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Calorimeter Impedance Study K. A. Barger, M. A. Lindeman, and L. E. Rocks Designing a Rocket payload to study the diffuse X-ray Background in the Galactic ISM This rocket will travel to the upper atmosphere of Earth and collect data for ~5min The last rocket flight was able to detect O VII, O VIII, C VI, and some silicon ions. This information can be used to: Investigate the galactic evolutionary processes. Determine the types and quantities of baryons which are important to Cosmology. The detectors The payload of the rocket contains 36 microcalorimeter detectors. Each of these detectors is composed of a silicon thermistor that is thermally connected to a HgTe absorber. Operate at 60mK for low thermal noise. They are highly sensitive detectors that detect small changes in energy. They are so sensitive that they are able to measure the energy of single X-ray photons to a part in ~1000. Why Studying the Impedance of the Detectors is Important The impedance measurements can be used to determine the Heat Capacity of the detectors. It is important to know the Heat Capacity because: The lower the Heat Capacity The more the temperature of the detector will change from a given amount of energy of an X-ray. The better the signal to noise ratio. Analogy Similarly, if you a microcalorimeter that hasone Take mass on ahave spring that is able to oscillate some impedance and introduce bias voltage dimensionally in response to a adriving force. to the circuit and an then the behavior Measuring theoscillating behaviorcurrent, of the spring that over a of the impedance a broad range of frequencies will broad range ofover frequencies enables you to yield information about the Heat Capacity. Remember determine the mass that is on the spring. that the impedance is frequency dependent. An ideal model of a thermal detector consists of a heat capacity (C) connected to a heat sink through a weak thermal link (G). Why is my Research Important? Detector Impadence Additional lobe The current model for the impedance the circuit used The predictedin and ideal behavior of to this curvethe for detector this particular detector is one bias is inaccurate in that curves in a semicircle manner and describing the physical effects that does not have any additional lobes are takingCurves place diverge within the circuit and does not match with the collected data. 2.5x10 5 Imaginary Z (Ohm) Strays Model Strays Data 2.0x10 5 1.5x10 5 1.0x10 5 5.0x10 4 0.0 5 2x10 5 3x10 5 4x10 5x10 5 Real Z (Ohm) 6x10 5 7x10 5 8x10 5 The Circuit V* – Voltage at point V V1* – Voltage In V2* – Voltage Out Vb* – Voltage bias RL* – Load Resister ZL – Load Impedance Zd – Detector Impedance Z – Stray Impedance Thevenin and Norton Equivalent Circuits Z Th Z nor Vopen Circuit I short Circuit VTh Vopen Circuit I Nor Znor I nor I short Circuit Current vs. Norton-R determine ToTo see the linear VTh andofZthis Th, behavior I plotted graph better I -1 I vs. RNor. only plotted the However, datathis for linear the frequencies at relationship Intercept n power. the is 10 hard to see Slope gets Theand datait below increasingly 1000Hz was 1 Z 1 Th I RDet inaccurate at relatively VTh VTh high frequencies. smooth data. 8 1.85x10 -1 -1 Real Norton-Current (Amp ) 8 1.80x10 1/In (1Hz) 1/In (10Hz) 1/In (100Hz) 1/In (1000Hz) 8 1.75x10 8 1.70x10 8 1.65x10 8 1.60x10 0 6 1x10 6 2x10 6 3x10 6 4x10 6 5x10 R of the Detector (Ohm) 6 6x10 6 7x10 6 8x10 Thevenin Impedance Zth (Ohm) 2.0x10 8 1.5x10 8 1.0x10 8 5.0x10 7 Real Zth Imaginary Zth 0.0 -5.0x10 7 -1.0x10 8 10 2 10 3 Frequency (Hz) 10 4 From the intercept and the slope of the line, Zth was found. As shown, Zth changes with frequency. Thevenin Voltage Real Vth Imaginary Vth 1.2 1.0 Imaginary Vth (V) 0.8 0.6 0.4 0.2 0.0 -0.2 -0.4 -0.6 2 10 3 10 Frequency (Hz) 10 4 From the slope of the line, Vth was found. As shown, Vth also changes with frequency. Results Remember that the predicted and ideal behavior of this curve for this particular detector is one that curves in a semicircle manner and does not have any additional lobs!!!! Applications of the New Impedance Model Now that the behavior of the detector’s Impedance is known, the thermal conductivities, and heat capacities can be determined from measurements of the resistance versus temperature relationship. This enables us to adjust the materials that the detectors are made from to ensure maximum efficiency The lower the Heat Capacity The more the temperature of the detector will change from a given amount of energy of an X-ray. The better the signal to noise ratio. Recap We are able to determine the Thevenin and Norton equivalent bias circuits of the microcalorimeter by measuring the Voltage across the circuit. This information can be then used to determine the impedance of the detectors. This information can then be used to determine the Heat Capacity of the detectors. By knowing the Heat Capacity of the detectors, we are able to optimize the detectors sensitivity. References J.E. Vaillancourt, Rev. Sci. Instrum. 76, 043107 (2005). M. A. Linderman, S. Bandler, R. P. Brekosky, J. A. Chervenak, E. Figueroa-Feliciano, F. M. Finkbeiner, M. J. Li, and C. A. Kibourne, Rev. Sci. Instrum. 75, 5 (2004). J. J. Brophy, 1990, Basic Electronics for Scientist (USA:McGraw-Hill, Inc.) Wikibooks http://en.wikibooks.org/wiki/Electronics:Thevenin/N orton_Equivalents A. J. Diefenderfer, B. E. Holton, 1994, Principles of Electronic Instrumentation X-ray Astrophysics, University of Wisconsin http://wisp11.physics.wisc.edu/xray/xr_microcalori meters.htm Acknowledgments I would like to thank the REU program at University of Wisconsin-Madison. I would also like to thank my mentor Dan McCammon as well as Mark Lindeman, and Lindsey Rocks their help and guidance. This work is based upon research conducted at the University of WisconsinMadison, which is supported by the NSF