Calorimeter ImpedanceCalorimeter ImpedanceStudy Study

K. A. Barger, M. A. Lindeman, and L. E. RocksK. A. Barger, M. A. Lindeman, and L. E. Rocks

Designing a Rocket payload to study the Designing a Rocket payload to study the diffuse X-ray Background in the Galactic ISMdiffuse X-ray Background in the Galactic ISM

This rocket will travel to the upper atmosphere This rocket will travel to the upper atmosphere

of Earth and collect data for ~5minof Earth and collect data for ~5minThe last rocket flight was able to detect The last rocket flight was able to detect O VII, O VII,

O VIII, C VI, and some silicon ions. O VIII, C VI, and some silicon ions.

This information can be used to:This information can be used to: Investigate the galactic evolutionary processes.Investigate the galactic evolutionary processes.Determine the types and quantities of baryons Determine the types and quantities of baryons

which are important to Cosmology.which are important to Cosmology.

The The detectorsdetectors The payload of the rocket contains 36 The payload of the rocket contains 36

microcalorimeter detectors. microcalorimeter detectors. Each of these detectors is composed of a silicon Each of these detectors is composed of a silicon

thermistor that is thermally connected to a HgTe thermistor that is thermally connected to a HgTe

absorber.absorber. Operate at 60mK for low thermal noise.Operate at 60mK for low thermal noise. They are highly sensitive detectors that detect They are highly sensitive detectors that detect

small changes in energy. They are so sensitive small changes in energy. They are so sensitive

that they are able to measure the energy of that they are able to measure the energy of

single X-ray photons to a part in ~1000. single X-ray photons to a part in ~1000.

Why Studying the Impedance of Why Studying the Impedance of the Detectors is Importantthe Detectors is Important

The impedance measurements can be used to The impedance measurements can be used to

determine the Heat Capacity of the detectors.determine the Heat Capacity of the detectors.It is important to know the Heat Capacity It is important to know the Heat Capacity

because:because:

The lower the Heat CapacityThe lower the Heat CapacityThe more the temperature of the detector will The more the temperature of the detector will

change from a given amount of energy of an X-ray.change from a given amount of energy of an X-ray.The better the signal to noise ratio.The better the signal to noise ratio.

AnalogyAnalogyTake mass on a spring that is able to oscillate one Take mass on a spring that is able to oscillate one dimensionally in response to a driving force. dimensionally in response to a driving force. Measuring the behavior of the spring that over a Measuring the behavior of the spring that over a broad range of frequencies enables you to broad range of frequencies enables you to determine the mass that is on the spring. determine the mass that is on the spring.

An ideal model of a thermal detector consists of a heat capacity (C) connected to a heat sink through a weak thermal link (G).

Similarly, if you have a microcalorimeter that has Similarly, if you have a microcalorimeter that has some impedance and introduce a bias voltage to the some impedance and introduce a bias voltage to the circuit and an oscillating current, then the behavior of circuit and an oscillating current, then the behavior of the impedance over a broad range of frequencies will the impedance over a broad range of frequencies will yield information about the Heat Capacity. Remember yield information about the Heat Capacity. Remember that the impedance is frequency dependent. that the impedance is frequency dependent.

Why is my Research Important?Why is my Research Important?

The current model for the The current model for the

impedance in the circuit used to impedance in the circuit used to

bias the detector is inaccurate in bias the detector is inaccurate in

describing the physical effects that describing the physical effects that

are taking place within the circuit are taking place within the circuit

and does not match with the and does not match with the

collected data.collected data.2x105 3x105 4x105 5x105 6x105 7x105 8x105

0.0

5.0x104

1.0x105

1.5x105

2.0x105

2.5x105

Strays Model Strays Data

Detector Impadence

Imaginary Z (Ohm)

Real Z (Ohm)

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 lobes

Additional lobeAdditional lobe

Curves divergeCurves diverge

The CircuitThe Circuit V* – Voltage at point VV* – Voltage at point V

V1* – Voltage InV1* – Voltage In

V2* – Voltage OutV2* – Voltage Out

Vb* – Voltage biasVb* – Voltage bias

RL* – Load ResisterRL* – Load Resister

ZL – Load ImpedanceZL – Load Impedance

Zd – Detector Zd – Detector

ImpedanceImpedance

Z – Stray Impedance Z – Stray Impedance

Thevenin and Norton Equivalent CircuitsThevenin and Norton Equivalent Circuits

Circuitshort nor

Nor ZnorCircuitopen Th

Circuitshort

Circuitopen norTh

I I

I V V

I

V ZZ

=

==

==

0 1x106 2x106 3x106 4x106 5x106 6x106 7x106 8x106

1.60x108

1.65x108

1.70x108

1.75x108

1.80x108

1.85x108

1/In (1Hz) 1/In (10Hz) 1/In (100Hz) 1/In (1000Hz)

Real Norton-Current

-1 (Amp

-1)

R of the Detector (Ohm)

Current vs. Norton-RCurrent vs. Norton-R

€

I−1 = RDet1

VTh

⎛

⎝ ⎜

⎞

⎠ ⎟+ZThVTh

To determine To determine VVThTh and Z and ZThTh, I , I

plotted plotted II-1-1

vs. Rvs. RNor.Nor.

However, However, this linear this linear

relationship relationship is hard to see is hard to see

and it gets and it gets increasingly increasingly inaccurate at inaccurate at

high frequencies. high frequencies.

Slope

Intercept

To see the linear To see the linear

behavior of this behavior of this

graph better I graph better I

only plotted the only plotted the

data for the data for the

frequencies at frequencies at

the 10the 10nn power. power.

The data below The data below

1000Hz was 1000Hz was

relatively relatively

smooth data.smooth data.

102 103 104

-1.0x108

-5.0x107

0.0

5.0x107

1.0x108

1.5x108

2.0x108

Real Zth Imaginary Zth

Zth

(Ohm

)

Frequency (Hz)

Thevenin ImpedanceThevenin ImpedanceFrom the From the intercept and intercept and the slope of the slope of the line, Zthe line, Zthth

was found. was found. As shown, ZAs shown, Zthth

changes with changes with frequency.frequency.

Thevenin VoltageThevenin Voltage

102 103 104

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2 Real Vth Imaginary Vth

Imag

inar

y V

th (

V)

Frequency (Hz)

From the From the slope of the slope of the line, Vline, Vthth was was

found. As found. As shown, Vshown, Vthth

also changes also changes with with frequency.frequency.

ResultsResults

Remember that Remember that the predicted and the predicted and ideal behavior of ideal behavior of this curve for this this curve for this particular particular detector is one detector is one that curves in a that curves in a semicircle semicircle manner and does manner and does not have any not have any additional lobs!!!!additional lobs!!!!

Applications of the New Impedance ModelApplications of the New Impedance Model

Now that the behavior of the detector’s Now that the behavior of the detector’s Impedance is known, the thermal conductivities, Impedance is known, the thermal conductivities,

and heat capacities can be determined from and heat capacities can be determined from measurements of the resistance versus measurements of the resistance versus

temperature relationship.temperature relationship.

The lower the Heat CapacityThe lower the Heat Capacity The more the temperature of the The more the temperature of the

detector will change from a given detector will change from a given amount of energy of an X-ray.amount of energy of an X-ray.

The better the signal to noise ratio. The better the signal to noise ratio.

This enables us to adjust the materials that the This enables us to adjust the materials that the

detectors are made from to ensure maximum efficiency detectors are made from to ensure maximum efficiency

RecapRecapWe are able to determine the Thevenin and We are able to determine the Thevenin and

Norton equivalent bias circuits of the Norton equivalent bias circuits of the

microcalorimetermicrocalorimeter by measuring the Voltage by measuring the Voltage

across the circuit. across the circuit. This information can be then used to determine This information can be then used to determine

the impedance of the detectors. This information the impedance of the detectors. This information

can then be used to determine the Heat Capacity can then be used to determine the Heat Capacity

of the detectors.of the detectors.By knowing the Heat Capacity of the detectors, By knowing the Heat Capacity of the detectors,

we are able to optimize the detectors sensitivity. we are able to optimize the detectors sensitivity.

ReferencesReferences J.E. Vaillancourt, J.E. Vaillancourt, Rev. Sci. InstrumRev. Sci. Instrum. . 7676, 043107 , 043107

(2005).(2005). M. A. Linderman, S. Bandler, R. P. Brekosky, J. A. M. A. Linderman, S. Bandler, R. P. Brekosky, J. A.

Chervenak, E. Figueroa-Feliciano, F. M. Chervenak, E. Figueroa-Feliciano, F. M. Finkbeiner, M. J. Li, and C. A. Kibourne, Finkbeiner, M. J. Li, and C. A. Kibourne, Rev. Sci. Rev. Sci. InstrumInstrum. . 7575, 5 (2004)., 5 (2004).

J. J. Brophy, 1990, Basic Electronics for Scientist J. J. Brophy, 1990, Basic Electronics for Scientist (USA:McGraw-Hill, Inc.)(USA:McGraw-Hill, Inc.)

Wikibooks Wikibooks http://en.wikibooks.org/wiki/Electronics:Thevenin/Nhttp://en.wikibooks.org/wiki/Electronics:Thevenin/Norton_Equivalentsorton_Equivalents

A. J. Diefenderfer, B. E. Holton, 1994, Principles of A. J. Diefenderfer, B. E. Holton, 1994, Principles of Electronic InstrumentationElectronic Instrumentation

X-ray Astrophysics, University of Wisconsin X-ray Astrophysics, University of Wisconsin http://wisp11.physics.wisc.edu/xray/xr_microcalorihttp://wisp11.physics.wisc.edu/xray/xr_microcalorimeters.htmmeters.htm

AcknowledgmentsAcknowledgmentsI would like to thank the REU program at I would like to thank the REU program at

University of Wisconsin-Madison. I would also University of Wisconsin-Madison. I would also like to thank my mentor Dan McCammon as like to thank my mentor Dan McCammon as well as Mark Lindeman, and Lindsey Rocks well as Mark Lindeman, and Lindsey Rocks

their help and guidance. their help and guidance.

This work is based upon research conducted at the University of Wisconsin-This work is based upon research conducted at the University of Wisconsin-Madison, which is supported by the NSFMadison, which is supported by the NSF