Indian Journal of Science and Technology, Vol 8(35), DOI: 10.17485/ijst/2015/v8i35/74692, December 2015
ISSN (Print) : 0974-6846
ISSN (Online) : 0974-5645
Overall Noise Analysis for Transisition Edge Sensor at
Optical and Infra-Red Wavelengths
Venkata Naga Vamsi Annepu1* and Annepu Bhujanga Rao2
Department of Electronics and Instrumentation, GITAM University, Visakhapatnam - 530045,
Andhra Pradesh, India; vamsi9441105975@gmail.com
2
Department of instrument technology, Andhra University, Visakhapatnam - 530003,
Andhra Pradesh, India; dr_abrao@yahoo.co.in
1
Abstract
Transition-Edge Sensors (TESs) are the most promising devices as single photon detectors in the visible and infrared
range. In particular ultra-fast TESs with few hundred ns response time and high quantum efficiency find application in different fields like quantum optics, quantum metrology and quantum information. In this work, the main objective is to
measure the noise effect on the performance of the TESs when operated at visible and infrared wavelengths as the TESs
performance depends on the sensor parameters and also on the noise level. The noise analysis is done by experimentally
calculating the noise generated by the different block of the Single quantum interface device and to the TES. We have also
seen from our numerical analysis that the overall noise of the system is 1 × 10−12 nV / Hz . The above estimate is valid for
the low-temperature steady –state biasing conditions of our TES device.
Keywords: Gain of Op-Amp, Photo Detectors, Single Quantum Interference Device, Tank Circuit
1. Introduction
The Transition Edge Sensors (TESs) are the best ­promising
devices for quantum analysis in photon detection in the
optical and infrared range. The full characterization of
such detectors from thermal, electrical and optical point
of view is not so simple as there are only some parameters which are directly measureable. This detector is a
micro calorimeter that working along its superconducting-normal transition, converts the absorbed energy of
the incident photon into electric signal proportional to
the induced resistance change. Mark A. Lindeman et al.1
measured the impedance of the TESs and modeled the
transition edge sensor. Jia Zeng et al.2 analysis of a dc
SQUID readout scheme with voltage feedback circuit.
E. Taralli et al.3 impedance measurement in a bandwidth
up to 1 MHz is only characterized. E. Taralliet al.4 impedance measurement of the TESs at infrared wavelengths
was modeled. E. Taralli et al.5 Impedance measurement
*Author for correspondence
for photon number counting TESs has been reported.
L. Lolli et al.6 high intrinsic energy in transition edge sensors is characterized. I. Haverkamp et al7 optimization
of a digital SQUID magnetometer in terms of noise and
distortion is been reported. P. Khosropanah et al.8 low
noise transition edge sensor for the SAFARI instrument
on SPICA for impedance measurement with low thermal
conductance (G) is reported. This motivates to do overall
noise analysis of the transition edge sensor at optical and
infrared wavelengths.
In this paper we have calculated the noise of the overall TESs theoretically. The noise analysis is done in three
steps. We have first did the noise analysis of the output
section9 (i.e. the SQUID circuit – opamp) and in the
second stage we have calculated the noise10 of the whole
SQUID circuit to determine the flux noise11 vs. the frequency as shown in Figure 1. And the final stage where
the tank circuit with the TESs device is analyzed for the
Overall Noise Analysis for Transisition Edge Sensor at Optical and Infra-Red Wavelengths
calculate the resistor R2 noise for 1kΩ is 400nV / Hz as
the input is a inverting terminal, the resistor R2 is multiplied by -100 and as there is no sense in +Ve or –Ve noise,
we say it to be as 400nV / Hz as show in Figure3.
2.1.2 Current Noise Analysis
Figure 1. Schematic block diagram of RF SQUID ckt
coupled to the Transition Edge Sensor.
noise. The sum of the three stages has given the noise of
the read out circuit.
2. Noise Analysis
The current source of the ADA 4004 op-amp as per the
data sheet is 1.2 pA / hz , which comes through the
resistor R2 to the inverting terminal of the op-amp. The
current multiplies times the parallel combination of the
resistor R2(1KΩ) so we get 1.2nV / Hz and we multiply
it by the gain (101) gives 120nV / Hz as current noise at
the output of the op-amp as show in Figure4.
2.1.3 Voltage Noise of the Amplifier
The voltage source of the ADA 4004 op-amp as per the
data sheet is of 1.8nV / Hz and we multiply it by the
Noise analysis of any circuits has two types of noises
1. Intrinsic noise and 2. Extrinsic noise. The intrinsic
Noise that is caused by the elements of the circuit like
resistors, diodes, transistors and the extrinsic noise is the
power noise along the wires and also from the outside of
the ­circuit.
There are four types of major noise sources and they
are 1. Power system noise. 2. RF interference. 3. Switching
noise. 4. Thermal noise of the circuit components.
2.1. Noise Analysis of Op-Amp ADA4004
The noise analysis of the low noise op-amp 4004 is done
three major noise sources.
Figure 2. ADA 4004 op-amp with noise of 40nV/√Hz at
the 100kΩ resistor.
• Resistor noise.
• Current noise.
• Voltage noise.
2.1.1. Resistor noise of the amplifier
Let us first ground the VIN and the 1kΩ resistor for
­calculating the noise across the output of the op-amp. As
the 1kΩ resistor provides 4nV / Hz of noise by which we
can calculate for 100kΩ resistors noise similarly, which is
40nV / Hz for 100kΩ as shown in the Figure2.
The ADA 4004 op-amp with the 100kΩ and a 1kΩ
resistor puts a total of 101 gain, so the referred output
noise of the resistor R1 is equal to 40nV / Hz . Let us now
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Vol 8 (35) | December 2015 | www.indjst.org
Figure 3. ADA 4004 op-amp with noise of 400nV/√Hz at
the 1kΩ resistor.
Indian Journal of Science and Technology
Venkata Naga Vamsi Annepu and Annepu Bhujanga Rao
DC SQUID device the situation is usually reversed. In
this paper we have calculated the intrinsic noise of a RF
SQUID equipped device. The tiny intrinsic flux noise in
the SQUID is of 1 ∗ 10−30 j / Hz .the intrinsic noise amplitude of the SQUID is proportional to 1 / wrf , where the
transfer co-efficient of the SQUID (i.e. ∂tV_t / ∂φa )is
proportional to wrf . In order to decrease the contribution to the overall noise, the amplifier can be placed close
to the SQUID, losses in the transmission line between
SQUID and room temp electronics do not contribute to
the system noise.
The flux noise in the SQUID is calculated with a 3 GHZ
RF SQUID, as the resonator is a 100- µm wide, 20- mm
long niobium strip on a 1 mm thick sapphire substrate
( εr=10,LT=16Nh). The loaded Q (quality factor) of the resonator is assumed to be 1000. for K 2Q ≈ 1, M ≈ 75 pH thus,
(∂tV_t ) / ∂φa ≈ 9mV / ∅_a across the tank circuit with
RT ≈ 320 KΩ, input impedance Rin ≈ 200 Ω. The ratio thus
is RT/Rin = 1600 resulting in a voltage ratio of 40.thus,a
noise of 70 k √ ( S_v ) ≈ 0.9nV / Hz at 200 Ω and white
noise of 4 × 106 ∅0 / Hz results. There are two parameters which could be varied (Q and LT), we could improve
Q further by reducing losses in the substrate and radiation
losses, and vary LT by changing the width of the resonator.
This applies well when the energy transfer from SQUID
to the amplifier occurs at K 2Q = 1 , as show in Figure6.
Figure 4. The ADA 4004 op-amp with current noise of
120 nV/√Hz.
(
Figure 5. ADA 4004 op-amp with noise of 400nV/√Hz at
the 1kΩ resistor.
gain (101) and we get a voltage noise of 120nV / Hz as
show in the Figure5.
Thus the total noise generated by the op-amp is the
sum of the three noises and it is given by squaring all the
noises and taking the square root of it.
Total noise of the op-amp is = √ (R1noise)2 + (R2noise)2 +
(current noise)2 +(voltage noise)2
Total noise of the amplifier =
 40nV / √ Hz


(
2
2
2
) + ( 400nV / √ Hz ) + (120nV / √ Hz ) + (182nV / √ Hz )
2



≈ 457nV / Hz
3. Noise Analysis of SQUID Circuit
In RF SQUID external circuit noise is almost always
much more important than its intrinsic noise and for a
Vol 8 (35) | December 2015 | www.indjst.org
)
4. Noise Analysis of the Tank
Circuit
The noise in the tank circuit is determined in three stages,
in the first stage the current noise of the input current
biasing is to be calculated and then in the second stage
we calculate the impedance resistance noise and the TES
resistance noise and in the third stage we calculate the flux
noise of the tank circuit (intrinsic flux noise) thus by summing the noises we get the total noise of the tank circuit.
4.1 The Current Noise
The tank circuit is biased by a current biasing system,
so when we calculate the current noise we ground the
input and outputs. The current noise of the circuit is
1.2pA / Hz as show in the Figure 6.
4.2 The Resistor Noise
The resistor noise is calculated for both resistors i.e.
for 200 Ω and the Transition edge sensor resistance
Indian Journal of Science and Technology
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Overall Noise Analysis for Transisition Edge Sensor at Optical and Infra-Red Wavelengths
Total noise of the tank circuit is equal to the sum of the
noises in tank circuit.
(1.2 pA / Hz )2 + (1280nV / Hz )2 + (1015 )2 = total noise
of the tank circuit
1 × 10−12 nV / Hz
5. Conclusion
The total noise of the system is calculated by taking the
noise generated by the amplifier, the RF SQUID circuit,
the tank circuit. Hence by calculation of the total noise of
the TESs with the SQUID circuit we get 1 × 10−12 nV / Hz
of noise in the system. The dependence of the TES resistance on current must be included in the model to fit the
noise calculations in experimental analysis of the overall
noise for the system under test. Our analysis of the above
experiment is now in progress.
Figure 6. Tank circuit with current noise of 1.2 pA/√Hz.
Figure 7. Resistor noise of 1280 nV/√Hz in the tank
circuit.
(RT) = 320 KΩ as shown in the Figure 7. The calculation is
similar to that of the resistor noise calculation in section
2.1.1. Thus the noise generated for 320KΩ resistor will
be 1280nV / Hz .
4.3 The Flux Noise
The flux noise of the tank circuit (intrinsic flux noise) is
equal to 1 × 10−30 J / Hz thus, the noise amplitude of the
tank circuit is proportional to 1/ wrf .
So the flux noise is = 1 / 1 × 10−30 J / Hz
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6. References
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Indian Journal of Science and Technology
Venkata Naga Vamsi Annepu and Annepu Bhujanga Rao
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