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Cryogenic On-chip In Situ S-parameter Calibration Using Superconducting Coplanar Waveguides

National Institute of Standards and Technology

@usgov.national_institute_of_standard_cryogenic_on_chip_in_si_0dc68f58

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About this Dataset

Cryogenic On-chip In Situ S-parameter Calibration Using Superconducting Coplanar Waveguides

These data will appear in [1]. The abstract for that paper is given below:This paper presents a new multi-impedance-state line (MISL) in situ scattering parameter (S-parameter) calibration technique using on-chip superconducting transmission lines at 4 K that enables cryogenic calibration in a fixed signal path without the need for cryogenic switches or a cryogenic probe station. The method uses coplanar waveguide (CPW) models based on various impedance states of niobium (Nb), which has zero dc resistance below 9 K and a monotonically increasing resistance from 10 K to room temperature. The different impedance states are accessed by heating the 4 K stage of a cryostat and injecting up to 245 mA of current into the line. Using these states, we solve for the unknowns in an 8-term error model through a least-squares analysis. We first validate the MISL calibration technique by comparing it with short-open-load-reciprocal (SOLR) calibrated measurements in a cryogenic probe station, finding transmission agreement within 0.2 dB and uncertainty overlap for nearly all frequencies up to 26.5 GHz. We then apply the method to calibrate Nb CPWs with and without embedded Josephson junctions (JJs), using a fixed wire bonded connection, and without the use of cryogenic switches or movable probes. Strong agreement with the CPW models is demonstrated, with uncertainty overlap and differences below 0.1 dB up to 4.6 GHz without JJs and up to 2.4 GHz with JJs; resonances cause interruptions beyond these frequencies.[1] Thomas, J. N., Hoffmann, J., Flowers-Jacobs, N. E., Fox, A. E., Jungwirth, N. R., Johnson-Wilke, R. L., Dresselhaus, P. D., & Benz, S. P., "Cryogenic On-chip In Situ S-parameter Calibration Using Superconducting Coplanar Waveguides" submitted to the IEEE Transactions on Microwave Theory and Techniques Journal which if accepted will be published and available on IEEE website at a later date.
Organization: National Institute of Standards and Technology
Last updated: 2025-07-12T14:39:30.140282
Tags: cryogenic-microwave-calibration, josephson-junctions-jjs, microwave-metrology, s-parameters, superconducting-circuits

Tables

Fig5Resistance Inductance Data

@usgov.national_institute_of_standard_cryogenic_on_chip_in_si_0dc68f58.fig5resistance_inductance_data
  • 474.14 KB
  • 2650 rows
  • 23 columns
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CREATE TABLE fig5resistance_inductance_data (
  "frequency_ghz" DOUBLE,
  "r_k_m_n_0" BIGINT,
  "r_k_m_n_1" DOUBLE,
  "r_k_m_n_2" DOUBLE,
  "r_k_m_n_3" DOUBLE,
  "r_k_m_n_4" DOUBLE,
  "r_k_m_n_5" DOUBLE,
  "r_k_m_n_6" DOUBLE,
  "r_unc_k_m_n_0" BIGINT,
  "r_unc_k_m_n_1" DOUBLE,
  "r_unc_k_m_n_2" DOUBLE,
  "r_unc_k_m_n_3" DOUBLE,
  "r_unc_k_m_n_4" DOUBLE,
  "r_unc_k_m_n_5" DOUBLE,
  "r_unc_k_m_n_6" DOUBLE,
  "l_nh_m_n_0" DOUBLE,
  "l_nh_m_n_2" DOUBLE,
  "l_nh_m_n_4" DOUBLE,
  "l_nh_m_n_6" DOUBLE,
  "l_unc_nh_m_n_0" DOUBLE,
  "l_unc_nh_m_n_2" DOUBLE,
  "l_unc_nh_m_n_4" DOUBLE,
  "l_unc_nh_m_n_6" DOUBLE
);

Fig6bottom SetupA CPWwithoutJJs

@usgov.national_institute_of_standard_cryogenic_on_chip_in_si_0dc68f58.fig6bottom_setupa_cpwwithoutjjs
  • 194.91 KB
  • 2650 rows
  • 22 columns
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CREATE TABLE fig6bottom_setupa_cpwwithoutjjs (
  "frequency_ghz" DOUBLE,
  "max_s_11" DOUBLE,
  "misl_s_11" DOUBLE,
  "solr_n_0" DOUBLE,
  "max_s_11_1" DOUBLE,
  "misl_s_11_1" DOUBLE,
  "solr_n_1" DOUBLE,
  "max_s_11_2" DOUBLE,
  "misl_s_11_2" VARCHAR,
  "solr_n_2" VARCHAR,
  "max_s_11_3" VARCHAR,
  "misl_s_11_3" VARCHAR,
  "solr_n_3" VARCHAR,
  "max_s_11_4" VARCHAR,
  "misl_s_11_4" VARCHAR,
  "solr_n_4" VARCHAR,
  "max_s_11_5" VARCHAR,
  "misl_s_11_5" VARCHAR,
  "solr_n_5" VARCHAR,
  "max_s_11_6" VARCHAR,
  "misl_s_11_6" VARCHAR,
  "solr_n_6" VARCHAR
);

Fig6middle SetupA CPWwithoutJJs

@usgov.national_institute_of_standard_cryogenic_on_chip_in_si_0dc68f58.fig6middle_setupa_cpwwithoutjjs
  • 367.83 KB
  • 2650 rows
  • 49 columns
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CREATE TABLE fig6middle_setupa_cpwwithoutjjs (
  "frequency_ghz" VARCHAR,
  "s_11" VARCHAR,
  "n__n_0_model_unc" VARCHAR,
  "s_11_1" VARCHAR,
  "n__n_0_model" VARCHAR,
  "s_11_2" VARCHAR,
  "n__n_0_misl_unc" VARCHAR,
  "s_11_3" VARCHAR,
  "n__n_0_misl" VARCHAR,
  "s_11_4" VARCHAR,
  "n__n_0_solr_unc" VARCHAR,
  "s_11_5" VARCHAR,
  "n__n_0_solr" VARCHAR,
  "s_11_6" VARCHAR,
  "n__n_2_model_unc" VARCHAR,
  "s_11_7" VARCHAR,
  "n__n_2_model" VARCHAR,
  "s_11_8" VARCHAR,
  "n__n_2_misl_unc" VARCHAR,
  "s_11_9" VARCHAR,
  "n__n_2_misl" VARCHAR,
  "s_11_10" VARCHAR,
  "n__n_2_solr_unc" VARCHAR,
  "s_11_11" VARCHAR,
  "n__n_2_solr" VARCHAR,
  "s_11_12" VARCHAR,
  "n__n_4_model_unc" VARCHAR,
  "s_11_13" VARCHAR,
  "n__n_4_model" VARCHAR,
  "s_11_14" VARCHAR,
  "n__n_4_misl_unc" VARCHAR,
  "s_11_15" VARCHAR,
  "n__n_4_misl" VARCHAR,
  "s_11_16" VARCHAR,
  "n__n_4_solr_unc" VARCHAR,
  "s_11_17" VARCHAR,
  "n__n_4_solr" VARCHAR,
  "s_11_18" VARCHAR,
  "n__n_6_model_unc" VARCHAR,
  "s_11_19" VARCHAR,
  "n__n_6_model" VARCHAR,
  "s_11_20" VARCHAR,
  "n__n_6_misl_unc" VARCHAR,
  "s_11_21" VARCHAR,
  "n__n_6_misl" VARCHAR,
  "s_11_22" VARCHAR,
  "n__n_6_solr_unc" VARCHAR,
  "s_11_23" VARCHAR,
  "n__n_6_solr" VARCHAR
);

Fig6top SetupA CPWwithoutJJs

@usgov.national_institute_of_standard_cryogenic_on_chip_in_si_0dc68f58.fig6top_setupa_cpwwithoutjjs
  • 348.43 KB
  • 2650 rows
  • 49 columns
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CREATE TABLE fig6top_setupa_cpwwithoutjjs (
  "frequency_ghz" VARCHAR,
  "s_21" VARCHAR,
  "n__n_0_model_unc" VARCHAR,
  "s_21_1" VARCHAR,
  "n__n_0_model" VARCHAR,
  "s_21_2" VARCHAR,
  "n__n_0_misl_unc" VARCHAR,
  "s_21_3" VARCHAR,
  "n__n_0_misl" VARCHAR,
  "s_21_4" VARCHAR,
  "n__n_0_solr_unc" VARCHAR,
  "s_21_5" VARCHAR,
  "n__n_0_solr" VARCHAR,
  "s_21_6" VARCHAR,
  "n__n_2_model_unc" VARCHAR,
  "s_21_7" VARCHAR,
  "n__n_2_model" VARCHAR,
  "s_21_8" VARCHAR,
  "n__n_2_misl_unc" VARCHAR,
  "s_21_9" VARCHAR,
  "n__n_2_misl" VARCHAR,
  "s_21_10" VARCHAR,
  "n__n_2_solr_unc" VARCHAR,
  "s_21_11" VARCHAR,
  "n__n_2_solr" VARCHAR,
  "s_21_12" VARCHAR,
  "n__n_4_model_unc" VARCHAR,
  "s_21_13" VARCHAR,
  "n__n_4_model" VARCHAR,
  "s_21_14" VARCHAR,
  "n__n_4_misl_unc" VARCHAR,
  "s_21_15" VARCHAR,
  "n__n_4_misl" VARCHAR,
  "s_21_16" VARCHAR,
  "n__n_4_solr_unc" VARCHAR,
  "s_21_17" VARCHAR,
  "n__n_4_solr" VARCHAR,
  "s_21_18" VARCHAR,
  "n__n_6_model_unc" VARCHAR,
  "s_21_19" VARCHAR,
  "n__n_6_model" VARCHAR,
  "s_21_20" VARCHAR,
  "n__n_6_misl_unc" VARCHAR,
  "s_21_21" VARCHAR,
  "n__n_6_misl" VARCHAR,
  "s_21_22" VARCHAR,
  "n__n_6_solr_unc" VARCHAR,
  "s_21_23" VARCHAR,
  "n__n_6_solr" VARCHAR
);

Fig7bottom SetupB CPWwithJJs

@usgov.national_institute_of_standard_cryogenic_on_chip_in_si_0dc68f58.fig7bottom_setupb_cpwwithjjs
  • 248.17 KB
  • 2650 rows
  • 33 columns
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CREATE TABLE fig7bottom_setupb_cpwwithjjs (
  "frequency_ghz" VARCHAR,
  "s_21" VARCHAR,
  "n__n_0_model_unc" VARCHAR,
  "s_21_1" VARCHAR,
  "n__n_0_model" VARCHAR,
  "s_21_2" VARCHAR,
  "n__n_0_misl_unc" VARCHAR,
  "s_21_3" VARCHAR,
  "n__n_0_misl" VARCHAR,
  "s_21_4" VARCHAR,
  "n__n_1_model_unc" VARCHAR,
  "s_21_5" VARCHAR,
  "n__n_1_model" VARCHAR,
  "s_21_6" VARCHAR,
  "n__n_1_misl_unc" VARCHAR,
  "s_21_7" VARCHAR,
  "n__n_1_misl" VARCHAR,
  "s_21_8" VARCHAR,
  "n__n_3_model_unc" VARCHAR,
  "s_21_9" VARCHAR,
  "n__n_3_model" VARCHAR,
  "s_21_10" VARCHAR,
  "n__n_3_misl_unc" VARCHAR,
  "s_21_11" VARCHAR,
  "n__n_3_misl" VARCHAR,
  "s_21_12" VARCHAR,
  "n__n_5_model_unc" VARCHAR,
  "s_21_13" VARCHAR,
  "n__n_5_model" VARCHAR,
  "s_21_14" VARCHAR,
  "n__n_5_misl_unc" VARCHAR,
  "s_21_15" VARCHAR,
  "n__n_5_misl" VARCHAR
);

Fig7top SetupB CPWwithoutJJs

@usgov.national_institute_of_standard_cryogenic_on_chip_in_si_0dc68f58.fig7top_setupb_cpwwithoutjjs
  • 316.51 KB
  • 2650 rows
  • 41 columns
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CREATE TABLE fig7top_setupb_cpwwithoutjjs (
  "frequency_ghz" VARCHAR,
  "s_21" VARCHAR,
  "n__n_0_model_unc" VARCHAR,
  "s_21_1" VARCHAR,
  "n__n_0_model" VARCHAR,
  "s_21_2" VARCHAR,
  "n__n_0_misl_unc" VARCHAR,
  "s_21_3" VARCHAR,
  "n__n_0_misl" VARCHAR,
  "s_21_4" VARCHAR,
  "n__n_1_model_unc" VARCHAR,
  "s_21_5" VARCHAR,
  "n__n_1_model" VARCHAR,
  "s_21_6" VARCHAR,
  "n__n_1_misl_unc" VARCHAR,
  "s_21_7" VARCHAR,
  "n__n_1_misl" VARCHAR,
  "s_21_8" VARCHAR,
  "n__n_2_model_unc" VARCHAR,
  "s_21_9" VARCHAR,
  "n__n_2_model" VARCHAR,
  "s_21_10" VARCHAR,
  "n__n_2_misl_unc" VARCHAR,
  "s_21_11" VARCHAR,
  "n__n_2_misl" VARCHAR,
  "s_21_12" VARCHAR,
  "n__n_3_model_unc" VARCHAR,
  "s_21_13" VARCHAR,
  "n__n_3_model" VARCHAR,
  "s_21_14" VARCHAR,
  "n__n_3_misl_unc" VARCHAR,
  "s_21_15" VARCHAR,
  "n__n_3_misl" VARCHAR,
  "s_21_16" VARCHAR,
  "n__n_4_model_unc" VARCHAR,
  "s_21_17" VARCHAR,
  "n__n_4_model" VARCHAR,
  "s_21_18" VARCHAR,
  "n__n_4_misl_unc" VARCHAR,
  "s_21_19" VARCHAR,
  "n__n_4_misl" VARCHAR
);

Fig8TempTestData

@usgov.national_institute_of_standard_cryogenic_on_chip_in_si_0dc68f58.fig8temptestdata
  • 29.96 KB
  • 2650 rows
  • 5 columns
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CREATE TABLE fig8temptestdata (
  "frequency_ghz" VARCHAR,
  "s_21_10_k" VARCHAR,
  "n" VARCHAR,
  "s_21_25_k" VARCHAR,
  "unnamed_4" VARCHAR
);

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