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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