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Low-noise SQUIDs with large transfer: two-stage SQUIDs based on DROSs
Physica C 372–376 (2002) 225–228 www.elsevier.com/locate/physc
Low-noise SQUIDs with large transfer: two-stage SQUIDs based on DROSs M. Podt *, J. Flokstra, H. Rogalla Low Temperature Division, Department of Applied Physics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
Abstract We have realized a two-stage integrated superconducting quantum interference device (SQUID) system with a closed loop bandwidth of 2.5 MHz, operated in a direct voltage readout mode. The corresponding flux slew rate was 1:3 105 p U0 /s and the measured white flux noise was 1.3 lU0 = Hz at 4.2 K. The system is based on a conventional dc SQUID with a double relaxation oscillation SQUID (DROS) as the second stage. Because of the large flux-to-voltage transfer, the sensitivity of the system is completely determined by the sensor SQUID and not by the DROS or the room-temperature preamplifier. Decreasing the Josephson junction area enables a further improvement of the sensitivity of the two-stage SQUID systems. Ó 2002 Elsevier Science B.V. All rights reserved. Keywords: Superconducting device; SQUID; Two-stage system
1. Introduction A superconducting quantum interference device (SQUID) is known to be the most sensitive sensor for magnetic flux, with a sensitivity that can approach the quantum limit. However, the small flux-to-voltage transfer of conventional dc SQUIDs results in an output voltage noise that is about one order of magnitude smaller than the room-temperature dc preamplifier input noise. To solve this problem, an impedance matching network with ac flux modulation and lock-in detection is often used. Unfortunately, this technique generally limits the measurement bandwidth.
*
Corresponding author. Tel.: +31-53-4894627; fax: +31-534891099. E-mail address: [email protected] (M. Podt).
A more elegant way to overcome the matching problem is the development of SQUIDs with a larger flux-to-voltage transfer, to allow a direct voltage readout mode without flux modulation. Much research has been done on these secondgeneration dc SQUIDs, such as SQUIDs with additional positive feedback [1], double relaxation oscillation SQUIDs (DROSs) [2], series SQUID arrays [3,4] and two-stage SQUID systems [5,6]. In a two-stage SQUID system, a second stage SQUID is used as a cryogenic low-noise preamplifier for the sensor SQUID. The sensor SQUID is biased at a constant voltage by means of a small bias resistor Rbias Rdyn , where Rdyn is the dynamic resistance of the sensor SQUID. The current through the sensor SQUID is fed through the input coil Lin;2 of the second stage, generating a flux U2nd . An important parameter in the design of a two-stage SQUID system is the flux gain
0921-4534/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 3 4 ( 0 2 ) 0 0 6 7 6 - 7
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M. Podt et al. / Physica C 372–376 (2002) 225–228
GU ¼ oU2nd =oUsig , where Usig is the flux applied to the sensor SQUID. The gain should be large enough to prevent sensitivity limitation by the second stage or the readout electronics [6]. For the second stage, there are two options. First, a series SQUID array can be used [5]. However, in practical systems their application is troublesome, which is mainly caused by the fact that all SQUIDs should be modulated coherently. Among other things, this means that the mutual inductance between the input coil and each SQUID has to be approximately the same and that there is no random flux offset between the SQUIDs, e.g. caused by frozen flux. Second, a single SQUID can be used, which is the simplest option. In this case, the linear flux range is somewhat smaller but the design and the practical use is less complicated. Since the second stage is used as a preamplifier, it is beneficial to use a SQUID with a large flux-to-voltage transfer. We have developed a two-stage SQUID system with a DROS as the second stage [6]. In this paper we will concentrate on the improvement of the closed loop bandwidth. 2. Design and fabrication We have designed and fabricated two-stage SQUID systems based on a sensor SQUID with an inductance of Lsq;1 ¼ 200 pH. The screening parameter bL ¼ 2I0 Lsq;1 =U0 equals about 1 and the McCumber parameter bc ¼ 2pI0 R2s Cj =U0 is 0.4. Here, I0 is the critical current of one junction, Rs is the shunt resistance and Cj is the junction capacitance. For the second stage, two different DROSs were used. DROS A had a SQUID inductance of Lsq;2 ¼ 550 pH and DROS B had an inductance of Lsq;2 ¼ 490 pH. The maximum flux gain in case of DROS A was GU ¼ 36 and for DROS B GU ¼ 26. The bandwidth that can be achieved in flux locked loop (FLL) can never exceed the cut-off frequency of the two-stage SQUID system, given by Rdyn þ Rbias fc ¼ : ð1Þ 2pLin;2 Thus to achieve a high bandwidth, the inductance of the input coil of the second stage should
not be made unnecessarily large. However, since Lin also affects the flux gain, one has to compromise between large gain and high cut-off frequency. The theoretical cut-off frequency for the system with DROS A was fc ¼ 5 MHz and with DROS B fc ¼ 9 MHz. The maximum bandwidth in FLL is given by fmax ¼
GMfb oV ; 2psint Rfb oUsig
ð2Þ
where G is the gain of the preamplifier, Mfb is the mutual inductance between the feedback coil and the sensor SQUID, sint is the time constant of the integrator and Rfb is the feedback resistance. To achieve higher bandwidths, the flux-to-voltage transfer can be increased by increasing the flux gain, but this limits fc as was discussed above. However, Mfb can be increased without changing the design of the two-stage SQUID itself. All other parameters are dependent on the FLL electronics. Previously, we have achieved a 3 dB bandwidth of 1 MHz using two-stage SQUIDs based on DROS A. This is well below the cut-off frequency of the first stage. The parameters of the system were: G ¼ 10, Mfb ¼ 61 pH, sint ¼ 12 ns, Rfb ¼ 10 kX and oV =oUsig ¼ 3:6 mV/U0 . In order to improve the FLL bandwidth, two-stage SQUIDs with a feedback coil of Mfb ¼ 340 pH were fabricated.
3. Experimental The two-stage SQUID systems were characterized using homemade FLL electronics based on direct voltage readout [7]. The maximum flux-tovoltage transfer was measured to be 3.6 p mV/U0 and the white flux noise was 1.3 lU0 = Hz. The actual flux gain depends on the bias voltage of the sensor SQUID and on the applied flux [6]. The flux gain is maximum for Usig ¼ ð1=4 þ n=2ÞU0 . At that point, the largest amount of wide band flux noise is coupled from the sensor SQUID to the second stage, which caused the voltage modulation depth of the DROS to decrease. For the systems with DROS A, this effect was small [6], but for the systems with DROS B, this effect was quite large. Fig. 1 shows the V–U characteristics of a two-stage
M. Podt et al. / Physica C 372–376 (2002) 225–228
227
mental bandwidth: oUsig =ot ¼ 2p dU fexp ¼ 1:1 105 U0 /s.
4. Conclusion and discussion
Fig. 1. Experimental flux-to-voltage characteristics of a twostage SQUID system with DROS B without (a) and with (b) additional inductance.
SQUID system based on DROS B with and without an additional inductance of 3Lin;2 added to the first stage. The additional inductance decreased the cut-off frequency from 9 to 2 MHz. As a result, the distortion of the DROS characteristics is reduced. Fig. 2 shows the frequency response of a twostage SQUID system with DROS A measured in FLL. In this case, the feedback resistance was decreased from 10 to 1 kX. The 3 dB bandwidth is fexp ¼ 2:5 MHz. Because of the limited bandwidth of the electronics, higher bandwidths could not be achieved. The flux slew rate was measured to be 1:3 105 U0 /s, see inset. This corresponds to the value that can be calculated from the measured linear flux range dU ¼ 6:7 mU0 and the experi-
Fig. 2. Closed loop gain, Ufb =Usig , as a function of the frequency. The inset shows the feedback flux measured in time, from which the flux slew rate was calculated to be 1:3 105 U0 /s.
We have realized two-stage SQUID systems with a closed loop bandwidth of 2.5 MHz. The slew rate was measured topbe 1:3 105 U0 /s and the flux noise was 1.3 lU0 = Hz. The sensitivity of the two-stage SQUID systems is completely determined by the sensor SQUID and not by the second stage or the readout electronics. Decreasing the junction area is one of the possibilities to further improve the sensitivity. In order to do so, we are currently developing SIS ramp-type junctions based on standard Nb/Al, AlOx /Al/Nb technology [8]. In many applications, like the readout of cryogenic particle detectors, SQUID systems with both low noise and high slew rate are required. This means that the ratio between the slew rate and the noise, the normalized slew rate, is important. Comparing our system to series SQUID arrays, the slew rate that can be achieved for arrays can easily be larger, since the linear flux range is much larger. But the total flux noise of a SQUID array will generally be larger because of the large number of SQUIDs [4]. Consequently, the normalized slew rates are comparable. However, the required coherent modulation in a series SQUID array results in practical complications. Two-stage SQUID systems based on a series array of SQUIDs suffer from the same problems. However, in a well-designed system the linear flux range does not necessarily have to decrease compared to a single SQUID. In practice, this means that one flux quantum in the sensor SQUID should not produce more than one flux quantum in each SQUID of the array. The gain should also not be much smaller, since then the full voltage modulation depth of the array is not used, i.e. for a typical array of 100 SQUIDs, the flux gain should be GU 100. This is much larger than the flux gain required for our system. Since the input noise of series SQUID arrays increases with the number of SQUIDs, in many cases SQUIDs with rather small inductances are used. As a result, the inductance of
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M. Podt et al. / Physica C 372–376 (2002) 225–228
the input coil of the second stage has to be quite large and this means a small cut-off frequency of the first stage [5]. This undoes the advantage of the possible large linear flux range. We can conclude that the normalized slew rates of series SQUID arrays, two-stage SQUIDs based on series SQUID arrays and two-stage SQUIDs based on DROSs are comparable. However, the application in practical systems is for two-stage SQUID systems based on DROSs less complicated.
References [1] [2] [3] [4] [5] [6] [7] [8]
D. Drung, Appl. Phys. Lett. 67 (1995) 1474. D.J. Adelerhof et al., Appl. Phys. Lett. 65 (1994) 2606. R.P. Welty et al., IEEE Trans. Magn. 27 (1991) 2924. K.G. Stawiasz et al., IEEE Trans. Appl. Supercond. 3 (1993) 1808. R.P. Welty et al., IEEE Trans. Appl. Supercond. 3 (1993) 2605. M. Podt et al., Appl. Phys. Lett. 75 (1999) 2316. A.W. Hamster et al., IEEE Trans. Appl. Supercond. 9 (1999) 2915. M. Podt et al., Supercond. Sci. Technol. 14 (2001) 1027.
Low-noise SQUIDs with large transfer: two-stage SQUIDs based on DROSs M. Podt *, J. Flokstra, H. Rogalla Low Temperature Division, Department of Applied Physics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
Abstract We have realized a two-stage integrated superconducting quantum interference device (SQUID) system with a closed loop bandwidth of 2.5 MHz, operated in a direct voltage readout mode. The corresponding flux slew rate was 1:3 105 p U0 /s and the measured white flux noise was 1.3 lU0 = Hz at 4.2 K. The system is based on a conventional dc SQUID with a double relaxation oscillation SQUID (DROS) as the second stage. Because of the large flux-to-voltage transfer, the sensitivity of the system is completely determined by the sensor SQUID and not by the DROS or the room-temperature preamplifier. Decreasing the Josephson junction area enables a further improvement of the sensitivity of the two-stage SQUID systems. Ó 2002 Elsevier Science B.V. All rights reserved. Keywords: Superconducting device; SQUID; Two-stage system
1. Introduction A superconducting quantum interference device (SQUID) is known to be the most sensitive sensor for magnetic flux, with a sensitivity that can approach the quantum limit. However, the small flux-to-voltage transfer of conventional dc SQUIDs results in an output voltage noise that is about one order of magnitude smaller than the room-temperature dc preamplifier input noise. To solve this problem, an impedance matching network with ac flux modulation and lock-in detection is often used. Unfortunately, this technique generally limits the measurement bandwidth.
*
Corresponding author. Tel.: +31-53-4894627; fax: +31-534891099. E-mail address: [email protected] (M. Podt).
A more elegant way to overcome the matching problem is the development of SQUIDs with a larger flux-to-voltage transfer, to allow a direct voltage readout mode without flux modulation. Much research has been done on these secondgeneration dc SQUIDs, such as SQUIDs with additional positive feedback [1], double relaxation oscillation SQUIDs (DROSs) [2], series SQUID arrays [3,4] and two-stage SQUID systems [5,6]. In a two-stage SQUID system, a second stage SQUID is used as a cryogenic low-noise preamplifier for the sensor SQUID. The sensor SQUID is biased at a constant voltage by means of a small bias resistor Rbias Rdyn , where Rdyn is the dynamic resistance of the sensor SQUID. The current through the sensor SQUID is fed through the input coil Lin;2 of the second stage, generating a flux U2nd . An important parameter in the design of a two-stage SQUID system is the flux gain
0921-4534/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 3 4 ( 0 2 ) 0 0 6 7 6 - 7
226
M. Podt et al. / Physica C 372–376 (2002) 225–228
GU ¼ oU2nd =oUsig , where Usig is the flux applied to the sensor SQUID. The gain should be large enough to prevent sensitivity limitation by the second stage or the readout electronics [6]. For the second stage, there are two options. First, a series SQUID array can be used [5]. However, in practical systems their application is troublesome, which is mainly caused by the fact that all SQUIDs should be modulated coherently. Among other things, this means that the mutual inductance between the input coil and each SQUID has to be approximately the same and that there is no random flux offset between the SQUIDs, e.g. caused by frozen flux. Second, a single SQUID can be used, which is the simplest option. In this case, the linear flux range is somewhat smaller but the design and the practical use is less complicated. Since the second stage is used as a preamplifier, it is beneficial to use a SQUID with a large flux-to-voltage transfer. We have developed a two-stage SQUID system with a DROS as the second stage [6]. In this paper we will concentrate on the improvement of the closed loop bandwidth. 2. Design and fabrication We have designed and fabricated two-stage SQUID systems based on a sensor SQUID with an inductance of Lsq;1 ¼ 200 pH. The screening parameter bL ¼ 2I0 Lsq;1 =U0 equals about 1 and the McCumber parameter bc ¼ 2pI0 R2s Cj =U0 is 0.4. Here, I0 is the critical current of one junction, Rs is the shunt resistance and Cj is the junction capacitance. For the second stage, two different DROSs were used. DROS A had a SQUID inductance of Lsq;2 ¼ 550 pH and DROS B had an inductance of Lsq;2 ¼ 490 pH. The maximum flux gain in case of DROS A was GU ¼ 36 and for DROS B GU ¼ 26. The bandwidth that can be achieved in flux locked loop (FLL) can never exceed the cut-off frequency of the two-stage SQUID system, given by Rdyn þ Rbias fc ¼ : ð1Þ 2pLin;2 Thus to achieve a high bandwidth, the inductance of the input coil of the second stage should
not be made unnecessarily large. However, since Lin also affects the flux gain, one has to compromise between large gain and high cut-off frequency. The theoretical cut-off frequency for the system with DROS A was fc ¼ 5 MHz and with DROS B fc ¼ 9 MHz. The maximum bandwidth in FLL is given by fmax ¼
GMfb oV ; 2psint Rfb oUsig
ð2Þ
where G is the gain of the preamplifier, Mfb is the mutual inductance between the feedback coil and the sensor SQUID, sint is the time constant of the integrator and Rfb is the feedback resistance. To achieve higher bandwidths, the flux-to-voltage transfer can be increased by increasing the flux gain, but this limits fc as was discussed above. However, Mfb can be increased without changing the design of the two-stage SQUID itself. All other parameters are dependent on the FLL electronics. Previously, we have achieved a 3 dB bandwidth of 1 MHz using two-stage SQUIDs based on DROS A. This is well below the cut-off frequency of the first stage. The parameters of the system were: G ¼ 10, Mfb ¼ 61 pH, sint ¼ 12 ns, Rfb ¼ 10 kX and oV =oUsig ¼ 3:6 mV/U0 . In order to improve the FLL bandwidth, two-stage SQUIDs with a feedback coil of Mfb ¼ 340 pH were fabricated.
3. Experimental The two-stage SQUID systems were characterized using homemade FLL electronics based on direct voltage readout [7]. The maximum flux-tovoltage transfer was measured to be 3.6 p mV/U0 and the white flux noise was 1.3 lU0 = Hz. The actual flux gain depends on the bias voltage of the sensor SQUID and on the applied flux [6]. The flux gain is maximum for Usig ¼ ð1=4 þ n=2ÞU0 . At that point, the largest amount of wide band flux noise is coupled from the sensor SQUID to the second stage, which caused the voltage modulation depth of the DROS to decrease. For the systems with DROS A, this effect was small [6], but for the systems with DROS B, this effect was quite large. Fig. 1 shows the V–U characteristics of a two-stage
M. Podt et al. / Physica C 372–376 (2002) 225–228
227
mental bandwidth: oUsig =ot ¼ 2p dU fexp ¼ 1:1 105 U0 /s.
4. Conclusion and discussion
Fig. 1. Experimental flux-to-voltage characteristics of a twostage SQUID system with DROS B without (a) and with (b) additional inductance.
SQUID system based on DROS B with and without an additional inductance of 3Lin;2 added to the first stage. The additional inductance decreased the cut-off frequency from 9 to 2 MHz. As a result, the distortion of the DROS characteristics is reduced. Fig. 2 shows the frequency response of a twostage SQUID system with DROS A measured in FLL. In this case, the feedback resistance was decreased from 10 to 1 kX. The 3 dB bandwidth is fexp ¼ 2:5 MHz. Because of the limited bandwidth of the electronics, higher bandwidths could not be achieved. The flux slew rate was measured to be 1:3 105 U0 /s, see inset. This corresponds to the value that can be calculated from the measured linear flux range dU ¼ 6:7 mU0 and the experi-
Fig. 2. Closed loop gain, Ufb =Usig , as a function of the frequency. The inset shows the feedback flux measured in time, from which the flux slew rate was calculated to be 1:3 105 U0 /s.
We have realized two-stage SQUID systems with a closed loop bandwidth of 2.5 MHz. The slew rate was measured topbe 1:3 105 U0 /s and the flux noise was 1.3 lU0 = Hz. The sensitivity of the two-stage SQUID systems is completely determined by the sensor SQUID and not by the second stage or the readout electronics. Decreasing the junction area is one of the possibilities to further improve the sensitivity. In order to do so, we are currently developing SIS ramp-type junctions based on standard Nb/Al, AlOx /Al/Nb technology [8]. In many applications, like the readout of cryogenic particle detectors, SQUID systems with both low noise and high slew rate are required. This means that the ratio between the slew rate and the noise, the normalized slew rate, is important. Comparing our system to series SQUID arrays, the slew rate that can be achieved for arrays can easily be larger, since the linear flux range is much larger. But the total flux noise of a SQUID array will generally be larger because of the large number of SQUIDs [4]. Consequently, the normalized slew rates are comparable. However, the required coherent modulation in a series SQUID array results in practical complications. Two-stage SQUID systems based on a series array of SQUIDs suffer from the same problems. However, in a well-designed system the linear flux range does not necessarily have to decrease compared to a single SQUID. In practice, this means that one flux quantum in the sensor SQUID should not produce more than one flux quantum in each SQUID of the array. The gain should also not be much smaller, since then the full voltage modulation depth of the array is not used, i.e. for a typical array of 100 SQUIDs, the flux gain should be GU 100. This is much larger than the flux gain required for our system. Since the input noise of series SQUID arrays increases with the number of SQUIDs, in many cases SQUIDs with rather small inductances are used. As a result, the inductance of
228
M. Podt et al. / Physica C 372–376 (2002) 225–228
the input coil of the second stage has to be quite large and this means a small cut-off frequency of the first stage [5]. This undoes the advantage of the possible large linear flux range. We can conclude that the normalized slew rates of series SQUID arrays, two-stage SQUIDs based on series SQUID arrays and two-stage SQUIDs based on DROSs are comparable. However, the application in practical systems is for two-stage SQUID systems based on DROSs less complicated.
References [1] [2] [3] [4] [5] [6] [7] [8]
D. Drung, Appl. Phys. Lett. 67 (1995) 1474. D.J. Adelerhof et al., Appl. Phys. Lett. 65 (1994) 2606. R.P. Welty et al., IEEE Trans. Magn. 27 (1991) 2924. K.G. Stawiasz et al., IEEE Trans. Appl. Supercond. 3 (1993) 1808. R.P. Welty et al., IEEE Trans. Appl. Supercond. 3 (1993) 2605. M. Podt et al., Appl. Phys. Lett. 75 (1999) 2316. A.W. Hamster et al., IEEE Trans. Appl. Supercond. 9 (1999) 2915. M. Podt et al., Supercond. Sci. Technol. 14 (2001) 1027.