the source of
a transistor using the transconductor itself to synthesize the matching.
In addition, an amplification ^A h is
applied between the source and the
gate to minimize the noise of the transistor. This voltage amplification can be
noiseless if realized by a reactive element as transformer [2], [6].
The presence of the feed-forward path A transforms the input
impedance of the transistor in
1/ (g m (1 + A)) that must be set equal
to R s . The noise factor for this LNTA
is given by
c
(A + 1) 2 g m R S
c
.
=1 +
(A + 1)
nfLNTA = 1 +
(a)
(b)
Iout
+
gm
Iin
(1+A) ⋅ Vin
Vin
-A
Zin = 1/(gm(1+A))
gm1
t
Ioutp
Vn
t
Rs
Vs
(Antenna)
k
LNTA
+
+
-
-gm
Ioutm
Zin = 1/gm1 = Rs
(c)
t
t
+
Iout
t
t
(d)
Figure 12: LTNA: (a) simple resistive termination, (b) inductive degeneration, (c) boosted
gm, and (d) noise cancelling.
46
s p r I n g 2 0 15
IEEE SOLID-STATE CIRCUITS MAGAZINE
(12)
This expression looks very similar
to (11). Only two contributions are
present since the input impedance is
realized with the transconductor itself
without the addition of any noisy
components. The noise produced by
the transistor is divided by (A + 1) 2
thanks to the amplification by A + 1
between gate and source. However
in this case, the matching condition
forces g m = 1/ (R s (A + 1)) leading to
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