Enhanced Sensitivity Cross-Correlation Method for ... - IEEE Xplore
IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 55, NO. 4, AUGUST 2006
1143
Enhanced Sensitivity Cross-Correlation Method for Voltage Noise Measurements Felice Crupi, Gino Giusi, Carmine Ciofi, Member, IEEE, and Calogero Pace
Abstract—Ultralow 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, a new method for the voltage noise measurement is proposed, which 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 equivalent input voltage noise of the amplifiers and by using a new threestep-measurement procedure that exploits different amplifierconfiguration measurements in order to subtract the contribution of the equivalent input current noise of the amplifiers. Index Terms—Amplifier noise, cross correlation, low-frequency noise, noise measurement, spectral analysis.
I. I NTRODUCTION TO THE P ROBLEM
T
HE PROBLEM of measuring ultralow 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 highly 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 by evaluating the cross correlation of their outputs (see Fig. 1), one can completely suppress, at least in principle, the uncorrelated noise contributions at the output of the two channels and, namely, the effects 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 contributions at the output of the two channels, 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 impedance. In this paper, we propose a novel noise-
Manuscript received June 15, 2005; revised March 16, 2006. F. Crupi and C. Pace are with the Dipartimento di Elettronica Informatica e Sistemistica (DEIS), University of Calabria, 87030 Arcavacata di Rende, Italy (e-mail: [email protected]). G. Giusi and C. Ciofi are with the Dipartimento di Fisica della Materia e Tecnologie Fisiche Avanzate (DFMTFA) and Instituto Nazionale Fisica della Materia (INFM), University of Messina, 98166 Messina, Italy. Digital Object Identifier 10.1109/TIM.2006.876392
measurement method that, besides taking advantage of the correlation method for the elimination of the uncorrelated noise contributions, also allows the elimination of the effects of the correlated noise contributions, thus, resulting, in many cases, in more sensitivity with respect to all the previously proposed methods. II. B ASIC I DEA 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, which is normally verified in the case of voltage noise measurements, the contribution of the EICN of all the amplifiers connected to the 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 two 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 S12 = SDUT + SC1 + SC2
(1)
where SDUT is the power spectral density (PSD) of the equivalent noise source of the DUT, and SCi is the PSD due to the EICN of the amplifier i. Let us now assume that we connect the inputs of the 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 S34 = SDUT + SC3 + SC4 .
(2)
Finally, let us assume that we connect all the amplifiers together to the DUT. In this last case, proceeding as before, we
0018-9456/$20.00 © 2006 IEEE
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IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 55, NO. 4, AUGUST 2006
Fig. 1. Block diagram of the correlation spectrum analyzer.
While the above requirements are common to almost all 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. III. E XPERIMENTAL V ALIDATION Fig. 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.
would obtain for the input referred cross spectrum evaluated between any two channels S1234 = SDUT + SC1 + SC2 + SC3 + SC4 .
(3)
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 SDUT = S12 + S34 − S1234 .
(4)
It is important to note that this measurement procedure allows the elimination of 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 the following. 1) The impedance of the DUT has to be much smaller than the input impedance of the amplifiers used for the measurements. 2) The evaluation of the cross spectrum has to be performed using a time record long enough in order to make the residual contribution of the (uncorrelated) EIVN of the amplifiers negligible with respect to the DUT noise to be measured.
In order to verify the validity of the proposed method, we have used the four-amplifier configuration shown in Fig. 3. If we take into consideration the case of a single-channel amplifier being connected to the DUT, it can be easily proven that the input referred voltage-noise PSD at low frequencies (f 1/2πR2 C2 ) is given by + 2 − Stot = SDUT + 4KT RP + Sen + RP Sin + |ZDUT |2 Sin (5) − where RP is the parallel between R1 and R2 , and Sen , Sin , + and Sin are the operational amplifier equivalent-input-voltage and current-noise sources [7], [8]. Note that the second, the third, and the fourth terms contribute to the actual EIVN of the voltage amplifier and, in the two-amplifier configuration, give rise to uncorrelated contributions of the two outputs. The fifth term coincides with the voltage-amplifier EICN and is responsible, in the two-amplifier configuration, for the correlated output terms. As discussed in the previous section, the uncorrelated contributions are suppressed by the cross-correlation method, while the correlated ones 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 used as a DUT a resistor amplifier, R9 = 1 kΩ, and we have chosen an OP27 low-noise √ which is characterized by an EIVN of 3 nV/ Hz at 100 Hz and √ an EICN of 0.6 pA/ Hz at 100 Hz. We followed the three-step
CRUPI et al.: ENHANCED SENSITIVITY CROSS-CORRELATION METHOD FOR VOLTAGE NOISE MEASUREMENTS
Fig. 3.
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Circuit implementation of the Fig. 2 schematics used for the experimental validation of the method.
procedure described in the previous section. By connecting the channels 1 and 2 to the DUT, we obtain + + S12 = SDUT + |ZDUT |2 Sin1 + |ZDUT |2 Sin2
(6)
+ where Sinj is the PSD of the EICN of the jth channel. In the case of channels 3 and 4 connected to the DUT, we obtain + + S34 = SDUT + |ZDUT |2 Sin3 + |ZDUT |2 Sin4 .
(7)
In the case of all the four channels connected to the DUT, we obtain + + S1234 = SDUT + |ZDUT |2 Sin1 + |ZDUT |2 Sin2 + + + |ZDUT |2 Sin3 + |ZDUT |2 Sin4 . (8)
The desired PSD of the DUT signal is therefore evaluated by using (4). In Fig. 4, we have compared the expected resistor thermal noise PSD [Fig. 4(d)] with the PSDs obtained: by connecting the DUT to a single-channel amplifier [Fig. 4(a)], by connecting the DUT to a two-channel amplifier, by applying the standard cross-correlation technique [Fig. 4(b)], by using the fourchannel-amplifier configuration, and by applying the proposed extraction method [Fig. 4(c)]. In the case of a single-channel amplifier, the PSD is due to the contribution of the DUT noise and to the contribution of all the measurement amplifier noise sources (5). In the case of a two-channel amplifier, the standard cross-correlation technique allows us to obtain a PSD due to the contribution of the DUT noise and to the correlated contributions of the measurement amplifier. Note
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IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 55, NO. 4, AUGUST 2006
Fig. 4. Input referred power spectra obtained (a) by connecting the 1-kΩ resistor DUT to a single-channel amplifier, (b) by connecting the DUT to a two-channel amplifier and by applying the standard cross-correlation technique, and (c) by using the four-channel-amplifier configuration and by applying the proposed extraction method. The power spectrum of the voltage noise generated by the DUT extracted by using the proposed method shows a good agreement with the expected (d) resistor thermal noise.
Fig. 6. Input referred cross spectra obtained by connecting the DUT of Fig. 5 to (a) the first couple of amplifiers, (b) the second couple of amplifiers, and (c) all four amplifiers. The extracted power spectrum of the voltage noise generated by the DUT is also reported.
its value is chosen large enough in order not to significantly interfere with the measurements in the explored bandwidth. The three measured spectra S12 , S34 , and S1234 are reported in Fig. 6 along with the extracted PSD of the DUT signal. It is important to note that, although at low frequency the effect of the EICN strongly increases due to the increase of the DUT impedance, the extracted SDUT is quite constant, as 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 effect of the EICN is up to 10 dB higher with respect to SDUT , is lower than 10%. IV. C ONCLUSION
Fig. 5. Power spectrum of the voltage noise generated by the DUT shown in the inset and squared modulus of the DUT impedance.
that at lower frequencies, the PSD corresponding to the twochannel amplifier is higher with respect to the case of a singlechannel amplifier due to the double effect of the correlated noise contributions, while at higher frequencies, it is lower due to the suppression of the uncorrelated noise contributions. In the case of the four-channel amplifier, the proposed method allows to extract only the desired SDUT . The average error with respect to the expected DUT thermal noise in the bandwidth between f = 1 Hz and f = 100 Hz, where the effect of the EICN is up to 10 dB higher with respect to SDUT , is lower than 5%. In order to further confirm the validity of our method, we used, as a DUT, the parallel between the series of a resistor RDUT = 1 kΩ and a capacitor CDUT = 0.22 µF with a resistor RSHUNT = 100 kΩ (see the inset of Fig. 5). Note that we put the capacitor in series with RDUT 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. 5), which, in the explored frequency range (f > 100 Hz), is essentially due to the thermal noise of RDUT . In fact, the resistor RSHUNT is needed in order to provide for a bias path to the input of the amplifiers, and
In this paper, we have presented and experimentally validated a new method for voltage noise measurements. With respect to the previous methods, the one we have presented 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 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 either the estimation of the EIVN and of the EICN of the amplifiers or 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 that allow the elimination of the contribution of the EIVN or of the EICN alone. R EFERENCES [1] C. Ciofi, M. De Marinis, and B. Neri, “Ultralow-noise PC-based measurement system for the characterization of the metallizations of integrated circuits,” IEEE Trans. Instrum. Meas., vol. 46, no. 4, p. 789, Aug. 1997. [2] M. Macucci and B. Pellegrini, “Very sensitive measurement method of electron device current noise,” IEEE Trans. Instrum. Meas., vol. 40, no. 1, pp. 7–12, Feb. 1991.
CRUPI et al.: ENHANCED SENSITIVITY CROSS-CORRELATION METHOD FOR VOLTAGE NOISE MEASUREMENTS
[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, May 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, no. 4, pp. 820–822, Aug. 2000. [6] C. Ciofi, F. Crupi, and C. Pace, “A new method for high sensitivity noise measurements,” IEEE Trans. Instrum. Meas., vol. 51, no. 4, pp. 656–659, Aug. 2002. [7] F. N. Trofimenkoff and O. A. Onwuachi, “Noise performances of operational amplifier circuits,” IEEE Trans. Educ., vol. 32, no. 1, pp. 12–17, Feb. 1989. [8] C. D. Motchenbacher and J. A. Connelly, Low-Noise Electronic System Design. Hoboken, NJ: Wiley, 1993, p. 55.
Felice Crupi received the M.Sc. 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. Since 1998, he was a Repeat Visiting Scientist at the Interuniversity Micro-Electronics Center (IMEC), Leuven, Belgium, and, in 2000, he was a Visiting Scientist with the IBM Thomas J. Watson Research Center, Yorktown Heights, NY. Since 2002, he has been with the University of Calabria, Arcavacata di Rende, Italy, where he is currently Associate Professor of electronics. His main research interests include reliability of very large scale integration (VLSI) CMOS devices, electrical characterization techniques for solid-state electronic devices, and the design of ultralownoise electronic instrumentation. He has authored or coauthored about 60 publications in international scientific journals and in international conference proceedings.
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Gino Giusi received the M.Sc. and Ph.D. degrees in electronic engineering from the University of Messina, Messina, Italy, in 2002 and 2005, respectively. In 2005, he was Visiting Scientist with the Interuniversity Micro-Electronics Center (IMEC), Leuven, Belgium. He is currently a Researcher with the University of Messina. His main research interests include the design of ultralow-noise instrumentation and the characterization of devices through noise measurements.
Carmine Ciofi (M’00) was born in Cosenza, Italy, in 1965. He received the M.Sc. degree in electronic engineering from the University of Pisa, Pisa, Italy, in 1989 and the Ph.D. degree from the Scuola Superiore di Studi Universitari e Perfezionamento S. Anna, Pisa, in 1993. He joined the Dipartimento di Ingegneria dell’Informazione, Elettronica Informatica e Telecomunicazioni, University of Pisa, where he remained until 1998. He is currently an Associate Professor of electronics at the University of Messina, Messina, Italy. His main research interests include the characterization and the reliability of electron devices, the design and realization of dedicated electronic instrumentation, and the design of mixed signal and RF application-specified integrated circuits (ASICs).
Calogero Pace was born in Palermo, Italy, in 1965. He received the M.Sc. and doctoral degrees in electronic engineering from the University of Palermo, Palermo, in 1990 and 1994, respectively. In 1996, he joined the University of Messina, Messina, Italy, as an Assistant Professor, and, in 2002, he moved to the University of Calabria, Arcavacata di Rende, Italy, where he is currently an Associate Professor of electronics. He is currently involved in research projects on the study of nanocrystal memory devices, on the design of lownoise electronic instrumentation, and on the design and characterization of electronic gas sensors.
1143
Enhanced Sensitivity Cross-Correlation Method for Voltage Noise Measurements Felice Crupi, Gino Giusi, Carmine Ciofi, Member, IEEE, and Calogero Pace
Abstract—Ultralow 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, a new method for the voltage noise measurement is proposed, which 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 equivalent input voltage noise of the amplifiers and by using a new threestep-measurement procedure that exploits different amplifierconfiguration measurements in order to subtract the contribution of the equivalent input current noise of the amplifiers. Index Terms—Amplifier noise, cross correlation, low-frequency noise, noise measurement, spectral analysis.
I. I NTRODUCTION TO THE P ROBLEM
T
HE PROBLEM of measuring ultralow 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 highly 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 by evaluating the cross correlation of their outputs (see Fig. 1), one can completely suppress, at least in principle, the uncorrelated noise contributions at the output of the two channels and, namely, the effects 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 contributions at the output of the two channels, 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 impedance. In this paper, we propose a novel noise-
Manuscript received June 15, 2005; revised March 16, 2006. F. Crupi and C. Pace are with the Dipartimento di Elettronica Informatica e Sistemistica (DEIS), University of Calabria, 87030 Arcavacata di Rende, Italy (e-mail: [email protected]). G. Giusi and C. Ciofi are with the Dipartimento di Fisica della Materia e Tecnologie Fisiche Avanzate (DFMTFA) and Instituto Nazionale Fisica della Materia (INFM), University of Messina, 98166 Messina, Italy. Digital Object Identifier 10.1109/TIM.2006.876392
measurement method that, besides taking advantage of the correlation method for the elimination of the uncorrelated noise contributions, also allows the elimination of the effects of the correlated noise contributions, thus, resulting, in many cases, in more sensitivity with respect to all the previously proposed methods. II. B ASIC I DEA 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, which is normally verified in the case of voltage noise measurements, the contribution of the EICN of all the amplifiers connected to the 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 two 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 S12 = SDUT + SC1 + SC2
(1)
where SDUT is the power spectral density (PSD) of the equivalent noise source of the DUT, and SCi is the PSD due to the EICN of the amplifier i. Let us now assume that we connect the inputs of the 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 S34 = SDUT + SC3 + SC4 .
(2)
Finally, let us assume that we connect all the amplifiers together to the DUT. In this last case, proceeding as before, we
0018-9456/$20.00 © 2006 IEEE
1144
IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 55, NO. 4, AUGUST 2006
Fig. 1. Block diagram of the correlation spectrum analyzer.
While the above requirements are common to almost all 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. III. E XPERIMENTAL V ALIDATION Fig. 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.
would obtain for the input referred cross spectrum evaluated between any two channels S1234 = SDUT + SC1 + SC2 + SC3 + SC4 .
(3)
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 SDUT = S12 + S34 − S1234 .
(4)
It is important to note that this measurement procedure allows the elimination of 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 the following. 1) The impedance of the DUT has to be much smaller than the input impedance of the amplifiers used for the measurements. 2) The evaluation of the cross spectrum has to be performed using a time record long enough in order to make the residual contribution of the (uncorrelated) EIVN of the amplifiers negligible with respect to the DUT noise to be measured.
In order to verify the validity of the proposed method, we have used the four-amplifier configuration shown in Fig. 3. If we take into consideration the case of a single-channel amplifier being connected to the DUT, it can be easily proven that the input referred voltage-noise PSD at low frequencies (f 1/2πR2 C2 ) is given by + 2 − Stot = SDUT + 4KT RP + Sen + RP Sin + |ZDUT |2 Sin (5) − where RP is the parallel between R1 and R2 , and Sen , Sin , + and Sin are the operational amplifier equivalent-input-voltage and current-noise sources [7], [8]. Note that the second, the third, and the fourth terms contribute to the actual EIVN of the voltage amplifier and, in the two-amplifier configuration, give rise to uncorrelated contributions of the two outputs. The fifth term coincides with the voltage-amplifier EICN and is responsible, in the two-amplifier configuration, for the correlated output terms. As discussed in the previous section, the uncorrelated contributions are suppressed by the cross-correlation method, while the correlated ones 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 used as a DUT a resistor amplifier, R9 = 1 kΩ, and we have chosen an OP27 low-noise √ which is characterized by an EIVN of 3 nV/ Hz at 100 Hz and √ an EICN of 0.6 pA/ Hz at 100 Hz. We followed the three-step
CRUPI et al.: ENHANCED SENSITIVITY CROSS-CORRELATION METHOD FOR VOLTAGE NOISE MEASUREMENTS
Fig. 3.
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Circuit implementation of the Fig. 2 schematics used for the experimental validation of the method.
procedure described in the previous section. By connecting the channels 1 and 2 to the DUT, we obtain + + S12 = SDUT + |ZDUT |2 Sin1 + |ZDUT |2 Sin2
(6)
+ where Sinj is the PSD of the EICN of the jth channel. In the case of channels 3 and 4 connected to the DUT, we obtain + + S34 = SDUT + |ZDUT |2 Sin3 + |ZDUT |2 Sin4 .
(7)
In the case of all the four channels connected to the DUT, we obtain + + S1234 = SDUT + |ZDUT |2 Sin1 + |ZDUT |2 Sin2 + + + |ZDUT |2 Sin3 + |ZDUT |2 Sin4 . (8)
The desired PSD of the DUT signal is therefore evaluated by using (4). In Fig. 4, we have compared the expected resistor thermal noise PSD [Fig. 4(d)] with the PSDs obtained: by connecting the DUT to a single-channel amplifier [Fig. 4(a)], by connecting the DUT to a two-channel amplifier, by applying the standard cross-correlation technique [Fig. 4(b)], by using the fourchannel-amplifier configuration, and by applying the proposed extraction method [Fig. 4(c)]. In the case of a single-channel amplifier, the PSD is due to the contribution of the DUT noise and to the contribution of all the measurement amplifier noise sources (5). In the case of a two-channel amplifier, the standard cross-correlation technique allows us to obtain a PSD due to the contribution of the DUT noise and to the correlated contributions of the measurement amplifier. Note
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IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 55, NO. 4, AUGUST 2006
Fig. 4. Input referred power spectra obtained (a) by connecting the 1-kΩ resistor DUT to a single-channel amplifier, (b) by connecting the DUT to a two-channel amplifier and by applying the standard cross-correlation technique, and (c) by using the four-channel-amplifier configuration and by applying the proposed extraction method. The power spectrum of the voltage noise generated by the DUT extracted by using the proposed method shows a good agreement with the expected (d) resistor thermal noise.
Fig. 6. Input referred cross spectra obtained by connecting the DUT of Fig. 5 to (a) the first couple of amplifiers, (b) the second couple of amplifiers, and (c) all four amplifiers. The extracted power spectrum of the voltage noise generated by the DUT is also reported.
its value is chosen large enough in order not to significantly interfere with the measurements in the explored bandwidth. The three measured spectra S12 , S34 , and S1234 are reported in Fig. 6 along with the extracted PSD of the DUT signal. It is important to note that, although at low frequency the effect of the EICN strongly increases due to the increase of the DUT impedance, the extracted SDUT is quite constant, as 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 effect of the EICN is up to 10 dB higher with respect to SDUT , is lower than 10%. IV. C ONCLUSION
Fig. 5. Power spectrum of the voltage noise generated by the DUT shown in the inset and squared modulus of the DUT impedance.
that at lower frequencies, the PSD corresponding to the twochannel amplifier is higher with respect to the case of a singlechannel amplifier due to the double effect of the correlated noise contributions, while at higher frequencies, it is lower due to the suppression of the uncorrelated noise contributions. In the case of the four-channel amplifier, the proposed method allows to extract only the desired SDUT . The average error with respect to the expected DUT thermal noise in the bandwidth between f = 1 Hz and f = 100 Hz, where the effect of the EICN is up to 10 dB higher with respect to SDUT , is lower than 5%. In order to further confirm the validity of our method, we used, as a DUT, the parallel between the series of a resistor RDUT = 1 kΩ and a capacitor CDUT = 0.22 µF with a resistor RSHUNT = 100 kΩ (see the inset of Fig. 5). Note that we put the capacitor in series with RDUT 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. 5), which, in the explored frequency range (f > 100 Hz), is essentially due to the thermal noise of RDUT . In fact, the resistor RSHUNT is needed in order to provide for a bias path to the input of the amplifiers, and
In this paper, we have presented and experimentally validated a new method for voltage noise measurements. With respect to the previous methods, the one we have presented 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 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 either the estimation of the EIVN and of the EICN of the amplifiers or 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 that allow the elimination of the contribution of the EIVN or of the EICN alone. R EFERENCES [1] C. Ciofi, M. De Marinis, and B. Neri, “Ultralow-noise PC-based measurement system for the characterization of the metallizations of integrated circuits,” IEEE Trans. Instrum. Meas., vol. 46, no. 4, p. 789, Aug. 1997. [2] M. Macucci and B. Pellegrini, “Very sensitive measurement method of electron device current noise,” IEEE Trans. Instrum. Meas., vol. 40, no. 1, pp. 7–12, Feb. 1991.
CRUPI et al.: ENHANCED SENSITIVITY CROSS-CORRELATION METHOD FOR VOLTAGE NOISE MEASUREMENTS
[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, May 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, no. 4, pp. 820–822, Aug. 2000. [6] C. Ciofi, F. Crupi, and C. Pace, “A new method for high sensitivity noise measurements,” IEEE Trans. Instrum. Meas., vol. 51, no. 4, pp. 656–659, Aug. 2002. [7] F. N. Trofimenkoff and O. A. Onwuachi, “Noise performances of operational amplifier circuits,” IEEE Trans. Educ., vol. 32, no. 1, pp. 12–17, Feb. 1989. [8] C. D. Motchenbacher and J. A. Connelly, Low-Noise Electronic System Design. Hoboken, NJ: Wiley, 1993, p. 55.
Felice Crupi received the M.Sc. 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. Since 1998, he was a Repeat Visiting Scientist at the Interuniversity Micro-Electronics Center (IMEC), Leuven, Belgium, and, in 2000, he was a Visiting Scientist with the IBM Thomas J. Watson Research Center, Yorktown Heights, NY. Since 2002, he has been with the University of Calabria, Arcavacata di Rende, Italy, where he is currently Associate Professor of electronics. His main research interests include reliability of very large scale integration (VLSI) CMOS devices, electrical characterization techniques for solid-state electronic devices, and the design of ultralownoise electronic instrumentation. He has authored or coauthored about 60 publications in international scientific journals and in international conference proceedings.
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Gino Giusi received the M.Sc. and Ph.D. degrees in electronic engineering from the University of Messina, Messina, Italy, in 2002 and 2005, respectively. In 2005, he was Visiting Scientist with the Interuniversity Micro-Electronics Center (IMEC), Leuven, Belgium. He is currently a Researcher with the University of Messina. His main research interests include the design of ultralow-noise instrumentation and the characterization of devices through noise measurements.
Carmine Ciofi (M’00) was born in Cosenza, Italy, in 1965. He received the M.Sc. degree in electronic engineering from the University of Pisa, Pisa, Italy, in 1989 and the Ph.D. degree from the Scuola Superiore di Studi Universitari e Perfezionamento S. Anna, Pisa, in 1993. He joined the Dipartimento di Ingegneria dell’Informazione, Elettronica Informatica e Telecomunicazioni, University of Pisa, where he remained until 1998. He is currently an Associate Professor of electronics at the University of Messina, Messina, Italy. His main research interests include the characterization and the reliability of electron devices, the design and realization of dedicated electronic instrumentation, and the design of mixed signal and RF application-specified integrated circuits (ASICs).
Calogero Pace was born in Palermo, Italy, in 1965. He received the M.Sc. and doctoral degrees in electronic engineering from the University of Palermo, Palermo, in 1990 and 1994, respectively. In 1996, he joined the University of Messina, Messina, Italy, as an Assistant Professor, and, in 2002, he moved to the University of Calabria, Arcavacata di Rende, Italy, where he is currently an Associate Professor of electronics. He is currently involved in research projects on the study of nanocrystal memory devices, on the design of lownoise electronic instrumentation, and on the design and characterization of electronic gas sensors.
