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Effects of magnetic fields induced by bias currents on operation of RSFQ circuits
Physica C 412–414 (2004) 1576–1579 www.elsevier.com/locate/physc
Effects of magnetic fields induced by bias currents on operation of RSFQ circuits Motohiro Suzuki *, Masaaki Maezawa, Fuminori Hirayama National Institute of Advanced Industrial Science and Technology, Central 2, 1-1-1 Umezono, Tsukuba, Ibaraki 305-8568, Japan Received 29 October 2003; accepted 15 December 2003 Available online 7 June 2004
Abstract We investigated the effects of magnetic fields induced by bias currents on rapid single flux quantum (RSFQ) circuits. We measured the mutual inductance between a signal line and a bias line in the circuit. The mutual inductance values obtained were in the range of 5–50 fH. We simulated operation of a 2-stage shift register under the magnetic fields induced by an additional control current. The calculated operating regions were significantly reduced by the magnetic fields induced by the control currents on the order of 10 mA. The experimental results obtained for the shift register agreed with the simulation. These results suggest that it is important to take the effects of current-induced magnetic fields into account in the design of large-scale RSFQ circuits. Ó 2004 Elsevier B.V. All rights reserved. PACS: 85.25.Am; 85.25.Cp Keywords: Josephson junction; Rapid single flux quantum; Superconductor integrated circuit; Operating region
1. Introduction Recently, it has been reported that the operating regions of rapid single flux quantum (RSFQ) circuits become small with increasing circuit bias current [1–3]. An explanation is that the magnetic field induced by the bias current affects the operation of the circuit. Although the circuits include ground planes, this degradation due to the magnetic fields is significant. This problem will become more serious with an increase in the circuit scale.
*
Corresponding author. Tel.: +81-29-861-5905; fax: +81-29861-5530. E-mail address: [email protected] (M. Suzuki).
For example, the final version of our digital-toanalog converter will need a bias current of a few amperes [4]. We will encounter this problem in the near future. We theoretically and experimentally investigated the effects of magnetic fields induced by bias currents. We measured the mutual inductance between a signal line and a bias line in the circuit, and obtained values of mutual inductance ranging from 5 to 50 fH. We investigated the effects of magnetic coupling on the operation of RSFQ circuits by simulation and experiments. Simulation of a 2-stage shift register showed that magnetic fields induced by bias currents on the order of 10 mA significantly reduced the operating region of the circuit. We fabricated a 2-stage shift register and
0921-4534/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2003.12.094
M. Suzuki et al. / Physica C 412–414 (2004) 1576–1579
measured its operating region. The experimental results agreed with the simulation.
2. Magnetic coupling between strip lines We quantitatively evaluated the magnetic coupling between the strip lines in RSFQ circuits. We measured the mutual inductance between a signal line and a bias line, which are orthogonal to each other in the circuit, because the signal line is close to the bias line at crossover. We measured the mutual inductance using SQUIDs whose layouts were extracted from our standard RSFQ cells. The loop inductance of the SQUID was formed by the circuit signal line, and the control line of the SQUID was formed by the circuit bias line (Fig. 1). We fabricated the SQUIDs using our standard process [5]. From the U–V characteristics of the SQUIDs, we obtained the values of mutual inductance. The SQUID extracted from the JTL cell has a symmetrical structure (Fig. 1(b)). A control current Icnt is applied through a control line that is orthogonal to the SQUID loop at the center. We therefore expected a small mutual inductance between the SQUID and the control line. We obtained mutual inductance M ¼ 5 fH in the symmetrical SQUID. SQUIDs based on a 2-stage shift register were also investigated. The layout of the SQUIDs was extracted from I/O ports connecting the shift register cells (Fig. 1(e)). The SQUIDs were asymmetrical in layout as well as parameters. We expected a larger mutual inductance in the asymmetrical SQUIDs than in the symmetrical type. Mutual inductances M1 ¼ 46 fH and M2 ¼ 31 fH were obtained in the asymmetrical SQUIDs. The measured values of mutual inductance may include the mutual inductance between the SQUID loop and external parts such as bonding lines and wiring on a chip carrier. We measured the mutual inductance contributed by the external parts. We used the symmetrical SQUID in Fig. 1(b) and a bonding pad that was about 1 mm distant from the SQUID. We connected the pad with several channels on the chip carrier. To apply the control current we used various pairs of
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channels for current injection and drain. The measured values of the mutual inductance between the external control line and the SQUID loop were lower than 1 fH, and were much smaller than those between the lines on the chip.
3. Effects of magnetic fields on circuit operation We investigated the effects of the magnetic fields induced by bias currents on the operation of RSFQ circuits. We used a modified version of a 2stage shift register consisting of our library cells. A bias line crossing two signal lines at the center was separated from the other bias lines. The separated bias line was used as a control line, like the SQUIDs in Fig. 1(e). An equivalent circuit of the shift register is shown in Fig. 2. The control line magnetically couples to the signal lines with the mutual inductances M1 and M2 . We simulated the operation of the 2-stage shift register using the measured values of the mutual inductances M1 and M2 . The calculated operating regions of the bias current are shown as a function of the control current Icnt in Fig. 3 (solid lines). The operating regions were reduced with increasing Icnt and disappeared at Icnt ¼ 20 mA. We tested the 2-stage shift register fabricated on the same chip as the SQUIDs that were used to measure the mutual inductances M1 and M2 . The operating regions are shown as dots with bars in Fig. 3. The experimental results agreed with the simulation, confirming the validity of the model.
4. Discussion Two types of magnetic coupling possibly contribute to the mutual inductance obtained. One is coupling at the crossover. Since strip lines have finite width, currents through the crossing lines have components parallel to each other (Fig. 4(a)). The other is coupling between parallel lines [1]. The signal line has portions parallel to the control line near the crossover, so finite coupling exists between the lines (Fig. 4(b)). Further investigation will be necessary to determine which type of coupling is dominant.
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M. Suzuki et al. / Physica C 412–414 (2004) 1576–1579
Fig. 1. RSFQ library cells and investigated SQUIDs: (a) layout of a JTL cell; (b) layout and (c) schematic of the SQUID extracted from the JTL cell; (d) layout of a 2-stage shift register; (e) layout and (f) schematic of SQUIDs extracted from the 2-stage shift register.
In Fig. 3, the experimental results slightly deviate from the simulation. This is possibly
caused by effects of mutual coupling that we did not consider in the equivalent circuit in Fig. 2. We
M. Suzuki et al. / Physica C 412–414 (2004) 1576–1579
Fig. 2. Equivalent circuit of the 2-stage shift register.
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currents and the sheet resistance were different from the designed values. It is important to reduce the effects of the magnetic fields induced by bias currents. Bias currents should flow uniformly in the circuits. Also, magnetic coupling between the signal line and the bias line should be reduced. A method of bias line shielding has been proposed to reduce magnetic coupling [1], but an extra superconductive layer is necessary to shield the bias line that crosses the signal line. It is important for layout design to decrease the magnetic coupling in the circuits.
5. Summary
Fig. 3. Operating regions of the bias current of the 2-stage shift register as a function of the control current Icnt . The solid lines show the simulated results and the dots with bars show the experimental results.
The operating regions of RSFQ circuits become small with increasing circuit bias current. We investigated the effects of the magnetic fields induced by bias currents on the operation of RSFQ circuits. We measured the mutual inductance between a signal line and a bias line on a chip, and obtained values of mutual inductance ranging from 5 to 50 fH. We investigated the effects of magnetic coupling on the operation of a 2-stage shift register by simulation and experiments. The magnetic fields induced by bias currents on the order of 10 mA significantly reduced the operating region of the circuit. These results suggest that we need to take into account the magnetic fields induced by bias currents in the design of large-scale RSFQ circuits.
References
Fig. 4. Magnetic coupling between the strip lines in the circuit: (a) coupling at the crossover and (b) coupling between parallel lines.
considered the rather simple case of only two mutual inductances, M1 and M2 . In addition, actual circuit parameters such as the junction critical
[1] H. Terai, Y. Kameda, S. Yorozu, A. Fujimaki, Z. Wang, IEEE Trans. Appl. Supercond. 13 (2003) 502. [2] S. Nagasawa, H. Hasegawa, S. Hirano, K. Miyahara, Y. Enomoto, private communication. [3] Y. Kameda, S. Yorozu, private communication. [4] H. Sasaki, V. Bubanja, S. Kiryu, F. Hirayama, M. Maezawa, A. Shoji, IEEE Trans. Instrum. Meas. 50 (2001) 318. [5] M. Maezawa, F. Hirayama, M. Suzuki, Physica C (2004), ISS 2003, these Proceedings.
Effects of magnetic fields induced by bias currents on operation of RSFQ circuits Motohiro Suzuki *, Masaaki Maezawa, Fuminori Hirayama National Institute of Advanced Industrial Science and Technology, Central 2, 1-1-1 Umezono, Tsukuba, Ibaraki 305-8568, Japan Received 29 October 2003; accepted 15 December 2003 Available online 7 June 2004
Abstract We investigated the effects of magnetic fields induced by bias currents on rapid single flux quantum (RSFQ) circuits. We measured the mutual inductance between a signal line and a bias line in the circuit. The mutual inductance values obtained were in the range of 5–50 fH. We simulated operation of a 2-stage shift register under the magnetic fields induced by an additional control current. The calculated operating regions were significantly reduced by the magnetic fields induced by the control currents on the order of 10 mA. The experimental results obtained for the shift register agreed with the simulation. These results suggest that it is important to take the effects of current-induced magnetic fields into account in the design of large-scale RSFQ circuits. Ó 2004 Elsevier B.V. All rights reserved. PACS: 85.25.Am; 85.25.Cp Keywords: Josephson junction; Rapid single flux quantum; Superconductor integrated circuit; Operating region
1. Introduction Recently, it has been reported that the operating regions of rapid single flux quantum (RSFQ) circuits become small with increasing circuit bias current [1–3]. An explanation is that the magnetic field induced by the bias current affects the operation of the circuit. Although the circuits include ground planes, this degradation due to the magnetic fields is significant. This problem will become more serious with an increase in the circuit scale.
*
Corresponding author. Tel.: +81-29-861-5905; fax: +81-29861-5530. E-mail address: [email protected] (M. Suzuki).
For example, the final version of our digital-toanalog converter will need a bias current of a few amperes [4]. We will encounter this problem in the near future. We theoretically and experimentally investigated the effects of magnetic fields induced by bias currents. We measured the mutual inductance between a signal line and a bias line in the circuit, and obtained values of mutual inductance ranging from 5 to 50 fH. We investigated the effects of magnetic coupling on the operation of RSFQ circuits by simulation and experiments. Simulation of a 2-stage shift register showed that magnetic fields induced by bias currents on the order of 10 mA significantly reduced the operating region of the circuit. We fabricated a 2-stage shift register and
0921-4534/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2003.12.094
M. Suzuki et al. / Physica C 412–414 (2004) 1576–1579
measured its operating region. The experimental results agreed with the simulation.
2. Magnetic coupling between strip lines We quantitatively evaluated the magnetic coupling between the strip lines in RSFQ circuits. We measured the mutual inductance between a signal line and a bias line, which are orthogonal to each other in the circuit, because the signal line is close to the bias line at crossover. We measured the mutual inductance using SQUIDs whose layouts were extracted from our standard RSFQ cells. The loop inductance of the SQUID was formed by the circuit signal line, and the control line of the SQUID was formed by the circuit bias line (Fig. 1). We fabricated the SQUIDs using our standard process [5]. From the U–V characteristics of the SQUIDs, we obtained the values of mutual inductance. The SQUID extracted from the JTL cell has a symmetrical structure (Fig. 1(b)). A control current Icnt is applied through a control line that is orthogonal to the SQUID loop at the center. We therefore expected a small mutual inductance between the SQUID and the control line. We obtained mutual inductance M ¼ 5 fH in the symmetrical SQUID. SQUIDs based on a 2-stage shift register were also investigated. The layout of the SQUIDs was extracted from I/O ports connecting the shift register cells (Fig. 1(e)). The SQUIDs were asymmetrical in layout as well as parameters. We expected a larger mutual inductance in the asymmetrical SQUIDs than in the symmetrical type. Mutual inductances M1 ¼ 46 fH and M2 ¼ 31 fH were obtained in the asymmetrical SQUIDs. The measured values of mutual inductance may include the mutual inductance between the SQUID loop and external parts such as bonding lines and wiring on a chip carrier. We measured the mutual inductance contributed by the external parts. We used the symmetrical SQUID in Fig. 1(b) and a bonding pad that was about 1 mm distant from the SQUID. We connected the pad with several channels on the chip carrier. To apply the control current we used various pairs of
1577
channels for current injection and drain. The measured values of the mutual inductance between the external control line and the SQUID loop were lower than 1 fH, and were much smaller than those between the lines on the chip.
3. Effects of magnetic fields on circuit operation We investigated the effects of the magnetic fields induced by bias currents on the operation of RSFQ circuits. We used a modified version of a 2stage shift register consisting of our library cells. A bias line crossing two signal lines at the center was separated from the other bias lines. The separated bias line was used as a control line, like the SQUIDs in Fig. 1(e). An equivalent circuit of the shift register is shown in Fig. 2. The control line magnetically couples to the signal lines with the mutual inductances M1 and M2 . We simulated the operation of the 2-stage shift register using the measured values of the mutual inductances M1 and M2 . The calculated operating regions of the bias current are shown as a function of the control current Icnt in Fig. 3 (solid lines). The operating regions were reduced with increasing Icnt and disappeared at Icnt ¼ 20 mA. We tested the 2-stage shift register fabricated on the same chip as the SQUIDs that were used to measure the mutual inductances M1 and M2 . The operating regions are shown as dots with bars in Fig. 3. The experimental results agreed with the simulation, confirming the validity of the model.
4. Discussion Two types of magnetic coupling possibly contribute to the mutual inductance obtained. One is coupling at the crossover. Since strip lines have finite width, currents through the crossing lines have components parallel to each other (Fig. 4(a)). The other is coupling between parallel lines [1]. The signal line has portions parallel to the control line near the crossover, so finite coupling exists between the lines (Fig. 4(b)). Further investigation will be necessary to determine which type of coupling is dominant.
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M. Suzuki et al. / Physica C 412–414 (2004) 1576–1579
Fig. 1. RSFQ library cells and investigated SQUIDs: (a) layout of a JTL cell; (b) layout and (c) schematic of the SQUID extracted from the JTL cell; (d) layout of a 2-stage shift register; (e) layout and (f) schematic of SQUIDs extracted from the 2-stage shift register.
In Fig. 3, the experimental results slightly deviate from the simulation. This is possibly
caused by effects of mutual coupling that we did not consider in the equivalent circuit in Fig. 2. We
M. Suzuki et al. / Physica C 412–414 (2004) 1576–1579
Fig. 2. Equivalent circuit of the 2-stage shift register.
1579
currents and the sheet resistance were different from the designed values. It is important to reduce the effects of the magnetic fields induced by bias currents. Bias currents should flow uniformly in the circuits. Also, magnetic coupling between the signal line and the bias line should be reduced. A method of bias line shielding has been proposed to reduce magnetic coupling [1], but an extra superconductive layer is necessary to shield the bias line that crosses the signal line. It is important for layout design to decrease the magnetic coupling in the circuits.
5. Summary
Fig. 3. Operating regions of the bias current of the 2-stage shift register as a function of the control current Icnt . The solid lines show the simulated results and the dots with bars show the experimental results.
The operating regions of RSFQ circuits become small with increasing circuit bias current. We investigated the effects of the magnetic fields induced by bias currents on the operation of RSFQ circuits. We measured the mutual inductance between a signal line and a bias line on a chip, and obtained values of mutual inductance ranging from 5 to 50 fH. We investigated the effects of magnetic coupling on the operation of a 2-stage shift register by simulation and experiments. The magnetic fields induced by bias currents on the order of 10 mA significantly reduced the operating region of the circuit. These results suggest that we need to take into account the magnetic fields induced by bias currents in the design of large-scale RSFQ circuits.
References
Fig. 4. Magnetic coupling between the strip lines in the circuit: (a) coupling at the crossover and (b) coupling between parallel lines.
considered the rather simple case of only two mutual inductances, M1 and M2 . In addition, actual circuit parameters such as the junction critical
[1] H. Terai, Y. Kameda, S. Yorozu, A. Fujimaki, Z. Wang, IEEE Trans. Appl. Supercond. 13 (2003) 502. [2] S. Nagasawa, H. Hasegawa, S. Hirano, K. Miyahara, Y. Enomoto, private communication. [3] Y. Kameda, S. Yorozu, private communication. [4] H. Sasaki, V. Bubanja, S. Kiryu, F. Hirayama, M. Maezawa, A. Shoji, IEEE Trans. Instrum. Meas. 50 (2001) 318. [5] M. Maezawa, F. Hirayama, M. Suzuki, Physica C (2004), ISS 2003, these Proceedings.