A novel ultra sensitive method for voltage noise ... - Felice Crupi

IMTC 2005 – Instrumentation and Measurement
Technology Conference
Ottawa, Canada, 17-19 May 2005
A novel ultra sensitive method for voltage noise measurements
Felice Crupi 1 , Gino Giusi 2 , Carmine Ciofi 2 , Calogero Pace 1
1 DEIS, University of Calabria, Via Pietro Bucci 42C, 87036 Arcavacata di Rende (CS), Italy
Phone: +39-984-494766, Fax: +39-984-494834, Email: crupi@unical.it
2 DFMTFA and INFM, University of Messina, Salita Sperone 31, 98166 Messina, Italy
Abstract – Ultra low noise measurements often require the
application of signal processing and correction techniques to go
beyond the noise performances of front-end amplifiers. In this paper
we propose a new method for the measurement of a voltage noise
source that allows, at least in principle, the complete elimination of
the noise introduced by the amplifiers used for the measurements.
This is obtained by resorting to the conventional cross correlation
technique for the elimination of the contribution of the EIVN of the
amplifiers and by using a new three step measurement procedure
that exploits different amplifier configuration measurements in
order to subtract the contribution of the EICN of the amplifiers.
DUT
ZDUT
VOLTAGE NOISE
AMPLIFIERS
EIVN
EIVN
EICN
SPECTRUM
ANALYZER
CROSS
SPECTRUM
S ( f )
Keywords – Amplifier noise, noise measurement, spectral analysis,
cross-correlation tecniques
VDUT
EICN
I. INTRODUCTION TO THE PROBLEM
The problem of measuring ultra low voltage noise in
electronic devices can be addressed by means of two different
approaches. The first approach consists of designing voltage
amplifiers with a background noise significantly lower, at
least 10 dB, with respect to the device under test (DUT)
signal [1]. When this is not possible, another possible
approach consists of using measurement methods capable of
increasing the sensitivity of the instrumentation by means of
correction techniques or signal elaboration [2-6]. Many high
sensitive methods rely on the properties of cross-correlation
[3-6]. In fact, by amplifying the DUT signal by means of two
independent channels and of evaluating the cross-correlation
of their outputs (see Fig. 1), one can completely suppress, at
least in principle, the effect of the noise sources of the two
channels which result uncorrelated to one another, and
namely the effect of the equivalent input voltage noise
(EIVN) of the two amplifiers. By using this method, a DUT
signal level 30 dB lower with respect to the amplifier
background noise has been measured [6].
The limit to the noise measurement is however imposed by
the not eliminated correlated noise sources, which are mainly
due to the equivalent input current noise (EICN) of the two
amplifiers, thus making the method ineffective in the case of
a high value DUT equivalent impedances. In this paper, we
propose a novel noise measurement method that besides
taking advantage of the correlation method for the
elimination of the uncorrelated noise sources, it also allows
the elimination of the effects of the correlated noise sources
thus resulting in several cases more sensitive with respect to
all the previous proposed methods.
Fig. 1. Block diagram of the correlation spectrum analyzer.
II. THE BASIC IDEA
The method we propose is based on the following
observation: if we connect the inputs of N voltage amplifiers
in parallel to the DUT, the cross-correlation between the
outputs of any two amplifiers will consist of the sum of the
noise spectrum generated by the DUT and of the spectrum
due to the EICN sources of all the amplifiers, the effect of the
EIVN sources being, at least in principle, completely
eliminated by the cross correlation procedure. Note that this
last statement is completely true only in the case in which the
impedance of the DUT is negligible in comparison with the
input impedance of the voltage amplifiers used for the
measurements. In this very same hypothesis, that is normally
verified in the case of voltage noise measurements, the
contribution of the EICN of all the amplifiers connected to
DUT to the measured noise spectrum is given by the sum of
the contributions that would be experienced by connecting
just one amplifier at a time to the DUT. Within this
hypothesis, and with reference to Fig. 2, let us assume that we
connect just 2 amplifiers (amplifiers 1 and 2) to the DUT and
we evaluate the cross spectrum at their outputs. By taking
into account the voltage gain of the amplifiers that we assume
to be exactly the same for all the amplifiers, we would obtain
for the input referred voltage noise:
S 12 = S DUT + S C1 + S C2 (1)
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where S DUT is the power spectral density (PSD) of the
equivalent noise source of the DUT, and S Ci is the PSD due to
the EICN of the amplifier i.
DUT
1
2
3
4
Spectrum
Analyzer
Figure 2 – Schematics of the proposed instrument for voltage noise
measurements. The DUT can be connected either to one of the two
couples of amplifiers or to both couples. The spectrum analyzer
performs the cross-correlation between the outputs of any two
amplifiers.
residual contribution of the (uncorrelated) EIVN of the
amplifiers negligible with respect to the DUT noise to be
measured.
While the above requirements are common to almost all
the high sensitivity methods mentioned above, the new
method has the very important advantages of not requiring
any preliminary characterization of the DUT impedance and
of the EICN of the amplifiers and of not relying on the
hypothesis of the EICN having a negligible effect. In fact, by
using the technique we propose, it is possible to accurately
estimate the voltage noise produced by the DUT even in the
case in which its impedance is so high that the contribution of
the EICN of the amplifiers becomes predominant.
Finally we would like to note that by using the very same
principle we have developed above, one can obtain similar
results by using just three amplifiers instead of four, at the
cost, however, of a further measurement step.
III.
EXPERIMENTAL VALIDATION
In order to verify the validity of the proposed method, we
have used the four amplifiers configuration shown in Fig. 3.
Let now assume that we connect the inputs of the just two
other amplifiers (amplifiers 3 and 4) in parallel to the DUT.
By evaluating the cross spectrum at their outputs and by
taking into account, as before, the voltage gain of the
amplifiers, we now obtain for the input referred voltage
noise:
R2 10k
U1
-
R1
100
R7
100
R8 10k
-
U4
S 34 = S DUT + S C3 + S C4 (2)
Finally, let us assume that we connect all the amplifiers
together to the DUT. In this last case, proceeding as before,
we would obtain for the input referred cross spectrum
evaluated among any two channels:
OP27
R9
R6 10k 1k
R4 10k
U3
-
+
+
SW1
R10
R5
R3
100k
100
100
C
220nF
SW4
-
OP27
U2
S 1234 = S DUT + S C1 + S C2 + S C3 + S C4 . (3)
OP27
+
SW3
D.U.T.
SW2
+
OP27
At this point it is apparent that we can evaluate the power
spectrum of the voltage noise generated by the DUT alone by
taking the sum:
S DUT = S 12 +S 34 - S 1234 . (4)
SW5 6
1 3 2 4
5
R11
1K
R12
-
10k
U5
It is important to note that this measurement procedure
allows to eliminate the contribution of the EICN sources of
the amplifiers without requiring the measurement of the DUT
impedance and the estimation of the EICN of the amplifiers.
The only requirements for this procedure to provide
accurate results are that:
a) the impedance of the DUT has to be much smaller than
the input impedance of the amplifiers used for the
measurements;
b) the evaluation of the cross spectrum has to be performed
using a time record long enough in order to make the
R14
R13
1K
+
+
-
AD743
10k
U6
AD743
SPECTRUM
ANALYZER
Figure 3 - A simple circuit implementation of the schematics of Fig. 2.
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If we take into consideration the case of a single amplifier
being connected to the DUT, it can be easily proven that the
input referred voltage noise PSD is given by:
S
tot
R1
⋅ R2
2
= SDUT
+ 4 KT + Sen
+ ZDUT
Sin
(5)
R + R
1
where S en and S in are the PSD of the EIVN and of the
EICN of the operational amplifier, respectively. Note that the
second and third noise contributions, due to the thermal noise
of the resistors and to the op-amp EIVN, represent the actual
EIVN contribution of the voltage amplifier while the fourth
contribution is due to the overall EICN of the voltage
amplifier. As discussed in the previous section, the noise
sources due to the EIVN of the voltage amplifier are
suppressed by the cross-correlation method and the ones due
to the EICN can be eliminated by applying the new method.
In order to have meaningful measurements, as far as the
validation of the new method is concerned, it is appropriate to
take into consideration a case in which we have comparable
levels for the noise produced by the DUT, for the noise due to
the amplifier EIVN and for the noise due to the amplifier
EICN. To fall into such a situation, we have chosen an OP27
low-noise amplifier, which is characterized by an EIVN of
3 nV/√Hz at 100 Hz and an EICN of 0.6 pA/√Hz at 100 Hz.
Moreover, we used as a DUT the parallel between the series
of a resistor R in = 1 kΩ and a capacitor C in = 0.22 µF with a
resistor R p = 100 kΩ (fig. 3).
Note that we put the capacitor in series with R in in order to
increase the DUT impedance at lower frequencies, thus
increasing the effect of the EICN, without varying the voltage
power spectrum generated by the DUT (see Fig. 4), which in
the explored frequency range (f > 100 Hz) is essentially due
to the thermal noise of R in . In fact, the resistor R p is needed in
order to provide for a bias path to the input of the amplifiers
and its value is chosen high enough in order not to interfere
significantly with the measurements in the explored
bandwidth.
S DUT
(V 2 /Hz)
10 -15
10 -16
10 -17
2
10 8
10 7
10 6
10 2 10 3 10 4
Frequency (Hz)
Figure 4 - Power spectrum of the voltage noise generated by the
DUT and squared modulus of the DUT impedance.
|ZDUT |2 (Ω 2 )
We followed the three steps procedure described in the
previous section. By connecting the channels 1 and 2 to the
DUT we obtain:
2
2
12
S
DUT
+ Z
DUT
Sin
1
Z
DUT
Sin2
S = +
(6)
where S ini is the PSD of the EICN of the i-th channel. In
the case of channels 3 and 4 connected to the DUT, we
obtain:
2
2
34
S
DUT
+ Z
DUT
Sin3
Z
DUT
Sin4
S = +
. (7)
In the case of all the four channels connected to the DUT,
we obtain:
S
+
= S
1234 DUT
2
Z
DUT
Sin3
+ Z
+ Z
DUT
DUT
2
2
S
in1
S
in4
+ Z
DUT
2
S
in2
The desired PSD of the DUT signal is therefore evaluated
by using Eq. 4.
The three measured spectra are reported in fig. 5 along
with the extracted PSD of the DUT signal. It is important to
underline that although at low frequency the effect of the
EICN strongly increases due to the increase of the DUT
impedance, the extracted S DUT results quite constant, as it was
expected. The average error with respect to the expected
DUT thermal noise in the bandwidth between f = 100 Hz and
f = 1 kHz, where the EICN is up to 10 dB higher with respect
to S DUT , results lower than 10 %.
Power Spectral Density (V 2 /Hz)
10 -15 S 1234
S
10 -16
34
S 12
S DUT
+
(8)
10 -17
10 2 10 3 10 4
Frequency (Hz)
Figure 5 – Input referred cross-spectra obtained by connecting the
DUT to: a) the first couple of amplifiers, b) the second couple of
amplifiers, c) all four amplifiers. The extracted power spectrum of the
voltage noise generated by the DUT is also reported.
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IV.CONCLUSIONS
In this work we have presented and experimentally
validated a new method for voltage noise measurements.
With respect to previous methods, the one we have presented
allow, at least in principle, the complete elimination of the
noise introduced by the amplifiers used for the
measurements. This is obtained by resorting to the
conventional cross correlation technique for the elimination
of the contribution of the EIVN of the amplifiers and to a
three step measurement procedure using different amplifier
configurations in order to subtract the contribution of the
EICN of the amplifiers. For the application of the method one
does not need neither the estimation of the EIVN and of the
EICN of the amplifiers, nor the estimation of the DUT
impedance. This fact makes the application of our method
quite straightforward. Moreover, as it is possible to eliminate
both the contribution of the EIVN and of the EICN of the
amplifiers, it is expected that the new method may provide by
far better results with respect to all other methods which
allow the elimination of the contribution of the EIVN or the
EICN alone.
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[2] M. Macucci and B. Pellegrini: “Very sensitive measurement method of
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[3] A. Van der Ziel, “Noise: Sources, Characterization, Measurement”,
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659, 2002
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