No Noise
Is Good Noise
Leonid Belostotski
R
esearchers have described the concept
of noise matching since at least the 1950s
[1]–[4], with studies demonstrating the
interrelationships among the noise factor
of a low-noise amplifier (LNA), the LNA’s
noise parameters, and the signal-source impedance
Z s . Noise matching is accomplished when an LNA is
driven by a signal source, the impedance (or admittance) of which is designed—perhaps using a matching
network—to equal the LNA’s optimum signal-source
impedance for minimum noise, or Z opt . The complex
Z opt = G opt + jX opt represents two of the four noise parameters that completely characterize the noise behav-
ior of a linear two-port device, such as an LNA. The
other two noise parameters are the minimum noise
factor, Fmin , and the Lange invariant N [5], [6], which
is, arguably, a more fundamental parameter than the
often-used equivalent noise resistance, R n.
To visualize and describe the effect of practical imperfections in noise-matching networks on the LNA noise
factor, noise circles have been adopted [7], [8]. Using
these, many noise-matched LNAs have been designed
and have demonstrated outstanding noise factors.
In contrast, noise-canceling LNAs are relatively new
to the field of LNA design, even though they have been
around for nearly 15 years [9]. Since its introduction,
Leonid Belostotski (lbelosto@ucalgary.ca) is with the Department of Electrical and Computer Engineering,
University of Calgary, Alberta, Canada.
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the concept of noise canceling has enjoyed great interest within the solid-state circuits community; however,
it has also met some criticism [10].
This article highlights similarities and differences
between these two approaches to designing LNAs,
with a focus on comparing their noise factors. The
intent here is to address common misconceptions
associated with noise-canceling LNAs and to show
that both LNA types employ noise cancelation and so
are not so dissimilar as they initially appear. Because
numerous previous publications have successfully
demonstrated noise-matched LNAs [11]–[16] and noisecanceling LNAs [9], [17]–[25], I will not try to convince
readers that the two approaches are viable. Instead, I
offer simplified concepts to demonstrate the key ideas
behind the two LNA design approaches. In addition,
I focus on complementary metal-oxide–semiconductor (CMOS) technologies only because most—if not
all—noise-canceling LNAs have been implemented in
CMOS. However, the discussions here apply to other
technologies, as well.
What Is Noise Matching?
The idea of noise matching an LNA comes from the
description of the LNA’s two-port-network noise factor
along with its noise parameters as
F = Fmin +
N
Z - Z s 2 (1)
R s R opt opt
4N C s - C opt 2
,
= 1 + Tmin +
T0
^ 1 - C opt 2 h^ 1 - C s 2 h (2)
where Z s = R s + jX s is the signal-source impedance with
its associated reflection coefficient of C s = ^Z s - Z 0 h /
^ Z s + Z 0 h in a network having Z0 as the characteristic
impedance; Z opt = R opt + jX opt and C opt = ^Z opt - Z 0 h /
^ Z opt + Z 0 h are the LNA’s optimum signal-source
impedance and reflection coefficient for minimum noise,
respectively; and T0 = 290 K is the reference temperature.
For the best possible F = Fmin and the corresponding minimum noise temperature, Tmin , Z s should be tuned so as
to be exactly Z opt . When this is accomplished, the LNA is
said to be noise matched.
The design of such an LNA starts with the determination of its noise parameters. There are many different ways of determining these. For example, an
impedance tuner can be used to vary Z s ; for each Z s,
the noise factor F is measured, and the noise parameters are extracted [26]–[31]. Other methods explore the
observation that noise parameters are relatively constant over a narrow band of frequencies; then, if Z s is
made highly frequency-dependent, the network, which
quickly varies Z s , becomes equivalent to an impedance
tuner. Similar methods can be employed to find noise
parameters [32], [33]. A six-port network has also been
used for noise parameter extraction [34].
In other approaches, F is measured for a known
Z s (usually Z s = 50 X), and, with some knowledge
of the LNA’s subcomponents, the noise parameters
are extracted [35]–[37]. Noise parameters can also be
obtained from circuit simulations based on established
transistor models [38]–[41], subcomponent models supplied by component manufacturers, or measurements
performed on various parts of the LNA before they are
put together to form the complete circuit.
Once the noise parameters are known, noise
matching is conceptually straightforward. It requires
a matching network (ideally lossless) to be placed
between the LNA and the source of the incoming signal so that the network presents Z opt to the LNA. In
this case, F = Fmin, and the LNA achieves its lowest
noise factor.
This approach has drawbacks, however. First, there
is no information regarding how to select the transistor
©istockphoto.com/ BeautifulLotus
noise image—image licensed by ingram publishing
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Since its introduction, the concept
of noise canceling has enjoyed great
interest in the solid-state circuits
community; however, it has also
met some criticism.
representations in Figure 1 can be used interchangeably: for each of these, noise-correlation matrices can
be formed to concisely describe the noise properties of
the LNAs [43], [44]. However, these noise-correlation
matrices tend to require that the discussion be based
on equations. Instead, to allow some physical insight
into circuit operation, I am restricting the discussion
here to analyzing traveling waves, voltages, and currents, which can be understood conceptually without
resorting to equations.
To facilitate visualization of how the noise factor of an LNA is minimized to its lowest value (i.e.,
to Fmin), I first use the concept of traveling noise
waves [45], as illustrated in Figure 1(a); however,
the approaches described in [46]–[48] can be used,
as well. In this traveling noise wave representation,
there are two correlated noise waves: one emitted
from the LNA input, c1, and one emitted from the
LNA output, c 2. As shown in Figure 2, the noise
wave c 1 partially reflects off the signal source, with
a reflection coefficient Cs, and interferes with the
noise wave c 2 at the LNA’s output. If Cs is selected
size. Second, the transistor biasing is not part of the
noise matching procedure. In addition, there is no
guarantee that the LNA is power-matched to the preceding circuitry—an antenna or a filter, for example.
Because of these drawbacks, the noise-matching
approach is often facilitated with descriptions of noise
sources attributed to the circuit components [42]. In
this way, the effect of changing the biasing and/or the
transistor size on the noise parameters is captured,
and LNA optimization can be performed.
How Is F Reduced to Fmin?
To illustrate what happens to an LNA noise factor when
Z opt is set near Z s, any of the equivalent noisy LNA
c2
Noisy LNA
Vdd
c1
Noiseless
LNA
S21
a1
b2
S22
S11
c2
b1
a2
S12
c1
(a)
Noisy LNA
Noisy LNA
Vdd
in1
Vdd
Noiseless
LNA
+–
vn1
in2
(b)
Noiseless
LNA
–+
vn2
(c)
Noisy LNA
Vdd
vn
+–
in
Noiseless
LNA
(d)
Figure 1. A noisy LNA. (a) A wave representation and its flow graph, where c1 and c2 are equivalent traveling noise waves,
a1 and a2 are incident traveling waves, and b1 and b2 are reflected traveling waves. (b) An admittance representation, where
i n1 and i n2 are input and output equivalent noise currents. (c) An impedance representation, where v n1 and v n2 are input and
output equivalent noise currents. (d) A chain representation, where vn and in are input equivalent noise voltage and current.
apply.
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properly (i.e., C s = C opt), some correlated portions of
c 1 and c 2 cancel each other, with a remaining portion
contributing to the LNA’s output noise and, as such,
to the LNA’s noise factor. When this happens, the
LNA’s noise factor reaches its minimum, Fmin . The
existence of cancelation is important here, as this
effect is similar to what happens in noise-canceling
LNAs (this will be discussed later in the article).
This cancelation, of course, can be illustrated with
the following analytical expressions that relate the
traveling noise waves c1 and c2 to the LNA’s noise
parameters [45]:
c 1 2 = kT0 B e 4N
1 - S 11 C opt 2 Tmin
^1 - S 11 2 ho, (3)
T0
1 - C opt 2
For wideband noise-matched LNAs,
in addition to achieving Fmin over
as large a portion of the band as
possible, input power matching is also
important to avoid gain variation
over the band.
in (2). If c1 and c2 were not correlated (i.e., c 1 c 2* = 0), the
noise factor of such a circuit would be
F ct = 0 = 1 +
1 - C s S 11 2
^1 - C s 2h
# = Tmin e 1 T0
C opt 2
o,
c 2 2 = kT0 B S 21 2 e Tmin + 4N
T0
1 - C opt 2 (4)
+
C s ^1 - S 11 2 h
o
1 - C s S 11 2
2
4N C opt 2
1 - S 11 C opt 2 C s 2
oG, (7)
2 e1 +
1 - C s S 11 2 C opt 2
1 - C opt
and
*
*
C opt
S 21
+ S 11 c 2 2, (5)
c 1 c 2* = - 4kT0 BN
1 - C opt 2 S 21
where R n / ^Z 0 1 + C opt 2 h in [45] has been replaced by
its equivalent N/ ^1 - C opt 2h, k is Boltzmann’s constant, and B is the noise bandwidth. Assuming that
an LNA is terminated with a matched load and using
the signal-flow graph in Figure 2, the available noise
power b 2 2 scaled to root mean square values at the
LNA output is
C s S 21 2
b 2 2 = c 2 2 + 20 ' c 1 c *2 C s S 21 1 + c 1 2
,
1 - C s S 11
1 - C s S 11 2 1444442
444443
(6)
ct
where ^C s S 21 h / ^1 - C s S 11 h models the reflection of c1
off the signal source and its propagation through the
LNA to the output; and ct denotes the correlation term.
We can, then, input-refer b 2 2, dividing it by the avail­­
2
able gain of the LNA, G A = ^(1 -|C s|)
(|1 - C s S 11|2) h|#
|S 21|2; this leads to an expression of the LNA noise factor
which depends on S11 and is, in general, much different
than what LNA designers are used to seeing in (2).
The reason for such a significant difference is that
we ignore the correlation between the two traveling
noise waves in (7). In fact, all terms containing S11 in
(7) are canceled by ct when it is not artificially set to
zero, and so they do not appear in (2). Interestingly, out
of the three terms in (2), the last two are the remaining uncanceled terms of ct, which means that not all
the correlated noise is canceled when noise matching
an LNA. Because there is “excess” correlated noise, it
may be possible to modify the amount of c1 that finds
its way to the LNA’s output by using an active circuit
such that b 2 ^C s = C opt h 2 is reduced, thus resulting in
the LNA’s noise factor being less than Fmin . I will return
to this later in the article.
Wideband Noise-Matched LNAs
For wideband noise-matched LNAs, in addition to
achieving Fmin over as large a portion of the band as
possible, input power matching is also important to
avoid gain variation over the band. Close examination of the requirements for Z opt versus frequency
c2
Noisy LNA
Vdd
Zs
Γs
c1
Noiseless
LNA
1
bs
c2
S21
a1
Γs
S11
b1
S12
b2
S22
a2
c1
Figure 2. The noise wave flow to the LNA output; bs is the traveling wave launched by the signal source.
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To avoid inductors, power matching
can be accomplished with either lossy
networks such as resistors, shuntfeedback LNAs, or common-gate LNAs.
On the other hand, above ~U, the difference between
the LNA noise factor and Fmin grows rapidly as a function of frequency according to [50]
6F ^~h - Fmin ^~h@ ~ & ~U ?
This suggests that noise matching at ~U is a reasonable
compromise between a complex realization of wideband −C behavior and minimization of the LNA noise
over the whole band. However, when noise matched
at ~U, the LNA exhibits unacceptably low return loss
below ~U, and so a conventional source-degenerated
LNA is not suitable for wideband designs.
A number of solutions have been proposed. Elaborate input matching networks have been used to
improve impedance matching [51]–[53] that, when
using low-loss inductors, could simultaneously provide noise matching. To reduce the number of lossy
reactive parts at the LNA input, the inherent feedbackthrough-transistor gate-drain capacitance has also
been employed to tune the power match independently
of the noise match [50], [54]–[59]. To further improve an
LNA noise factor, lossy input matching circuits could
be taken off-chip.
To avoid inductors, power matching can be accomplished with either lossy networks such as resistors,
shunt-feedback LNAs, or common-gate LNAs. Passive lossy matching introduces significant noise and
is seldom used. Shunt-feedback LNAs use a resistor
connecting their input and output; this resistor provides matching but also increases noise. Commongate LNAs do not employ resistors for matching but
reveals that Z opt exhibits a negative capacitance (−C)
behavior [49]. For noise matching across a wide band
of frequencies, this poses the design challenge of
transferring a typical 50-Ω impedance of a preceding circuit to Z s that is near Z opt and that exhibits
the −C frequency behavior. Such a transformation
would require a few reactive components or an
active circuit.
Fortunately, Fmin of a transistor reduces with frequency, and some mismatch between Z opt and Z s does
not significantly increase the noise factor of an LNA.
This is illustrated with a simulation of a source-degenerated transistor in Figure 3, where noise matching is
accomplished with a gate inductor Lg and a sourcedegeneration inductor Ls at the upper edge of the
desired band, ~U. The resulting noise factor deviates
from Fmin at lower frequencies but does not exceed the
maximum value at ~U. It can be shown that the noise
penalty at frequencies below ~U is roughly constant
and can be expressed as the following [50]:
6F ^~h - Fmin ^~h@ ~ % ~U .
N
,
R s # 0 " Yopt , (8)
-1
where Yopt = Z opt
.
1
Desired Return Loss
Transistor Fmin
Noise Factor When Noise Matched at ωU
Return Loss When Noise Matched at ωU
Out
Lg
Noise Figure (dB)
0.8
6
Band of Interest
0.6
10-dB Return Loss
10
0.4
14
0.2
LNA Is Noise
Matched
Ls
0
(a)
2
0.5
ωL = 0.7
1
ωU = 1.4
Frequency (GHz)
(b)
2
Return Loss (dB)
Vdd
In
4
N
~
4 . (9)
R s # 0 " Yopt , ~ U
18
4
Figure 3. A source-degenerated cascode LNA: (a) a simplified schematic (biasing not shown) and (b) an illustration of the
noise-factor behavior across a wide band of frequencies and the associated input reflection coefficient. The desired input
reflection coefficient is also shown.
apply.
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rather rely on their transistor transconductances for
power matching; however, in such cases noise matching is not simultaneously achieved, and LNA noise
figures remain relatively high—above the theoretical
minimum of 2.2 dB [49]. In contrast to power matching with a lossy network, both shunt-feedback and
common-gate LNAs are active structures that provide
gain and power match. The problem, however, is that
they also generate noise. Noise-canceling LNAs have
been devised to remove some of that noise but preserve their power matching features.
What Are Noise-Canceling LNAs?
Since their first appearance in the literature in the early
2000s [9], noise-canceling (and even partially noise-canceling) LNAs have been widely discussed [20]–[25]. The
simplified schematics for two such LNAs are shown
in Figure 4. The noise-canceling concepts underlying
these two circuits are best explained by ignoring one
of the two noise currents in the admittance representation [see Figure 1(b)] of the transistor M1.
The LNA in Figure 4(a) originates from a shuntfeedback LNA topology, augmented with an adder
and an amplifier (identified in the figure as “−A”). A
shunt-feedback amplifier provides wideband input
impedance matching and, thus, is often of interest.
For such an LNA, the two key noise contributors are
the transistor M1 and the feedback resistor Rf . Ignoring parasitic reactive components, the train of thought
leading to the idea behind the noise cancelation in
­Figure 4(a) is as follows.
••The drain-noise current i dn induces in-phase
noise voltages at the drain and the gate of M1,
as illustrated by the red noisy waveforms in
­Figure 4(a).
•• The amplifier −A is used to scale the noise voltage
at the gate of M1 and invert its phase so that, when
the two noise voltages appear at the adder, they
cancel each other out.
•• The input signals traveling through M1 and −A
generate in-phase components at the adder input
that add constructively, as illustrated by the blue
sine waves in Figure 4(a).
The discussion of such an LNA in [60] showed the
noise figure dropping from around 5 dB to below
2.5 dB when noise canceling is enabled.
The explanation of the operation of the more favored
noise-canceling LNA in Figure 4(b) is as follows.
•• A common-gate, M1, provides wideband input
power match.
•• M1 drain noise i dn flowing into Rs and into R L2
generates a noise voltage vns at the gate of M2
and a noise voltage v no+ at the output node O+,
respectively.
•• Noise voltages vns and v no+ are 180˚ out of phase,
as illustrated by the red noisy waveforms in
Figure 4(b).
Since their first appearance in the
literature in the early 2000s, noisecanceling (and even partially noisecanceling) LNAs have been
widely discussed.
•• vns at the gate of M2 results in a current flowing
through R L1 that generates a noise voltage v no- at
the output node O –.
•• The resulting v no+ and v no- are in phase, as illustrated in Figure 4(b).
•• The input signal vin generates out-of-phase voltages v o+ and v o- at output nodes O+ and O-,
respectively, as illustrated by the blue sine waves
in Figure 4(b).
•• When the output is taken differentially, the out-ofphase v o+ and v o- add constructively, whereas the
in-phase v no+ and v no- are either completely canceled if their magnitudes are exactly the same or partially canceled if their magnitudes are not the same.
The use of the term noise-canceling LNAs and the
preceding general explanation of their operation
sometimes create two misconceptions, which I discuss
in the following sections.
Cdc
-A
vni
vin
Rs
Rf
vn2
vo2
vn1
idn
vo1
+
+
+
=
=
M1
vs
(a)
Vdd
Vdd
RL2
Vb
o+
M1
Cdc
RL1
vno+ vno–
vo+Output
vo–
idn
–
–
=
=
M2
vns
Rs
o– Differential Output
Ibias
vin
(b)
Figure 4. Two typical noise-canceling LNAs: the canceling
of M1 drain noise in (a) a shunt-feedback LNA and (b) a
common-gate LNA. The drain-current noise of M1 and the
resulting noise voltages are shown in red; the input signal
waveforms are shown in blue. Ibias and V b are used to bias
M1, and Cdc is a dc block.
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While it is reasonable to ignore noise
due to relatively small ohmic losses
in the transistor terminals, the other
noise current of the admittance
representation—known as the gate
noise of M1—requires extra attention.
Misconception 1: M1 Noise
Is Completely Canceled
The previous explanation of noise-cancelation circuits
appears to suggest that the noise of M1 is completely
removed, which seems counterintuitive as the noise
factor of a noise-matched LNA is limited to Fmin [10].
The reason for this misconception is that, intentionally,
not all noise of M1 is accounted for in discussions of
noise cancelation. While it is reasonable to ignore noise
due to relatively small ohmic losses in the transistor terminals, the other noise current of the admittance representation—known as the gate noise of M1—requires
extra attention.
Consider a design of a noise-matched LNA based
on a common-source transistor that has only drain
noise present and whose input admittance is determined by its gate-to-source capacitance, Cgs, as shown
in Figure 5(a). In such a case, if at frequency ~ 0 the
signal-source admittance Ys is designed such that
Ys = G s - j~ 0 C gs, the resulting G -s 1 impedance at the
transistor gate would make the ac gate voltage large
when Gs is very small. Therefore, the ac drain current
would be very large as well, making the drain-noise
current relatively insignificant. This, in turn, means
that Fmin ^~ 0 h . 0.
Similarly, if only the gate-current noise is present,
as in Figure 5(b), then a voltage signal source vin with
very small Rs would make the gate noise insignificant.
The conclusion is that if there is only one noise source
in a circuit, Fmin can be made nearly zero.
Vdd
Vbias
Vdd
RL
Rb
M
iin Ys
Cgs
(a)
Vbias
Output
Rb
idn
Rs
ign Cgs
RL
Output
M
vin
(b)
Figure 5. Representations of a matching problem when only
one noise source is considered: (a) with drain noise only and
(b) with gate noise only. Rb here is a very large bias resistor.
Noise-canceling LNAs are designed to cancel only
one of the transistor noise sources, often the drain noise
as it directly flows through the output node. Therefore,
noise cancelation refers only to that noise source and not
all the noises generated inside the transistor.
Misconception 2: Noise-Canceling LNAs Can
Achieve Noise Factors Lower Than Fmin
The noise-canceling methodologies shown in Figure 4
attempt to cancel only one of the two noise sources
necessary to fully model the noise of M1; they do not
at all attempt to cancel the noise of M 2 and of amplifier −A. As the drain noise and gate noise of transistor M2 in Figure 4 are not canceled, M2 needs to be
noise matched if there is a need to minimize its noise
contribution. Similarly, amplifier −A also needs to
be noise matched. In addition, in both circuits, noise
cancelation assumes that noise voltages at their summing node are perfectly out of phase. This, of course,
is not always possible. Parasitic capacitances at various
nodes reduce the effectiveness of noise cancelation at
high frequencies.
Noise-canceling LNAs embed a transistor in a network of one or more active devices. The fundamental
limits on such circuit-noise performance are determined by the individual subcircuit noise parameters
and S-parameters. These limitations are described
by Haus and Adler [3], [61]. An obvious corollary of
their work is that the noise factor of any circuit can be
reduced to unity (i.e., no noise) by simply connecting
the output of the circuit to the input, thereby bypassing the noisy active devices. Of course, the gain is also
unity, and, thus, LNA optimization must be cognizant of the circuit gain. This leads to a noise measure
1
h, with the noise factor F and the
M / ^F - 1 h / ^1 - G -ave
available gain Gave being the fundamental variables to
optimize. A remarkable result is that the minimum
noise measure of a circuit is invariant to a lossless
circuit, which embeds the active devices. However, a
lossy or active and noisy circuit embedding, such as
that with noise-canceling LNAs, can only degrade the
minimum noise measure.
As the “How Is F Reduced to Fmin?” section describes,
noise-matched LNAs use a “passive” noise-cancelation
approach by means of reflecting c1 off a properly
designed signal-source impedance. Noise-canceling
LNAs, on the other hand, provide an “active” and,
inevitably, noisy means of accomplishing a similar
task, while at the same time achieving wideband input
power matching.
Similarities of Noise-Matched and
Noise-Canceling LNAs
Another View of Noise-Matched LNAs
To begin this discussion of how the two design methods are similar, I refer back to the explanation of the
apply.
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noise-matched LNA design based on the traveling
waves c1 and c2. In that discussion, noise cancelation
was observed by setting C s = C opt . However, while
this is the conventional—and, arguably, the most practical—approach, it is not a unique way of achieving
Fmin . Another method for imitating noise-wave propagation, shown in Figure 2, is to employ some sensing
network capable of measuring c1, properly scaling it,
and adding it back either to the input of the LNA or at
the output of the LNA.
Conceptual representations of such networks are
shown in Figure 6. Either of the two networks transfer
some part of c1 to the LNA output, where correlated
portions of c1 and c2 cancel each other out. If this could
be accomplished, then it would resemble what happens in noise-canceling LNAs, where the drain noise
is sensed, scaled, and sent to the LNA output via an
alternative path to provide noise cancelation. In this
sense, noise matching and noise cancelation would not
be as dissimilar as they initially appear.
Keeping in mind the ideas illustrated in Figure 6,
we can consider a noise-matched common-source
LNA [Figure 7(a)] as a combination of two (or more)
transistors Ma and Mb placed in parallel [illustrated in
Figure 7(b)]. It is important to note that the individual
Fmin s of Ma and Mb in Figure 7(b) are the same as and
equal to the Fmin of transistor M in Figure 7(a) [49]. In
Figure 7(b), Ma senses the noise emitted by Mb, and
vice versa; the resulting circuit is an implementation
of the circuit in Figure 6(b).
If this could be accomplished, then
it would resemble what happens in
noise-canceling LNAs, where the drain
noise is sensed, scaled, and sent to the
LNA output via an alternative path to
provide noise cancelation.
Vdd
RL
c1
iin
(a)
Noiseless
LNA
c
Vdd
RL
Output
c2a
iin
c1a
Ma
0.5 × W
c1b
c2b
Mb
0.5 × W
Zs = Zopt
Γs = Γopt
Vdd
c1
M
Width = W
Zs = Zopt
Γs = Γopt
Noisy LNA
Zs
Γs
Output
c2
2
(b)
Vdd
Auxiliary Amplifier
RL
(a)
+
Noisy LNA
vn1a
Vdd
Zs
Γs
c1
Noiseless
LNA c
2
+
iin
– +
vn2a
Ma
0.5 × W
–
Ys = Yopt
(b)
Figure 6. Sensing and scaling c1 for noise matching
with an auxiliary circuit: (a) c1 is scaled and reapplied
at the LNA input; (b) c1 is scaled and reapplied at the
LNA output.
Output
Mb
0.5 × W
Γs = Γopt
Auxiliary Amplifier
=
(c)
Figure 7. Noise-matched LNA conceptual models: (a)
a single noise-matched LNA; (b) a noise-matched LNA
decomposed into two identical LNAs: traveling wave
representation; and (c) a noise-matched LNA decomposed
into two identical LNAs: impedance representation.
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Because Ma and Mb are the same,
they should contribute only half the
total LNA noise factor, and it appears
that each of the two identical LNAs
contributes only half its Fmin, i.e.,
less than what is possible with noise
matching each of them individually.
Let us investigate this further, but only considering
the noise generated by Ma as an example. Some of c 1a
is reflected off both Cs and Mb to flow back into Ma and,
ultimately, interfere with c 2a at the output. In addition, some of c 1a propagates through Mb to the output,
where it also interferes with c 2a . Because the circuits
in Figure 7(b) are exactly equivalent to the circuit in
Figure 7(a), setting C s = C opt again allows the complete
LNA in Figure 7(b) to operate at its Fmin .
Because Ma and Mb are the same, they should contribute only half the total LNA noise factor, and it
appears that each of the two identical LNAs contributes only half its Fmin , i.e., less than what is possible
with noise matching each of them individually. We can
say, then, that the other half of Fmin is canceled because,
rather than having c 1a only reflect off a passive signal
source, a part of c 1a also arrives at the output via a different path and optimizes the noise cancelation with
c 2a . The possibility of doing this was anticipated at the
end of the “How Is F Reduced to Fmin?” section.
How can this happen? To explain this intuitively, we
model the Ma noise with its impedance representation,
Vdd
RL
Ma Replacement
Mc
iin
–A
Vbias
Zs
Γs
Matching
Network
Mb
Figure 8. An example of noise matching leading to the
noise-canceling topology. In the low-noise gain stage,
−A can be implemented, for example, with a common
source amplifier.
shown in Figure 7(c). As in the earlier discussion of
noise-canceling LNAs, my focus here is only on one
equivalent noise source of Ma. In this case, the noise
source is v n1a . From Figure 7(c), we see that the gates
of Ma and Mb are connected to the v n1a noise source’s
negative and positive terminals, respectively; therefore, the noise voltages at the gates are out of phase.
These out-of-phase noise voltages generate out-ofphase noise currents flowing through the channels of
the two transistors to the output node where they are
partially canceled, with the remaining portion reducing the noise due to v na2 .
Relative to the signal strength of just M a on its
own, having Mb in parallel doubles the output signal voltage. Together, the two effects result in an
apparent reduction of Fmin for each individual transistor. In this circuit, M a is embedded in an active
network, the noise of which is uncorrelated and
can be treated separately. In this situation (in contrast to a transistor embedded in a passive lossless network), M a transistor’s Fmin is reduced, and
the minimum noise contribution of M a as a part
of the total circuit is halved relative to what it can
be for a stand-alone M a. This combination of noise
matching and noise cancelation for each individual transistor can result in less noise contri­
bution
than would be expected from their individual Fmins.
Note, however, that Fmin of the total circuit remains
unchanged.
Transition from Noise-Matched
to Noise-Canceling LNAs
As the noise parameters are the same for same-sized
and identically biased common-source transistors,
common-gate transistors, and even common-drain
transistors operating at frequencies much lower than
their unity-current-gain frequency (~T), the commonsource Ma in Figure 7(b) [or the auxiliary amplifier
in Figure 6(b)] can be replaced with one of the other
two transistor configurations—perhaps augmented
with an additional gain stage for proper signal scaling.
Replacing Ma with a common-gate Mc and a low-noise
gain stage, the minimum noise factor of the resulting
circuit (Figure 8) can be made the same.
However, because the input impedance of Mc is
not the same as that of M a, a matching network is
needed at the gate of M b to allow the achievement
of Fmin . It is important to note that the circuit in
­Figure 8 resembles the noise-canceling LNA in Figure 4(b). The two differences are 1) the matching
network is not used in Figure 4(b), as the achievement of Fmin is not the main goal; and 2) the output of
the latter is taken differentially, thus implementing
the phase reversal of the gain stage −A of the former without any additional noise. Of course, if −A is
implemented, its noise would affect the overall noise
of the amplifier.
apply.
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The key difference between the noise-matched
LNA circuits in Figure 7 and noise-canceling LNAs
like the one in Figure 8 is fairly simple: for the noisecanceling LNA, the design goal is to provide a wideband input power match without adding significant
extra noise and without using area-consuming matching circuitry; for noise-matched LNAs, on the other
hand, a wideband input power match is secondary to
the lowest possible noise factor. Therefore, for noisecanceling LNAs, transistor Mc is set to have its transconductance be near 1/R s; for noise-matched LNAs,
an input matching network is designed to achieve Fmin .
A Bit of Both Noise Canceling
and Noise Matching
For the noise-canceling LNA, the
design goal is to provide a wideband
input power match without adding
significant extra noise and without
using area-consuming matching
circuitry; for noise-matched LNAs,
on the other hand, a wideband input
power match is secondary to the
lowest possible noise factor.
matching. Of course, just as in all other noise-canceling
LNAs, only some of the noise is canceled, and some
additional noise is added; in this example, the differential gain stage, M3, R L2 , and other passives contribute
noise, and the gate noise currents in M1 and M2 contribute noise as well. To bring the LNA noise factor close
to its Fmin, the circuit in Figure 9 incorporates resistor
R L2, which results in a negative capacitance at the input
needed to noise-match the LNA.
The measured and simulated results of this circuit
are shown in Figure 10. As Figure 10(d) illustrates,
the measured minimum noise figure, NFmin / 10 #
log ^Fmin h, and the LNA noise figure, NF / 10 # log ^F h,
are in close proximity to each other across the
10-MHz–2-GHz frequency range. However, as expected, the cascode circuit by itself would have a
lower noise figure than the complete circuit [see Figure 10(d)]. This supports the discussion in the “Misconception 2: Noise-Canceling LNAs Can Achieve
Noise Factors Lower than Fmin” section, where we
have seen that, while noise cancelation does occur,
this does not necessarily mean the noise figure
of the complete circuit will be less than the NFmin
of its individual parts. The complete LNA is both
50 Ω
10 kΩ
Buffer for
Measurement
Purposes
2.7 kΩ
50 Ω
10 kΩ
Noise-matched LNAs do achieve, by far, the lowest
noise factors (or figures). For example, sub-0.5-dB
ambient-temperature CMOS LNAs have already been
demonstrated experimentally [42], [50], [58], [59], [62],
[63]. In contrast, noise-canceling LNAs have typically
been able to break only the 2-dB noise-figure threshold [17]. However, the two key advantages for noise-­
canceling LNAs are the ease for wideband input
power matching and the availability of differential
outputs, which are preferred for many integrated
circuits. Therefore, a circuit that combines noise canceling and noise matching would be of considerable
interest, as it could be expected to achieve better
noise figures than what has been possible with noisecanceling LNAs but would still provide the input
power matching and differential output of noise-canceling LNAs.
An example of such a circuit is shown in Figure 9.
This circuit is based on the noise-canceling circuit in Figure 4(a) and consists of two parts. The first is a modified
shunt-feedback cascode LNA (labeled “Core LNA” in
the figure). The second is a differential gain stage [which
implements amplifier −A in Figure 4(a)], the differential
output of which would be
used if this LNA were a part
of a larger integrated system.
Core LNA
For measurements, only one of
the two outputs is connected
to the output port through a
RL2 RL1
Cdc Cdc
buffer [64]. In this circuit, the
Differential
drain noises of M1 and M2
Output
Cdc
(as well as R L1) generate noise
Noise
from
M2
M3
voltage across resistor R L1 .
M1, M2, and RL1
V1
Cgs2
M3 is a source follower, which
V2
replaces Rf in Figure 4(a), and
M1
induces an in-phase replica of
Differential Gain Stage
that noise voltage at the input
node, as illustrated in Figure 9.
Cdc
vin
The differential gain stage
subtracts the two in-phase
noise components. M3 also pro­­­­
vides wideband input power Figure 9. A combined noise-canceling and noise-matched LNA.
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Simulated S21
Measured S21
40
LNA (0.02 mm2) Output
Second Stage (0.01 mm2)
S-Parameters (dB)
20
Simulated S11
Simulated S22
0
Measured S21
Measured S22
−20
Simulated S12
Measured S12
−40
Buffer (0.005 mm2)
Input
−60
0
2
4
Frequency (GHz)
(b)
(a)
Calculated NF Based on
Measured Noise Parameters
Measured LNA NFmin
2.5
Noise Figure (dB)
4 GHz
4 GHz
Measured LNA’s Γopt
Simulated LNA’s Γopt
Measured LNA’s S11
6
2
1.5
1
NFmin of M1,2 Cascode Biased Through R3
0.5
0
1
(c)
2
3
Frequency (GHz)
4
(d)
Figure 10. (a) A micrograph of the LNA shown in Figure 9. (b)–(d) The measured and simulated S-parameters and noise
parameters of the LNA (including the buffer). (d) also shows the minimum noise factor (NFmin) of a stand-alone M 1, 2 cascode
with bias supplied through the 2.7-kΩ resistor shown in Figure 9.
TABLE 1. A performance summary comparing the discussed LNA [64] with other sub-2-dB wideband CMOS LNAs.
PDC (mW)
Noise
Figure
(min)
Area
(mm2)
CMOS
Inductors
32 dB
40
1 dB
0.035
65 nm
No
-10
25 dB
42
1.9 dB
0.025
90 nm
No
0.15–1.8
-12
14 dB
35
1.9 dB
0.075
250 nm
No
0.7–1.4
-11
17 dB
43
0.2
0.825
90 nm
Yes
S11 (dB)
Voltage
Gain
0.01–2.8
-10
SF
0.5–6
[17]
NC
[59]
NM
Work
LNA
Topology
Frequency
(GHz)
[64]
NM + NC
[65]
NC: noise canceling; NM: noise matched; SF: shunt feedback.
noise- and power-matched because both LNA S11 and
Copt are near the center of the Smith chart and C *opt . S 11 .
The performance parameters of this LNA and of
some other fully integrated, inductorless wideband
sub-2-dB CMOS LNAs are shown in Table 1.
Conclusions and Discussion
This article has focused on noise-matched and noisecanceling LNAs and, in particular, on the similarities
the two share. Despite these similarities, the design
approaches for the two LNAs are driven by different
apply.
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2016
goals. Noise-matched LNAs are capable of achieving
the best possible noise factor for a given semiconductor technology. Although noise-canceling LNAs cannot
achieve such low noise factors, they do have key advantages that are responsible for their wide use in CMOS
integrated circuits. The main advantage lies in their
wideband input power match without the fundamental
need for inductors, although inductors are sometimes
used as RF chokes. To achieve this wideband match, the
noise factor is compromised; but, because modern transistors have very low Fmin, the noise penalty of avoiding
noise matching is not significant for most applications.
Even though noise-canceling LNAs do not achieve
Fmin, their noise factors (at around 2 dB) are lower than
the Global System for Mobile noise figure specifications (around 5 dB), as well as the wireless local area
network noise figure specifications (6 dB); they are
also lower than what could be achieved if other wideband power-matched alternatives (such as a commongate LNA, with a typical noise factor of >3 dB) were
used instead. Other important reasons for selecting
noise-canceling LNAs include the availability of differential outputs, which are much preferred for most
integrated circuits, and the possibility of distortion
cancelation [19].
The following summarizes some main points to
remember in considering noise-matching and noisecanceling LNAs.
•• Noise cancelation occurs in all LNA designs. In
the simplest case, the noise cancelation is between
the two partially correlated noise sources, which
are required to represent the noise in a transistor,
as shown in Figure 1. Noise matching uses signalsource impedance to maximize the cancelation
between the two sources, whereas noise-cancelation techniques can cancel the effect of one of the
sources, but not both.
•• Noise-canceling LNAs utilize two or more transistors to cancel noise at an output; this could be
described as “active” noise cancelation to differentiate it from the single-device cancelation just
described. The noise factor of the circuit is no better than the noise factor obtained by noise-matching one of the transistors; however, the input
power match is improved. This improvement does
not reduce the noise factor but lowers the gain
variation due to mismatches at the LNA input.
•• It should be noted that a circuit cannot distinguish signal from noise. Consequently, designs for
noise-canceling LNAs must also consider whether
the signal is canceled. It is important to make input
signals add at the node where noise subtracts. At
low frequencies, this is fairly straightforward;
however, as reactive parasitics become dominant
at high frequencies, the resulting inevitable phase
shifts introduce difficulties associated with subtracting noise while adding signals.
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