IEEE Solid-States Circuits Magazine - Spring 2023 - 32

Thus, the NEF is not dependent on
nonfundamental parameters such as technology
node, area, and supply voltage and thus
provides a fair way of comparing the noise
efficiency of different amplifier topologies.
minimize the input capacitance of
the following stage; thus, a unity
gain buffer is typically adopted
[9], [10]. At the same time, the bottom
capacitance of the CS reduces
the gain or the input impedance of
the SPA, which can be resolved by
adopting an adiabatic switching
technique [10].
Trends
The stringent energy budget of implantable
and wearable systems has
motivated the design of amplifiers
with high noise efficiency for sensor
interface circuits, particularly
in arrayed applications such as multichannel
neural recording. As a result,
the NEF of biomedical amplifiers
has slowly decreased over the last
several decades, as shown in Figure
4. From 2006 to 2016, the NEF
was primarily reduced by operating
MOSFETs in subthreshold and using
inverter-based amplifiers. However,
as shown earlier, the reduced transconductor
efficiency of MOSFETs
limits the NEF of a common-source
amplifier to ~1, which is why these
designs saturated at ~1.2.
In 2017,
inverter-stacking amplifiers were
reported, resulting in NEFs below
one. In 2020, the discrete-time SPA
was introduced, resulting in NEFs
below 0.5 for the first time. In the
meantime, many of these new topologies
have spread beyond biomedical
applications and have been used in
ADCs [11], general-purpose amplifiers
[12], and oscillators [13].
Concluding Remarks
In this article, we introduced the
implication and application of the
NEF, which aims to quantify the fundamental
tradeoff between the supply
current of an amplifier and its
32
SPRING 2023
input-referred noise. Therefore,
the NEF of an amplifier can be interpreted
as " how much noise it
generates for a given bias current "
or " how much current must be invested
to achieve a given inputreferred
noise. "
We also explained a common mistake
in the measurement of the NEF.
The definition of the NEF assumes
that the amplifier's bandwidth is
limited by a 1st order low-pass filter.
If this is not the case, the filter's
equivalent noise bandwidth should
be accounted for by scaling the integrated
input-referred noise in the
signal bandwidth by / 2r . If the filter
is implemented, the full spectrum of
the input-referred noise beyond the
maximum signal bandwidth needs to
be integrated.
Unlike other empirical FOMs, the
NEF describes the fundamental noise
and current tradeoffs between the input-referred
noise, current consumption,
and bandwidth based on their
physical relationship. Thus, the NEF
is not dependent on nonfundamental
parameters such as technology node,
area, and supply voltage and thus
provides a fair way of comparing the
noise efficiency of different amplifier
topologies.
Finally, it should be noted that
the NEF is limited to the tradeoff between
supply current and noise and
does not capture all aspects of amplifier
performance. For example, it
does not take the technology into account,
so for the same topology, BJTbased
amplifiers will outperform
their MOSFET-based counterparts.
It also does not consider frequency-dependent
noise sources like
flicker or
induced gate noise. So,
for a given bandwidth and topology,
low-frequency amplifiers whose
IEEE SOLID-STATE CIRCUITS MAGAZINE
in-band noise PSD is dominated by
flicker noise will have a higher NEF
than amplifiers whose in-band noise
PSD is dominated by thermal noise.
Last, besides reducing noise, the
supply current is also required to
improve other aspects of amplifier
performance. For instance, achieving
a wide bandwidth, high CMRR
or PSRR, good linearity, or good
input and output
impedance may
increase current consumption without
reducing the noise, which worsens
NEF. So, besides the NEF, other
performance metrics must always
be considered when evaluating an
amplifier's performance.
References
[1] M. S. J. Steyaert, W. M. C. Sansen, and C.
Zhongyuan, " A micropower low-noise
monolithic instrumentation amplifier for
medical purposes, " IEEE J. Solid-State Circuits,
vol. 22, no. 6, pp. 1163-1168, Dec.
1987, doi: 10.1109/JSSC.1987.1052869.
[2] M. Bazes, " Two novel fully complementary
self-biased CMOS differential amplifiers, "
IEEE J. Solid-State Circuits, vol. 26,
no. 2, pp. 165-168, Feb. 1991, doi: 10.1109/
4.68134.
[3] M. S. Chae, Z. Yang, M. R. Yuce, L. Hoang,
and W. Liu, " A 128-channel 6 mW wireless
neural recording IC with spike feature extraction
and UWB transmitter, " IEEE Trans.
Neural Syst. Rehabil. Eng., vol. 17, no. 4,
pp. 312-321, Aug. 2009, doi: 10.1109/TNSRE.2009.2021607.
[4]
G. Cecchin and F. H. Hilbert, " Stacked differential
amplifiers, " U.S. Patent US3603894A,
Sep. 7, 1971.
[5] B. Johnson and A. Molnar, " An orthogonal
current-reuse amplifier for multi-channel
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10.1109/JSSC.2013.2257478.
[6] Y.-P. Chen, D. Blaauw, and D. Sylvester,
" A 266nW multi-chopper amplifier with
1.38 noise efficiency factor for neural signal
recording, " in Proc. Symp. VLSI Circuits
Dig. Tech. Papers, Jun. 2014, pp. 1-2, doi:
10.1109/VLSIC.2014.6858431.
[7] S. Mondal and D. A. Hall, " An ECG chopper
amplifier achieving 0.92 NEF and 0.85
PEF with AC-coupled inverter-stacking for
noise efficiency enhancement, " in Proc.
IEEE Int. Symp. Circuits Syst. (ISCAS), May
2017, pp. 1-4, doi: 10.1109/ISCAS.2017.
8050957.
[8] S. Mondal and D. A. Hall, " A 13.9-nA ECG
amplifier achieving 0.86/0.99 NEF/PEF
using AC-coupled OTA-stacking, " IEEE J.
Solid-State Circuits, vol. 55, no. 2, pp. 414-
425, Feb. 2020, doi: 10.1109/JSSC.2019.
2957193.
[9] G. Atzeni, A. Novello, G. Cristiano, J. Liao,
and T. Jang, " A 0.45/0.2-NEF/PEF 12-nV/√Hz
highly configurable discrete-time low-noise
amplifier, " IEEE Solid-State Circuits Lett., vol.
3, pp. 486-489, Oct. 2020, doi: 10.1109/
LSSC.2020.3029016.
[10] G. Atzeni et al., " An impedance-boosted
switched-capacitor low-noise amplifier
achieving 0.4 NEF, " in Proc.
Symp. VLSI Technol. Circuits, Jun. 2022,
IEEE
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