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IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 51, NO. 4, AUGUST 2002
A New Method for High-Sensitivity
Noise Measurements
Carmine Ciofi, Felice Crupi, and Calogero Pace
Abstract—A new method for high-sensitivity noise measurement, based on the elaboration in the time domain of the signals
coming from two identical amplifiers, is presented in this paper.
The most important advantage of this method, which in most cases
allows obtaining an equivalent background noise 30 dB below that
of the amplifiers which are used in the measurement chain, lies in
its simplicity and in the fact that it does not depend on the method
used for the estimation of the noise spectra.
Index Terms—Correlation, noise measurement, spectral analysis, time domain analysis.
Fig. 1. Block diagram of the spectrum analyzer based on the cross-correlation
technique.
I. INTRODUCTION
I
N NOISE measurement systems, the sensitivity of the
measurement chain is ultimately limited by the equivalent
input noise sources of the input preamplifier coupled to the
device under test (DUT). The sensitivity that can be obtained
by means of standard commercial spectrum analyzers is not
sufficient for a large number of applications, especially in
the case of the characterization of the low-frequency noise of
modern electron devices [1]. In such cases, very low-noise,
high-gain preamplifiers must be used between the DUT and the
input of the spectrum analyzer in order to conveniently increase
the signal level without introducing a significant supplemental
noise contribution. The choice of the input preamplifier is rather
challenging, especially because of the dependence of the final
supplemental noise contribution on the equivalent impedance
of the DUT. To reach the ultimate sensitivity levels, one must
often resort to a custom design of the input preamplifier. By
means of a careful design, the total noise contribution of the
preamplifier can be reduced to that introduced by the active
element used in the first stage of the amplifying chain. As a
general rule, noise measurements are easily performed when
the spectral density of the noise produced by the DUT is at least
10 dB higher than the background noise of the measurement
chain in the frequency range of interest. However, the lowest
background noise levels that can be obtained are still too
high for many applications. Therefore, noise measurement
methods capable of overcoming the limitation imposed by
the background noise of the input preamplifiers are of great
interest.
The possibility of performing reliable noise measurements
when the noise produced by the DUT is comparable to, or even
much lower than, the background noise of the input pream-
plifier has been demonstrated using different methods [2]–[6].
These methods take advantage of the noncorrelation of the noise
sources of the measurement chain with the noise produced by
the DUT. A recently proposed approach employs the topology
reported in Fig. 1 [3], [4]. It uses two independent amplifiers
connected to the DUT. A discrete Fourier transform (DFT) processor follows the output of each amplifier, and the numerical
results are processed in order to obtain an estimate of the cross
spectrum of the signals at the output of the two amplifiers, with
the result of eliminating most of the contribution of the noise
introduced by the amplifiers. In this way, under proper conditions, a direct estimate of the sole noise contribution of the DUT
is obtained. In this paper, we present another method for performing reliable very low noise measurements that, although in
principle equivalent to the one just described, is based on a rather
different approach. The measurement principle, the practical issues involved in its actual implementation, and the advantages
and limitations of the method we propose, are discussed in the
following sections.
II. PROPOSED MEASUREMENT METHOD
The circuit configuration of the proposed high-sensitivity
measurement system is reported in Fig. 2 for the case of voltage
is simultanenoise measurements. The DUT voltage noise
ously amplified by two different channels with identical gains,
and the two amplified signals are fed to the addition and the
and
can be
subtraction blocks. The output voltages
written as
(1)
Manuscript received May 29, 2001; revised April 30, 2002.
The authors are with the Dipartimento di Fisica della Materia e Tecnologie, Fisiche Avanzate and INFM, Messina, Italy (e-mail: ciofi@ingegneria.unime.it).
Digital Object Identifier 10.1109/TIM.2002.803080
is due to the input signal and to the equivalent input
where
is due to the
current noise (EICN) of the two amplifiers,
equivalent input voltage noise (EIVN) of the first amplifier, and
0018-9456/02$17.00 © 2002 IEEE
CIOFI et al.: NEW METHOD FOR HIGH-SENSITIVITY NOISE MEASUREMENTS
Fig. 2.
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Schematics of the proposed voltage noise measurement system.
Fig. 3. Schematics of the transimpedance noise amplifiers for the case of
current noise measurements.
is due to the EIVN of the second amplifier. Therefore, at
the output of the addition and subtraction blocks we have
(2)
At least in the case of low-frequency noise measurements, one
, and
are uncorrelated and,
can assume that
therefore, at the output of each channel of the spectrum analyzer in Fig. 2 we have
(3)
is the power spectral density (PSD) of the signal
where
. By subtracting
from
, we obtain an estimate
alone. It is clear that, in the frequency range in which
of
the contribution of the EICN of the amplifiers is negligible, we
obtain a direct estimate of the PSD of the noise signal we are
interested in. Since the contributions of the EIVN of the amplifiers cancel out, the sensitivity of the measurement method is
limited by the contributions of the EICN, whose effect depends
on the equivalent impedance of the DUT. This fact implies that
in order to measure very low voltage noise, the EICN of the
amplifier represents the limiting factor rather than the EIVN.
Therefore, using the measurement configuration we propose,
one may obtain better noise performances from MOSFET input
stage amplifiers (high EIVN and low EICN) rather than from
those employing BJTs (low EIVN and high EICN), even in the
case of low DUT impedances. Another advantage is that this
method allows the PSD evaluation of the input signal without
requiring the exact evaluation of the single noise sources of the
input amplifiers and of the DUT impedance, which can change
because of bias or temperature variations or because of drift with
time. Moreover, while the PSD of the noise introduced by the
preamplifiers is the sum of the PSD of the noise due to each
single channel, the PSD of the input signal is proportional to
the square of the sum of the signals relative to the two channels. Therefore, the dual-channel configuration is characterized
by a doubled signal-to-noise ratio with respect to the case of
a single-channel amplifier. It is worth noticing that the method
we propose is, in principle, equivalent to the one discussed with
reference to Fig. 1. In a sense, we are just performing the evaluation of the cross spectrum by way of a different approach.
However, the operations needed for separating the correlated
noise contribution from the uncorrelated ones at the output of the
amplifiers are performed analogically in the time domain rather
than numerically in the frequency domain. Besides resulting in
many cases in a simpler implementation, our method does not
depend on the properties of the DFT-based spectrum analysis
(i.e., using a DFT-based spectrum analyzer for spectrum estimation is not mandatory in our case) and can be successfully
performed even by using a single-channel spectrum analyzer.
In fact, one can evaluate the PSD of the channel alone, then
that of the channel alone, and finally perform the subtraction
of the two PSDs thus obtained.
By replacing the voltage noise amplifiers of Fig. 2 with the
transimpedance amplifiers shown in Fig. 3, it is possible to measure the current noise of a DUT using the same principle described for the case of voltage noise measurements. It can be
easily verified that in such a case all the previous considerations
are still valid, provided that the roles of the addition block and
of the subtraction block and all the statements relative to EIVN
and EICN are exchanged. The results obtained by using the new
method are reported in the following section, both in the case of
the voltage noise measurement configuration and in the case of
the current noise measurement configuration.
III. EXPERIMENTAL RESULTS
The actual circuit used for demonstrating the new measurement method in the case of voltage noise measurements is
reported in Fig. 4. The voltage noise amplifiers are based on
the TLC2201 by Texas Instruments, which is characterized by
Hz) and by an
a relatively high EIVN (10 nV/ Hz,
excellent level of EICN (0.6 fA/ Hz). The gain of each single
658
Fig. 4.
IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 51, NO. 4, AUGUST 2002
Implementation of the schematics of Fig. 2.
Fig. 5. Input referred PSDs of the signals at the output of the addition and
subtraction blocks of the circuit of Fig. 4 with a 10 resistor at the input,
difference between the two spectra and theoretical PSD of the thermal noise
of the input resistor.
stage is set to 100 by means of 0.1% precision resistors. The
dB).
resulting bandwidth is from dc up to about 19 kHz (
The EICN of each stage coincides with that of the TLC2201,
whereas its EIVN depends on the values of the resistors used
for the feedback. Because of the values of the resistors we
used, however, the EIVN of each amplifying stage reduces to
that of the TLC2201 alone. The U3 unity gain instrumentation
amplifier is used both for inverting the output of one of the
voltage amplifiers (U2) and for allowing offset compensation
in order not to saturate the following stages. The other unity
gain instrumentation amplifier could be avoided, but it may be
useful, as before, for offset compensation. If no offset compensation is required, the two terminals marked “Offset null”
in the figure can be simply grounded. The two INA141 at the
end of the amplifying chain realize the addition and subtraction
Fig. 6. Input referred PSDs of the signals at the output of the addition and
subtraction blocks for the case of the current noise measurements with a 1 G
resistor at the input, difference between the two spectra and theoretical PSD of
the thermal noise of the input resistor.
blocks. The gain
of these stages can be set to either 10 or
100, and their accuracy is guaranteed by the manufacturer to be
and 750
ppm of the nominal
within 500
value. We measured the PSD of the voltage fluctuations at
the outputs of the addiction and subtraction blocks by means
of a dual-channel FFT spectrum analyzer based on a National
of 10
was
Instruments PCI-4451 board. A resistance
used as DUT. It acted as a source of voltage noise with a power
, where is the Boltzmann constant
spectral density of
and is the absolute temperature. At room temperature, the
value of the PSD of the voltage fluctuation to be measured
is about 407 pV/ Hz. The contribution of the two EICN of
the input amplifiers is negligible (less than 100 fV/ Hz). As
can be verified in Fig. 5, the estimation of the PSD of the
, as obtained by using
voltage fluctuations at the ends of
CIOFI et al.: NEW METHOD FOR HIGH-SENSITIVITY NOISE MEASUREMENTS
the proposed method, is rather good, with an average value of
409 pV/ Hz and a standard deviation of 270 pV/ Hz after
averages with a frequency resolution of 25 Hz, within
the investigated bandwidth. It must be noted that the noise
produced by the DUT is, in the low-frequency range of the
spectrum, almost 30 dB below the EIVN of the input amplifying stages. The maximum sensitivity that can be obtained
clearly depends on the mismatch between the addition and
subtraction amplifying chains (including the input amplifiers
and data conversion stages of the spectrum analyzers) and on
the overall time length employed for spectrum estimation. An
estimate of the sensitivity that can be obtained for a given
setting of the measurement parameters can be obtained by
performing a measurement with the input short-circuited. In
this case, indeed, the difference between the spectra at the
output of the addition and subtraction channels represents the
error that will be added to the estimate of the noise produced
by the DUT.
We have also tested a possible implementation for current
noise measurements. In order to obtain the new circuit, we had
only to replace the voltage noise amplifier stages in Fig. 4 with
a transimpedance amplifier stage realized following the scheme
of Fig. 3 with two TLC2201 and 10 M feedback resistors.
Since, in this case, the outputs of the two transimpedance amplifiers are inverted, the roles of the addition and subtraction
blocks in Fig. 2 are reversed. The equivalent EIVN of each
transimpedance stage coincides with the EIVN of the operational amplifier, while the EICN is mostly due to the thermal
noise of the feedback resistor, i.e., about 41 fA/ Hz in the flat
bandwidth of the transimpedance amplifier. The data reported
in Fig. 6 were obtained by using a 1 G resistor as a DUT.
Therefore, the input current noise was 20 dB below the EICN
of each single transimpedance amplifier. The average value we
estimated for the input current noise was 4.1 fA/ Hz, substantially coincident with the theoretically expected value, with a
averages with a frestandard deviation of 1.2 fA/ Hz after
quency resolution of 50 Hz within the investigated frequency
range.
IV. CONCLUSION
A new method for high-sensitivity noise measurements was
presented in this paper. The method is based on the separate
estimation of the correlated and uncorrelated noise at the output
of two nominally identical voltage (for voltage noise measurements) or transimpedance (for current noise measurements)
amplifiers. The method is equivalent, in principle, to other
methods based on the cross-correlation technique. However,
while in the case of the cross-correlation technique, it is mandatory to employ a two-channel FFT-based spectrum analyzer,
the approach we propose is independent of the method used
for spectrum estimation and could, in principle, be extended to
very high frequency ranges. By using standard commercially
available operational amplifiers and without any calibration,
we have been able to measure voltage noise levels as low as
400 pV/ Hz superimposed to a noise level 30 dB higher and
current noise levels as low as 4.1 fA/ Hz superimposed to a
noise level 20 dB higher. Future work will be devoted to the
development of calibration procedures for compensating the
659
mismatch in the amplification channels in order to ascertain
the ultimate possibilities offered by the method we propose.
REFERENCES
[1] C. Ciofi and B. Neri, “Low-frequency noise measurements as a characterization tool for degradation phenomena in solid-state devices,” J.
Phys. D, vol. 33, 2000. R199.
[2] M. Macucci and B. Pellegrini, “Very sensitive measurement method of
electron device current noise,” IEEE Trans. Instrum. Meas., vol. 40, pp.
7–12, Feb. 1991.
[3] A. van der Ziel, Noise: Sources, Characterization, Measurement. Englewood Cliffs, NJ: Prentice-Hall, 1970, p. 54.
[4] M. Sampietro, L. Fasoli, and G. Ferrari, “Spectrum analyzer with noise
reduction by cross correlation technique on two channels,” Rev. Sci. Instrum., vol. 70, no. 5, pp. 2520–2525, 1999.
[5] M. Sampietro, G. Accomando, L. G. Fasoli, G. Ferrari, and E. C. Gatti,
“High sensitivity noise measurement with a correlation spectrum analyzer,” IEEE Trans. Instrum. Meas., vol. 49, pp. 820–822, Aug. 2000.
[6] E. Rubiola and V. Giordano, “A correlation-based noise measrurement
scheme showing sensitivity below the thermal floor,” in Proc. Int. Conf.
Noise Phys. Syst. and 1=f Fluctuations, Hong Kong, 1999, pp. 483–486.
Carmine Ciofi was born in Cosenza, Italy, in 1965.
He received the degree in electronic engineering
in 1989 from the University of Pisa, Pisa, Italy. In
1993, he received the Ph.D. degree in electronic
engineering from the Scuola Superiore S. Anna,
Pisa.
From 1993 to 1998, he was with the Dipartimento
di Ingegneria dell’Informazione, University of Pisa.
In 1998, he left the University of Pisa and joined the
University of Messina, Messina, Italy, where he is
currently an Associate Professor of electronics. He
has been and is currently involved in research projects on the characterization
of electron devices by means of transmission electron microscopy (TEM), on
the evaluation of the reliability of metallic interconnections, and on the design
and realization of low noise electronic instrumentation. He has published more
than 50 papers on international journals and congress proceedings.
Felice Crupi was born in Lamezia Terme, Italy, on
December 21, 1972. He received the degree in electronic engineering from the University of Messina,
Messina, Italy, in 1997 and the Ph.D. degree from the
University of Firenze, Firenze, Italy, in 2001.
In 2000, he joined the University of Messina as Research Contractor. In 1997, in 1998 and in 2001 he
was visitor at the Interuniversity Micro-Electronics
Center (IMEC), Leuven, Belgium, and in 2000, he
was visitor at the IBM Thomas J. Watson Research
Center, Yorktown Heights, NY. His main research interests include the modeling of the degradation and of the breakdown processes
in thin oxide layers, the study of the noise in MOSFET devices, and the design
of ultra low-noise instrumentation.
Calogero Pace was born in Palermo, Italy, in 1965.
He received the degree in electronic engineering in
1990 from the University of Palermo. In 1994, he
received the Ph.D. degree in electronic engineering
from the University of Palermo.
In 1996, he joined the University of Messina,
Messina, Italy, where he is currently Assistant
Professor of electronics. He is currently involved in
research projects on the evaluation of the reliability
of metallic interconnections, on the design and
realization of low-noise electronic instrumentation,
and on the design and characterization of electronic gas sensors. He has
been involved in research projects supported by Ministero dell’Università e
della Ricerca Scientifica e Tecnologica and by the Consiglio Nazionale delle
Ricerche (P.F.T.E.O.).