Abstract

We present an experimental study of a composite voltage-biased superconducting bolometer (VSB). The tested VSB consists of a Ti-film superconducting thermometer (T c ∼ 375 mK) on a Si substrate suspended by NbTi superconducting leads. A resistor attached to the substrate provides calibrated heat input into the bolometer. The current through the bolometer is measured with a superconducting quantum interference device ammeter. Strong negative electrothermal feedback fixes the bolometer temperature at T c and reduces the measured response time from 2.6 s to 13 ms. As predicted, the measured current responsivity of the bolometer is equal to the inverse of the bias voltage. A noise equivalent power of 5 × 10-17 W/√Hz was measured for a thermal conductance G ∼ 4.7 × 10-10 W/K, which is consistent with the expected thermal noise. Excess noise was observed for bias conditions for which the electrothermal feedback strength was close to maximum.

© 1998 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. P. L. Richards, “Bolometers for infrared and millimeter waves,” J. Appl. Phys. 76, 1–24 (1994).
    [CrossRef]
  2. S. T. Tanaka, A. C. Clapp, M. J. Devlin, N. Figueiredo, J. O. Gundersen, S. Hanany, V. V. Hristov, A. E. Lange, M. A. Lim, P. M. Lubin, P. R. Meinhold, P. L. Richards, G. F. Smoot, J. Staren, “Measurements of anisotropy in the cosmic microwave background radiation at 0.5° scales near the stars HR5127 and ϕ Herculis,” Astrophys. J. L81, 468 (1996).
  3. A. T. Lee, J. M. Gildemeister, S.-F. Lee, P. L. Richards, “Voltage-biased high-Tc superconducting infrared bolometer with strong electrothermal feedback,” IEEE Trans. Appl. Supercond. 7, 2378–2381 (1997).
    [CrossRef]
  4. A. T. Lee, P. L. Richards, S. Nam, B. Cabrera, K. D. Irwin, “A superconducting bolometer with strong electrothermal feedback,” Appl. Phys. Lett. 69, 1801–1803 (1996).
    [CrossRef]
  5. K. D. Irwin, “An application of electrothermal feedback for high resolution cryogenic particle detection,” Appl. Phys. Lett. 66, 1998–2000 (1995).
    [CrossRef]
  6. This term is a modification of the effective thermal conductance defined in Ref. 1.
  7. P. Horowitz, W. Hill, The Art of Electronics (Cambridge U Press, Cambridge, UK, 1989), Chap. 4.
  8. J. C. Mather, “Bolometer noise: nonequilibrium theory,” Appl. Opt. 21, 1125–1129 (1982).
    [CrossRef] [PubMed]
  9. J. Clarke, T. Y. Hsiang, “Low-frequency noise in tin and lead films at the superconducting transition,” Phys. Rev. B 13, 4790–4800 (1976).
    [CrossRef]
  10. Y. B. Kim, C. F. Hempstead, A. R. Strnad, “Resistive states of hard superconductors,” Rev. Mod. Phys. 36, 43–45 (1964).
    [CrossRef]
  11. Epoxy 907, Miller-Stephenson Chemical Company Inc., George Washington Hwy., Danbury, Conn. 06810.
  12. H20E, Epoxy Technology Inc., 14 Fortune Drive, Billerica, Mass. 01821.
  13. L. Duband, D. Alsop, A. Lange, P. Kittel, “A rocket-borne 3He refrigerator,” Adv. Cryog. Eng. 35, 1447–1456 (1989).
  14. J. J. Bock, “Rocket-borne observation of singly ionized carbon 158 μm emission from the diffuse interstellar medium,” Ph. D. dissertation (University of California, Berkeley, Calif., 1994).
  15. Model 50 SQUID and Model 550 Single Channel SQUID Controller, Quantum Design, 11578 Sorrento Valley Road, San Diego, Calif. 92121.
  16. HP35660A Dynamic Signal Analyzer, Hewlett Packard Corporation, Everett, Wash. 98205.
  17. This value was obtained by W. Holmes in a previous study.
  18. A. T. Lee, S-F. Lee, J. M. Gildemeister, P. L. Richards, “Voltage-biased superconducting bolometers for infrared and mm-wave astronomy,” in Proceedings of the 7th International Workshop on Low Temperature Detectors LTD-7 (Max Planck Institute of Physics, Munich, Germany, 1997) available from urg@mppmu.mpg.de and at http://bolo.berkeley.edu .

1997 (1)

A. T. Lee, J. M. Gildemeister, S.-F. Lee, P. L. Richards, “Voltage-biased high-Tc superconducting infrared bolometer with strong electrothermal feedback,” IEEE Trans. Appl. Supercond. 7, 2378–2381 (1997).
[CrossRef]

1996 (2)

A. T. Lee, P. L. Richards, S. Nam, B. Cabrera, K. D. Irwin, “A superconducting bolometer with strong electrothermal feedback,” Appl. Phys. Lett. 69, 1801–1803 (1996).
[CrossRef]

S. T. Tanaka, A. C. Clapp, M. J. Devlin, N. Figueiredo, J. O. Gundersen, S. Hanany, V. V. Hristov, A. E. Lange, M. A. Lim, P. M. Lubin, P. R. Meinhold, P. L. Richards, G. F. Smoot, J. Staren, “Measurements of anisotropy in the cosmic microwave background radiation at 0.5° scales near the stars HR5127 and ϕ Herculis,” Astrophys. J. L81, 468 (1996).

1995 (1)

K. D. Irwin, “An application of electrothermal feedback for high resolution cryogenic particle detection,” Appl. Phys. Lett. 66, 1998–2000 (1995).
[CrossRef]

1994 (1)

P. L. Richards, “Bolometers for infrared and millimeter waves,” J. Appl. Phys. 76, 1–24 (1994).
[CrossRef]

1989 (1)

L. Duband, D. Alsop, A. Lange, P. Kittel, “A rocket-borne 3He refrigerator,” Adv. Cryog. Eng. 35, 1447–1456 (1989).

1982 (1)

1976 (1)

J. Clarke, T. Y. Hsiang, “Low-frequency noise in tin and lead films at the superconducting transition,” Phys. Rev. B 13, 4790–4800 (1976).
[CrossRef]

1964 (1)

Y. B. Kim, C. F. Hempstead, A. R. Strnad, “Resistive states of hard superconductors,” Rev. Mod. Phys. 36, 43–45 (1964).
[CrossRef]

Alsop, D.

L. Duband, D. Alsop, A. Lange, P. Kittel, “A rocket-borne 3He refrigerator,” Adv. Cryog. Eng. 35, 1447–1456 (1989).

Bock, J. J.

J. J. Bock, “Rocket-borne observation of singly ionized carbon 158 μm emission from the diffuse interstellar medium,” Ph. D. dissertation (University of California, Berkeley, Calif., 1994).

Cabrera, B.

A. T. Lee, P. L. Richards, S. Nam, B. Cabrera, K. D. Irwin, “A superconducting bolometer with strong electrothermal feedback,” Appl. Phys. Lett. 69, 1801–1803 (1996).
[CrossRef]

Clapp, A. C.

S. T. Tanaka, A. C. Clapp, M. J. Devlin, N. Figueiredo, J. O. Gundersen, S. Hanany, V. V. Hristov, A. E. Lange, M. A. Lim, P. M. Lubin, P. R. Meinhold, P. L. Richards, G. F. Smoot, J. Staren, “Measurements of anisotropy in the cosmic microwave background radiation at 0.5° scales near the stars HR5127 and ϕ Herculis,” Astrophys. J. L81, 468 (1996).

Clarke, J.

J. Clarke, T. Y. Hsiang, “Low-frequency noise in tin and lead films at the superconducting transition,” Phys. Rev. B 13, 4790–4800 (1976).
[CrossRef]

Devlin, M. J.

S. T. Tanaka, A. C. Clapp, M. J. Devlin, N. Figueiredo, J. O. Gundersen, S. Hanany, V. V. Hristov, A. E. Lange, M. A. Lim, P. M. Lubin, P. R. Meinhold, P. L. Richards, G. F. Smoot, J. Staren, “Measurements of anisotropy in the cosmic microwave background radiation at 0.5° scales near the stars HR5127 and ϕ Herculis,” Astrophys. J. L81, 468 (1996).

Duband, L.

L. Duband, D. Alsop, A. Lange, P. Kittel, “A rocket-borne 3He refrigerator,” Adv. Cryog. Eng. 35, 1447–1456 (1989).

Figueiredo, N.

S. T. Tanaka, A. C. Clapp, M. J. Devlin, N. Figueiredo, J. O. Gundersen, S. Hanany, V. V. Hristov, A. E. Lange, M. A. Lim, P. M. Lubin, P. R. Meinhold, P. L. Richards, G. F. Smoot, J. Staren, “Measurements of anisotropy in the cosmic microwave background radiation at 0.5° scales near the stars HR5127 and ϕ Herculis,” Astrophys. J. L81, 468 (1996).

Gildemeister, J. M.

A. T. Lee, J. M. Gildemeister, S.-F. Lee, P. L. Richards, “Voltage-biased high-Tc superconducting infrared bolometer with strong electrothermal feedback,” IEEE Trans. Appl. Supercond. 7, 2378–2381 (1997).
[CrossRef]

Gundersen, J. O.

S. T. Tanaka, A. C. Clapp, M. J. Devlin, N. Figueiredo, J. O. Gundersen, S. Hanany, V. V. Hristov, A. E. Lange, M. A. Lim, P. M. Lubin, P. R. Meinhold, P. L. Richards, G. F. Smoot, J. Staren, “Measurements of anisotropy in the cosmic microwave background radiation at 0.5° scales near the stars HR5127 and ϕ Herculis,” Astrophys. J. L81, 468 (1996).

Hanany, S.

S. T. Tanaka, A. C. Clapp, M. J. Devlin, N. Figueiredo, J. O. Gundersen, S. Hanany, V. V. Hristov, A. E. Lange, M. A. Lim, P. M. Lubin, P. R. Meinhold, P. L. Richards, G. F. Smoot, J. Staren, “Measurements of anisotropy in the cosmic microwave background radiation at 0.5° scales near the stars HR5127 and ϕ Herculis,” Astrophys. J. L81, 468 (1996).

Hempstead, C. F.

Y. B. Kim, C. F. Hempstead, A. R. Strnad, “Resistive states of hard superconductors,” Rev. Mod. Phys. 36, 43–45 (1964).
[CrossRef]

Hill, W.

P. Horowitz, W. Hill, The Art of Electronics (Cambridge U Press, Cambridge, UK, 1989), Chap. 4.

Horowitz, P.

P. Horowitz, W. Hill, The Art of Electronics (Cambridge U Press, Cambridge, UK, 1989), Chap. 4.

Hristov, V. V.

S. T. Tanaka, A. C. Clapp, M. J. Devlin, N. Figueiredo, J. O. Gundersen, S. Hanany, V. V. Hristov, A. E. Lange, M. A. Lim, P. M. Lubin, P. R. Meinhold, P. L. Richards, G. F. Smoot, J. Staren, “Measurements of anisotropy in the cosmic microwave background radiation at 0.5° scales near the stars HR5127 and ϕ Herculis,” Astrophys. J. L81, 468 (1996).

Hsiang, T. Y.

J. Clarke, T. Y. Hsiang, “Low-frequency noise in tin and lead films at the superconducting transition,” Phys. Rev. B 13, 4790–4800 (1976).
[CrossRef]

Irwin, K. D.

A. T. Lee, P. L. Richards, S. Nam, B. Cabrera, K. D. Irwin, “A superconducting bolometer with strong electrothermal feedback,” Appl. Phys. Lett. 69, 1801–1803 (1996).
[CrossRef]

K. D. Irwin, “An application of electrothermal feedback for high resolution cryogenic particle detection,” Appl. Phys. Lett. 66, 1998–2000 (1995).
[CrossRef]

Kim, Y. B.

Y. B. Kim, C. F. Hempstead, A. R. Strnad, “Resistive states of hard superconductors,” Rev. Mod. Phys. 36, 43–45 (1964).
[CrossRef]

Kittel, P.

L. Duband, D. Alsop, A. Lange, P. Kittel, “A rocket-borne 3He refrigerator,” Adv. Cryog. Eng. 35, 1447–1456 (1989).

Lange, A.

L. Duband, D. Alsop, A. Lange, P. Kittel, “A rocket-borne 3He refrigerator,” Adv. Cryog. Eng. 35, 1447–1456 (1989).

Lange, A. E.

S. T. Tanaka, A. C. Clapp, M. J. Devlin, N. Figueiredo, J. O. Gundersen, S. Hanany, V. V. Hristov, A. E. Lange, M. A. Lim, P. M. Lubin, P. R. Meinhold, P. L. Richards, G. F. Smoot, J. Staren, “Measurements of anisotropy in the cosmic microwave background radiation at 0.5° scales near the stars HR5127 and ϕ Herculis,” Astrophys. J. L81, 468 (1996).

Lee, A. T.

A. T. Lee, J. M. Gildemeister, S.-F. Lee, P. L. Richards, “Voltage-biased high-Tc superconducting infrared bolometer with strong electrothermal feedback,” IEEE Trans. Appl. Supercond. 7, 2378–2381 (1997).
[CrossRef]

A. T. Lee, P. L. Richards, S. Nam, B. Cabrera, K. D. Irwin, “A superconducting bolometer with strong electrothermal feedback,” Appl. Phys. Lett. 69, 1801–1803 (1996).
[CrossRef]

Lee, S.-F.

A. T. Lee, J. M. Gildemeister, S.-F. Lee, P. L. Richards, “Voltage-biased high-Tc superconducting infrared bolometer with strong electrothermal feedback,” IEEE Trans. Appl. Supercond. 7, 2378–2381 (1997).
[CrossRef]

Lim, M. A.

S. T. Tanaka, A. C. Clapp, M. J. Devlin, N. Figueiredo, J. O. Gundersen, S. Hanany, V. V. Hristov, A. E. Lange, M. A. Lim, P. M. Lubin, P. R. Meinhold, P. L. Richards, G. F. Smoot, J. Staren, “Measurements of anisotropy in the cosmic microwave background radiation at 0.5° scales near the stars HR5127 and ϕ Herculis,” Astrophys. J. L81, 468 (1996).

Lubin, P. M.

S. T. Tanaka, A. C. Clapp, M. J. Devlin, N. Figueiredo, J. O. Gundersen, S. Hanany, V. V. Hristov, A. E. Lange, M. A. Lim, P. M. Lubin, P. R. Meinhold, P. L. Richards, G. F. Smoot, J. Staren, “Measurements of anisotropy in the cosmic microwave background radiation at 0.5° scales near the stars HR5127 and ϕ Herculis,” Astrophys. J. L81, 468 (1996).

Mather, J. C.

Meinhold, P. R.

S. T. Tanaka, A. C. Clapp, M. J. Devlin, N. Figueiredo, J. O. Gundersen, S. Hanany, V. V. Hristov, A. E. Lange, M. A. Lim, P. M. Lubin, P. R. Meinhold, P. L. Richards, G. F. Smoot, J. Staren, “Measurements of anisotropy in the cosmic microwave background radiation at 0.5° scales near the stars HR5127 and ϕ Herculis,” Astrophys. J. L81, 468 (1996).

Nam, S.

A. T. Lee, P. L. Richards, S. Nam, B. Cabrera, K. D. Irwin, “A superconducting bolometer with strong electrothermal feedback,” Appl. Phys. Lett. 69, 1801–1803 (1996).
[CrossRef]

Richards, P. L.

A. T. Lee, J. M. Gildemeister, S.-F. Lee, P. L. Richards, “Voltage-biased high-Tc superconducting infrared bolometer with strong electrothermal feedback,” IEEE Trans. Appl. Supercond. 7, 2378–2381 (1997).
[CrossRef]

A. T. Lee, P. L. Richards, S. Nam, B. Cabrera, K. D. Irwin, “A superconducting bolometer with strong electrothermal feedback,” Appl. Phys. Lett. 69, 1801–1803 (1996).
[CrossRef]

S. T. Tanaka, A. C. Clapp, M. J. Devlin, N. Figueiredo, J. O. Gundersen, S. Hanany, V. V. Hristov, A. E. Lange, M. A. Lim, P. M. Lubin, P. R. Meinhold, P. L. Richards, G. F. Smoot, J. Staren, “Measurements of anisotropy in the cosmic microwave background radiation at 0.5° scales near the stars HR5127 and ϕ Herculis,” Astrophys. J. L81, 468 (1996).

P. L. Richards, “Bolometers for infrared and millimeter waves,” J. Appl. Phys. 76, 1–24 (1994).
[CrossRef]

Smoot, G. F.

S. T. Tanaka, A. C. Clapp, M. J. Devlin, N. Figueiredo, J. O. Gundersen, S. Hanany, V. V. Hristov, A. E. Lange, M. A. Lim, P. M. Lubin, P. R. Meinhold, P. L. Richards, G. F. Smoot, J. Staren, “Measurements of anisotropy in the cosmic microwave background radiation at 0.5° scales near the stars HR5127 and ϕ Herculis,” Astrophys. J. L81, 468 (1996).

Staren, J.

S. T. Tanaka, A. C. Clapp, M. J. Devlin, N. Figueiredo, J. O. Gundersen, S. Hanany, V. V. Hristov, A. E. Lange, M. A. Lim, P. M. Lubin, P. R. Meinhold, P. L. Richards, G. F. Smoot, J. Staren, “Measurements of anisotropy in the cosmic microwave background radiation at 0.5° scales near the stars HR5127 and ϕ Herculis,” Astrophys. J. L81, 468 (1996).

Strnad, A. R.

Y. B. Kim, C. F. Hempstead, A. R. Strnad, “Resistive states of hard superconductors,” Rev. Mod. Phys. 36, 43–45 (1964).
[CrossRef]

Tanaka, S. T.

S. T. Tanaka, A. C. Clapp, M. J. Devlin, N. Figueiredo, J. O. Gundersen, S. Hanany, V. V. Hristov, A. E. Lange, M. A. Lim, P. M. Lubin, P. R. Meinhold, P. L. Richards, G. F. Smoot, J. Staren, “Measurements of anisotropy in the cosmic microwave background radiation at 0.5° scales near the stars HR5127 and ϕ Herculis,” Astrophys. J. L81, 468 (1996).

Adv. Cryog. Eng. (1)

L. Duband, D. Alsop, A. Lange, P. Kittel, “A rocket-borne 3He refrigerator,” Adv. Cryog. Eng. 35, 1447–1456 (1989).

Appl. Opt. (1)

Appl. Phys. Lett. (2)

A. T. Lee, P. L. Richards, S. Nam, B. Cabrera, K. D. Irwin, “A superconducting bolometer with strong electrothermal feedback,” Appl. Phys. Lett. 69, 1801–1803 (1996).
[CrossRef]

K. D. Irwin, “An application of electrothermal feedback for high resolution cryogenic particle detection,” Appl. Phys. Lett. 66, 1998–2000 (1995).
[CrossRef]

Astrophys. J. (1)

S. T. Tanaka, A. C. Clapp, M. J. Devlin, N. Figueiredo, J. O. Gundersen, S. Hanany, V. V. Hristov, A. E. Lange, M. A. Lim, P. M. Lubin, P. R. Meinhold, P. L. Richards, G. F. Smoot, J. Staren, “Measurements of anisotropy in the cosmic microwave background radiation at 0.5° scales near the stars HR5127 and ϕ Herculis,” Astrophys. J. L81, 468 (1996).

IEEE Trans. Appl. Supercond. (1)

A. T. Lee, J. M. Gildemeister, S.-F. Lee, P. L. Richards, “Voltage-biased high-Tc superconducting infrared bolometer with strong electrothermal feedback,” IEEE Trans. Appl. Supercond. 7, 2378–2381 (1997).
[CrossRef]

J. Appl. Phys. (1)

P. L. Richards, “Bolometers for infrared and millimeter waves,” J. Appl. Phys. 76, 1–24 (1994).
[CrossRef]

Phys. Rev. B (1)

J. Clarke, T. Y. Hsiang, “Low-frequency noise in tin and lead films at the superconducting transition,” Phys. Rev. B 13, 4790–4800 (1976).
[CrossRef]

Rev. Mod. Phys. (1)

Y. B. Kim, C. F. Hempstead, A. R. Strnad, “Resistive states of hard superconductors,” Rev. Mod. Phys. 36, 43–45 (1964).
[CrossRef]

Other (9)

Epoxy 907, Miller-Stephenson Chemical Company Inc., George Washington Hwy., Danbury, Conn. 06810.

H20E, Epoxy Technology Inc., 14 Fortune Drive, Billerica, Mass. 01821.

This term is a modification of the effective thermal conductance defined in Ref. 1.

P. Horowitz, W. Hill, The Art of Electronics (Cambridge U Press, Cambridge, UK, 1989), Chap. 4.

J. J. Bock, “Rocket-borne observation of singly ionized carbon 158 μm emission from the diffuse interstellar medium,” Ph. D. dissertation (University of California, Berkeley, Calif., 1994).

Model 50 SQUID and Model 550 Single Channel SQUID Controller, Quantum Design, 11578 Sorrento Valley Road, San Diego, Calif. 92121.

HP35660A Dynamic Signal Analyzer, Hewlett Packard Corporation, Everett, Wash. 98205.

This value was obtained by W. Holmes in a previous study.

A. T. Lee, S-F. Lee, J. M. Gildemeister, P. L. Richards, “Voltage-biased superconducting bolometers for infrared and mm-wave astronomy,” in Proceedings of the 7th International Workshop on Low Temperature Detectors LTD-7 (Max Planck Institute of Physics, Munich, Germany, 1997) available from urg@mppmu.mpg.de and at http://bolo.berkeley.edu .

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (10)

Fig. 1
Fig. 1

Predicted noise current of the VSB tested, referred to the input of the SQUID. The total noise current is obtained when Johnson, thermal fluctuation (phonon) and SQUID noise are added in quadrature with Eq. (8). The input parameters for the plots are V b = 8.8 μV, = 3.5 × 10-10 W/K, R = 5 Ω, T = 375 mK, T 0 = 270 mK, dR/dT = 2.5 × 103 Ω/K, τ0 = 2.6 s, τ = 0.13 s, and i SQUID 2 = (5 × 10-13)2 + (4 × 10-13)2/f A/√Hz at f > 0.1 Hz. These parameters correspond to a relatively low gain ℒ = 20, which gave the best experimental noise performance.

Fig. 2
Fig. 2

Diagram of the VSB tested. A NiCr heater chip is attached to the back of the substrate. The bolometer substrate is 1.5 mm × 1.5 mm.

Fig. 3
Fig. 3

Voltage-biased bolometer circuit with SQUID read-out amplifier. The VSB operates on the superconducting transition with 2 ≤ R ≤ 5 Ω. The reactance of the SQUID input coil is negligible.

Fig. 4
Fig. 4

Measured temperature dependence of the thermometer resistance. The largest value of α observed with this film is ∼1000.

Fig. 5
Fig. 5

Total power and current response measured with V b = 5.4 μV. (a) The total power dissipated in the VSB is roughly constant and equal to 36 pW for a wide range of heater power (8 pW ≤ ΔPheater ≤ 33 pW) that corresponds to the steep part of the superconducting transition where the ETF is strong. (b) The VSB has a linear response to changes of heater power in the strong ETF regime, and the responsivity is given by S i = -1/V b .

Fig. 6
Fig. 6

Product of VSB responsivity and bias voltage S i V b is constant over the range of bias voltage that corresponds to the steep part of the transition.

Fig. 7
Fig. 7

Response of the VSB to a step in heater power. The data with negligible feedback is obtained when the VSB is operated above the transition where ℒ ≪ 1, giving an intrinsic time constant τ0 = 2.6 s. A time constant of 13 ms was observed with ℒ ∼ 170.

Fig. 8
Fig. 8

Measured effective time constant τ as a function of gain ℒ. The curve gives the predicted dependence of τ = τ0/(ℒ + 1), with τ0 = 2.6 s.

Fig. 9
Fig. 9

Measured noise spectra for V b = 8.8 μV and R = 2, 3.5, and 5 Ω. The operating point on the resistive transition is set when the heater power is changed. The estimated thermal fluctuation noise and Johnson noise are indicated for each plot. The noise is predicted to approach thermal fluctuation noise for f < 1/2πτ and Johnson noise for f > 1/2πτ. Except for 1/f noise for f < 0.6 Hz, the data for R = 5Ω (where ℒ = 20) agree with the theory plotted in Fig. 1. Excess broadband noise is seen for R = 3.5 and 2 Ω where ℒ ∼ 80 and 150.

Fig. 10
Fig. 10

Calculation of the effect of an internal time constant τ i on the bolometer responsivity |S i (f) V b |. The model assumes that the bias power enters a thermometer with heat capacity C i and thermal conductance C i i to the rest of the bolometer. The bolometer is biased so that τ ∼ 15 ms (ℒ = 170). For τ i ≪ τ, V b S i (f) has a Lorentzian roll off at 1/2πτ. For values of τ i comparable with τ, there is a peak in S i (f) near 1/2πτ, which causes a peak in the output noise arising from thermal fluctuations. This feature disappears as the gain is reduced.

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

P + δ P   exp i ω t + V b 2 R - V b 2 R 2 d R d T   δ T   exp i ω t = G ¯ T - T 0 + G δ T   exp i ω t + i ω C δ T   exp i ω t ,
δ P   exp i ω t = P b T   α + G + i ω C δ T   exp i ω t ,
G eff = P b T   α + G + i ω C .
ω δ P + δ P b = ω δ P total = - δ P b ,
ω = P b α GT 1 + i ω τ 0 = 1 + i ω τ 0 ,
S i = - 1 V b + 1 1 1 + i ω τ ,
NEP 2   =   NEP photon 2 + γ 4 kT 2 G + 4 kT / R | S i | 2 τ τ 0 2 1 + ω 2 τ 0 2 1 + ω 2 τ 2 + i SQUID 2 | S i | 2 + NEP excess 2 ,
I n 2 = | S i | 2 γ 4 kT 2 G + 4 kT R τ τ 0 2 1 + ω 2 τ 0 2 1 + ω 2 τ 2 + i SQUID 2 + i excess 2 .

Metrics