26
Low noise measurement of photocurrent in IR photodiodes for continuous glucose monitoring
D. W. Cooley1,a), David R. Andersen1,2,b), and Jonathon T. Olesberg3,4
1Department of Electrical and Computer Engineering2Department of Physics and Astronomy3Department of Chemistry4Optical Science and Technology Center
The University of Iowa
Iowa City, Iowa 52242
a)Electronic mail: [email protected])Electronic mail: [email protected]
ABSTRACT
We have developed a data acquisition unit (DAU) for continuous, low noise measurement of glucose
concentration in subcutaneous interstitial fluid (ISF). The system is comprised of a specialized glucose
sensor1, analog circuitry for signal conditioning, and delta-sigma ( - ) analog to digital converters� �
(ADCs). The glucose sensor has two infrared (IR) LEDs designed to emit light in the 2.2 to 2.4 m�
wavelength range where glucose has absorption features that allow concentration measurement. The IR
light propagates through a glass fluid chamber containing ISF, propagates through a linearly variable
bandpass filter, and impinges on a 32 channel photodiode (PD) array. The center wavelength of the
linearly variable filter is graded along one dimension of the filter so that each element of the
photodiode array is sensitive to a different wavelength. Transimpedance amplifiers (TIAs) convert the
photodiode photocurrents into voltages that are sampled by the ADCs. The ADC serial data busses are
daisy chained together and the ADC samples are sent via the serial bus to a computer system that
archives the data for further processing. We developed a noise model that predicts the noise
characteristics of the system. In this paper we use low noise metal film resistors to verify the DAU
noise characteristics in preparation for future use with glucose sensors. A high signal-to-noise ratio
(SNR) is needed to accurately quantify the concentration of glucose in ISF. The SNR available is
limited by the low radiative power available at the photodiodes and the low impedance of the
photodiodes (RPD). The noise model we developed shows that the system operates in a region where the
1
SNR is proportional to the square root of RPD. Even with these difficulties the data acquisition unit
provides low noise (41.7 dB SNR) measurements which compare well with the thermal noise limit of
the system and are suitable for use in a continuous glucose monitoring system.
2
I. INTRODUCTION
We have designed and demonstrated a data acquisition unit (DAU) capable of performing
continuous, low noise measurement of glucose concentration in subcutaneous ISF. This paper discusses
the design of circuitry for utilizing prototype glucose sensors to measure the glucose concentration in
ISF with maximum SNR. In the future the glucose sensor and DAU will be miniaturized for use in an
implantable, continuous glucose monitor. The motivation for this research is clear as 23.8 million
people in the USA had diabetes as of 20072. Self monitoring of blood glucose (SMBG) is one
important method used to control diabetes3,4. Efforts towards continuous monitoring of blood glucose
are under way to prevent high and low blood sugar conditions and to use as part of an artificial
pancreas offering a type of "cure" for diabetes4. The measurement method developed in this research
measures the glucose concentration in ISF instead of whole blood. Measuring glucose concentration in
ISF is equally valid as using blood samples5,6. Using ISF to measure glucose concentration also has
several advantages when compared to testing whole blood. Measuring ISF glucose by an implanted
device is less painful and less invasive than repeated use of finger-sticks to measure blood glucose
concentration6. An implantable glucose monitor would also require limited user intervention and not
require the cost of materials required for SMBG with finger-sticks1.
The glucose sensor measures the absorption spectrum of glucose in ISF by passing IR light
through a fluid chamber containing ISF. A linearly variable bandpass filter and a 32 element
photodiode array form a spectrometer to measure the absorption spectrum. Two IR LEDs are utilized in
the sensor. The LEDs were designed to emit light in the range of 2.2 to 2.4 m where there are three�
peaks in the glucose absorption spectrum. Due to qualities of the photodiode I-V curves the
photodiodes may not be reverse biased. Reverse biasing is often used with Si photodiodes to improve
the diode temporal response. The IR photodiodes have lower photocurrent due to limited amounts of
LED light reaching the linearly variable filter and the limited amount of luminous power transmitted
3
through the filter to each photodiode. The shunt resistance, RPD, of the photodiodes is relatively low
which limits the system SNR. The goal of this research is to maximize the SNR of the measurement
despite these limitations. The DAU must measure the photocurrent from the photodiodes and provide
low noise glucose measurements at a frequency of 1 Hz on a continuous basis. The prototype sensors
are mounted to a 40 pin DIP header. Low noise metal film resistors are used to simulate the glucose
sensor while evaluating noise characteristics of the DAU.
The remainder of this paper is organized as follows. Section II discusses the theory of sensor
operation, noise model, and circuit design. Section III contains details of experimental methods and
results. Section IV discusses additional sources of noise that will be present when testing actual
photodiodes and Section V concludes the paper.
II. THEORY
A. Glucose Sensor
Fig. 1 shows a diagram of the glucose sensor. The sensor has two IR LEDs: LED1 and LED2.
LED1 emits light that flows through the ISF sample in a fluid chamber, through the linearly variable
filter, and impinges on the 32 channel photodiode array. LED1 is mounted to the fluid chamber and
uses back-side geometry so that light is emitted directly into the fluid chamber. The LEDs emit IR light
in the range of 2.2 to 2.4 µm, near three peaks in the glucose absorption spectrum. The fluid chamber is
a thin-walled capillary with square cross section and 0.8 mm inner dimensions. The center wavelength
of the linearly variable bandpass filter changes along the length of the filter within the 2.2 to 2.4 µm
wavelength range. Thus each photodiode collects light from a different portion of the glucose
absorption spectrum when LED1 is on. As IR light from LED1 propagates through the ISF sample,
glucose absorbs a portion of the light near the peaks in the glucose absorption spectrum. Light from
LED2 does not pass through the analyte on its way to the photodiodes and photocurrent measurements
from LED2 are necessary to normalize and compensate the sensor data for temperature changes. We
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need measurements of the photocurrent with both LEDs off, LED1 on only, and LED2 on only to
calculate the glucose concentration when the glucose sensor is used. To verify the DAU noise
characteristics in preparation for use with glucose sensors we use low noise metal film resistors with
resistance equal to the photodiode shunt resistance in place of the photodiodes. We will determine
whether the DAU has sufficiently high SNR for use with the glucose sensor by evaluating the SNR
results with the resistors. A mathematical model for the noise present in the DAU analog circuitry must
be developed to evaluate the SNR performance.
B. Noise Model
1. Transimpedance Amplifier Issues
Two types of noise that affect the system operation are thermal noise and shot noise7. The
random motion of charge carriers in a conductor causes thermal noise, also known as Johnson noise.
The thermal noise voltage of a resistor R is in series with that resistor and is
f4kTRET ∆= , (1)
where k is Boltzmann's constant, T is temperature in Kelvin, and f is the measurement bandwidth.�
The series combination of the resistor and its thermal noise voltage may be converted into a current
source of value ET/R in parallel with the resistor. Shot noise occurs in transistors and diodes and is due
to the quantization of current flow across a potential barrier. The shot noise current for I amps of
current is
f2qIIS ∆= , (2)
where q is the electronic charge. Two uncorrelated noise sources, VA and VB, are added incoherently:
2
B
2
A VVV += . (3)
We chose the transimpedance amplifier, Fig. 2, to convert photodiode current into a voltage for
measurement by an ADC. Another method would be to use a current input ADC, but we chose the TIA
in order to maximize the system SNR8. We also developed a noise model to check the noise
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performance of the TIA. To develop the noise model we start with a schematic for the TIA including
op amp noise terms9 as shown in Fig. 3. Here ENI is the op amp input noise voltage, IBI is the op amp
input current noise, RT is the resistor simulating the photodiode shunt resistance, IRT is the noise current
equivalent to the thermal noise from RT, RF is the feedback resistor, and ERT is the feedback resistor
thermal noise. We omitted the photodiode series resistance from the noise model because of its
relatively small magnitude. We find an expression for the noise at the TIA output by incoherently
adding the noise terms (ENI, IBI, IRT, and ERF) multiplied by the gain between the noise term and the TIA
output. With GN = 1 + RF /RT and combining some terms, the noise voltage at the TIA output is10
( ) ( ) NF
2
FBI
2
NNIO G4kTRRIGEE ++= . (4)
Including a term for the ADC noise voltage, V� ADC, and the voltage reference noise, V� REF, in Eq. 4 we
find a noise model for the TIA:
( ) ( ) 2REF
2ADCNF
2FBI
2NNIO V/NVG4kTRRIGEE ∆+∆+++= , (5)
where N ADC samples are averaged per data point. Fig. 4 is a plot of the SNR for this noise model
versus RT. Initially we recorded experimental data using N = 100 and N = 250 in Eq. 5. We noted that
using N = 250 provided a slightly better SNR and chose N = 250 for all subsequent experiments. The
system can record a maximum of 255 samples without overflow errors so we chose N = 250 to prevent
overflow.
We calculate the SNR of the noise model using the expression
( )OFPC10 E/RIlog10SNR = , (6)
where IPC is the photocurrent and RF is the feedback resistor. One multiplies the logarithm in Eq. 6 by
10 instead of 20 when calculating the SNR because the photocurrent is proportional to the luminosity
of light arriving at the photodiode and luminosity is luminous power per unit area. From our
experimental results, IPC is typically 10 nA. We chose a value of 10 M for R� F in order to yield a signal
6
voltage of 0.1 V that is within the input range of the ADC. To calculate the SNR of an experimental
data set replace EO in Eq. 6 with the standard deviation of the data set, .�
The graph of the noise model has three straight segments and a different term from Eq. 5 is
dominant in each segment. The left segment has a slope proportional to 1/RT and is due to the ENI term
in Eq. 5. As ENI increases the left segment of the curve will shift down. Here RT is approximately 30 k�
and if ENI is too large the left segment will drop down and meet the second segment where RT = 30 k ,�
degrading the SNR. The middle segment has a slope proportional to TR1 and is due to the third
term, the thermal noise. An increase in thermal noise will reduce the SNR in the middle segment. The
middle section of the curve also shows that increasing RT increases the SNR. The final, flat section
arises from the combination of noise from thermal noise of the feedback resistor (ERF), input current
noise (IBI), V� ADC, and V� REF. Calculating these noise voltages with our final component values shows
that ERF = 0.41 V, I� BIRF = 5.0 nV, N/V� ADC = 0.35 V, and V� � REF = 1.5 V. Therefore the voltage�
reference noise provides the SNR limit within the right segment of Fig. 4. If RF or the ADC noise
increases enough to be comparable to V� REF the SNR will be reduced in the right segment of the noise
model.
2. Photodiode Issues
The IR photodiode I-V characteristic differs from typical Si photodiode characteristic curves in
several ways. Fig. 5 shows a typical I-V characteristic curve for the IR photodiodes near the origin. The
IR photodiodes have lower reverse breakdown voltage, higher reverse saturation current, lower shunt
resistance, and, when operating as part of the glucose sensor, lower photocurrent than typical Si
photodiodes. For example the IR photodiodes have reverse breakdown of 1 to 2 volts and reverse
saturation current of approximately 100 A. When used in a more typical application, the S1133 has a�
maximum reverse voltage of 10V and dark current of 15 pA at 10V reverse voltage11. Since
photocurrent flows from the diode in the reverse direction, photocurrent pushes the I-V curve below the
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dark current curve by an amount equal to the photocurrent. Because of the low radiant powers available
in the sensor, the photocurrent from each photodiode is small, approximately 10 nA. This results in
reduced signal voltage from the TIA as determined by the load line through the I-V origin, limiting the
SNR. The relatively small photocurrent in this case drastically reduces the achievable SNR when
compared to typical Si photodiodes. For example in a more typical application the S1133 Si photodiode
can provide 100 A of output current� 11, 10,000 times more current than our IR photodiodes when
installed in the sensor.
Our IR photodiodes have shunt resistance of approximately 30 k . The S1133 shunt resistance�
is typically 100 G�11, much greater than the IR photodiode shunt resistance. This also increases the
difficulty in obtaining high SNR since the thermal noise is proportional to the amplifier gain, 1 + RF/RT.
A decrease in shunt resistance, RT, increases the thermal noise, reducing the SNR. The low shunt
resistance is due to the increased wavelength of the IR photodiodes relative to silicon diodes. To prove
this we find the relationship between wavelength and shunt resistance. When the photon has energy
equal to the bandgap energy,
gap
GapE
hc
f
c==λ . (7)
The reverse saturation current of a diode is given by12
+=
DP
2iP
AN
2iN
oNL
nD
NL
nDqAI . (8)
For the IR photodiodes DA NN ≈ , so Eq. 8 becomes
+=
P
P
N
N
A
2i
0L
D
L
D
N
qAnI . (9)
Under equilibrium, degenerate conditions12,
⋅==
2i
DABIGap
n
NNlnkTqVE . (10)
8
Solving Eq. 10 for 2in we find
kT/E
DA2i
GapeNNn−= . (11)
Substituting Eq. 11 into Eq. 9 shows
kT/E
P
P
N
NDo
GapeL
D
L
DqANI
−
+= . (12)
Now we note that the slope of the ideal diode equation,
( )1eII kT/qV0 −= , (13)
at the origin is 1/RShunt or 1/RT. Differentiating Eq. 13 with respect to voltage we find
qI
kTRR
0
TShunt == . (14)
Since Si,Gapλ = 1.1 m for Si diodes and the target wavelength for the IR diodes is � IR,Gapλ = 2.5 m,�
IR,Gapλ = (2.5/1.1) Si,Gapλ . (15)
From equation 7 the gap energy of the IR photodiode is less than half that of the silicon diode. The
reverse saturation current of the IR diode, Eq. 12, is exponentially larger than that of the silicon diode.
Eq. 14 shows that the increase in reverse saturation current drastically reduces the shunt resistance of
our IR photodiodes relative to Si photodiodes due to the increase of Gapλ from 1.1 to 2.5 m.�
The high reverse saturation current seen in the I-V curve of the IR PDs (Fig. 5) shows that they
cannot be reverse biased. Reverse bias would generate significant dark current and shot noise from that
dark current would dominate the other noise sources and degrade the SNR. Also, since the dark current
increases with more reverse bias while the photocurrent remains constant, a smaller portion of the
current flowing into the TIA would be due to the photocurrent, reducing the SNR.
C. Circuit Design
A block diagram of the DAU is shown in Fig. 6. Power conditioning circuitry filters and
generates several voltages for the LED drivers and analog and digital circuitry. LED drivers control the
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two LEDs in the glucose sensor. Four photodiode channels are connected to each of the eight quad op
amps configured as TIAs. We chose eight channel ADCs, so we require four ADCs to sample all 32
channels. Timing signals from the PC control operation of the ADCs. A low noise voltage reference is
provided to the ADCs. The serial ports of the ADCs are daisy chained so that all sample data is sent to
the PC.
Fig. 7 shows the circuit design used for each channel of the photodiode array. We compared
noise performance of several op amps by combining shot noise on the offset current, op amp input
current noise, and op amp voltage noise in order to select an op amp for the TIA. Here the offset
current is the sum of the op amp input offset current and the current in RPD due to the op amp offset
voltage. We included shot noise on the offset current since the source of the photodiode current is a
diode junction. We chose the MAX447813 because it minimized the sum of these noise voltages.
The chief factors affecting choice of the ADC are the resolution, number of delta-sigma ( - )� �
blocks in the device, ability to daisy-chain serial data ports of devices, and conversion time. We chose a
24-bit - ADC with 8 channels, � � 8 - blocks, and maximum sampling rate of 52.7 kHz when using� �
high resolution mode14. Four ADCs are necessary to sample all 32 channels simultaneously. We need a
minimum of 20 bit ADC resolution to keep the quantization error well below the system noise. Having
more - blocks in the ADC utilizes time more efficiently allowing a faster overall sampling rate.� �
Since there is one - block for each photodiode channel multiplexing ADCs is unnecessary, allowing� �
time efficiency and simplifying the software required to archive data. The serial ports of the ADC we
chose can be daisy-chained which also simplifies the system because only one serial port is required.
We need to record four types of samples to calculate the glucose concentration: with LED 1 on/LED2
off, both LEDs off, LED1 off/LED2 on, and both LEDs off. Since we sample all channels
simultaneously, recording 4 types of data samples 250 times a second requires a sampling rate of 1
kHz, well below the ADS1278 maximum sample rate. We selected a low noise voltage reference with
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noise voltage of 1.5 V and a low temperature coefficient of 0.6 PPM/deg. C.� 15
III. EXPERIMENT AND RESULTS
Fig. 8 shows the method we use to record experimental data. The time per data point, TData, is 1
second and N = 250 so that TSample = 1/250 second. The DAU samples the voltage on all channels at
points labeled Sn. At points labeled Dm the average value of the samples for channel m are calculated
using the expression
∑=
=N
n
nm SN
D1
1, (16)
where Sn are samples from channel m and Dm is the resulting data point. We display and record each
data point with a PC for further analysis. When we use the glucose sensor the four types of data
mentioned above must be recorded in each sample period to calculate the glucose concentration. While
verifying the SNR of the DAU system in this paper we utilize low noise resistors and only one of the
four types of data is required since there are no LEDs present without the glucose sensor.
To test the SNR we record a large (>1k data points) set of experimental data and calculate the
SNR as in Eq. 6. Fig. 9 shows a plot of channel voltage vs. time for a representative channel. Fig. 9
shows 2000 data points from channel 1 taken at a rate of 1 Hz � the last 1000 data points were used to
calculate the SNR. The plot shows +/- 10 µV noise superimposed on top of 20 µV of drift. We
calculate the SNR using the last 1000 data points to allow the temperature of the components to
stabilize. The standard deviation of this portion of data is 9.12 V and the SNR for channel 1 is�
calculated to be 40.4 dB. Fig. 10 shows the SNR for all 32 channels. The mean SNR is 41.7 dB and the
standard deviation of the SNR is 2.0 dB. Channels 15 and 31 do have 5 to 7 dB more noise than the
other channels. This may be due to slight differences in noise characteristics of the op amps. Fig. 11
compares thermal noise, the noise model, and experimental data for RT values of 30 k and an open�
circuit. We use 1E+9 for the value of open circuit resistance since theoretically an open circuit has�
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infinite resistance. We show thermal noise in Fig. 11 to indicate the maximum SNR possible if the op
amps, ADCs, and voltage reference were ideal components. The experimental results are within one
standard deviation of both the expected noise and thermal noise for RT = 30 k but the experimental�
result with an open circuit for RT is 45.4 dB with standard deviation 0.6 dB and the noise model
predicts 48.0 dB. This discrepancy has been traced to excess ripple voltage on the power supply line to
the voltage reference IC.
IV. DISCUSSION
The experimental measurements of SNR agree very well with the noise model for the TIA. The
experimental result for RT = 30 k is also very close to the thermal noise limit, i.e., it is the maximum�
SNR possible with this TIA design and RT of 30 k . This indicates the DAU is acceptable for use with�
prototype glucose sensors and for future miniaturization of the DAU system and glucose sensor.
A fan cooled the DAU to reduce the effects of thermal drift during our experiments. This is
reasonable here since when the DAU and glucose sensor are designed into an implantable device the
system will be in an environment with constant temperature.
Although thermal noise limits the DAU SNR when using low noise metal film test resistors,
additional noise sources will be present when using actual glucose sensors with the DAU. The
photocurrent and dark current would both provide shot noise since they originate from a diode junction.
In order to eliminate shot noise from dark current the photodiodes cannot be reverse biased. The shot
noise from 10 nA of photocurrent is 57 fA. The voltage created by this current passing through RF is
0.57 µV. The mean SNR of 41.7 dB corresponds to 6.76 µV of noise voltage. Adding these two noise
voltages still results in 41.7 dB SNR so the shot noise on the photocurrent will not significantly degrade
the SNR.
V. CONCLUSION
The DAU circuit design has acceptably large SNR (41.7 dB) to be used for testing prototype
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glucose sensors as well as to be miniaturized for use in an implantable, continuous glucose monitoring
system. The DAU was designed using TIAs and - ADCs to measure the photocurrents from a 32� �
photodiode array in a specialized glucose sensor. A noise model was developed for the DAU and
experimental data verified that the system works as expected by theory. In the future the DAU will be
used with glucose sensors to study absorption spectra of glucose solutions. We also plan studies using
ISF with the glucose sensors before miniaturization of the sensor and DAU electronics into an
implantable glucose monitoring system. The shot noise on the photocurrent will not significantly
degrade the system noise characteristics when glucose sensors are used.
ACKNOWLEDGEMENTS
The authors would like to acknowledge support from NIH Grant No. DK064569.
REFERENCES
1 J. T. Olesberg, C. Cao, J. R. Yager, J. P. Prineas, C. Coretsopoulos, M. A. Arnold, L. J. Olafsen, and
M. Santilli, Proc. of SPIE 694, 609403, (2006).
2 "National Diabetes Fact Sheet, 2007", Department of Health and Human Services - Centers for
Disease Control and Prevention (www.cdc.gov).
3 C. D. Saudek, R. L. Derr, and R. R. Kalyani, JAMA 295 No. 14 p. 1688 (2006).
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277 p. 561 (1999).
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7 C. D. Motchenbacher and J. A. Connelly, Low-Noise Electronic System Design, (John Wiley and
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8 K. S. Kanukurthy, �Wireless controller for a near infrared multi-channel optical glucose sensor,� PhD
thesis, The University of Iowa, Iowa City, IA, 2007.
13
9 Application Report SBOA066A, "Noise Analysis for High-Speed Op Amps,� (www.ti.com).
10 Equation 2 from Ref. 9 with RS = 0.
11 S1133 datasheet (www.hamamatsu.com).
12 R. F. Pierret, Semiconductor Device Fundamentals, (Addison-Wesley, Reading 1996).
13 MAX4478 datasheet (www.maxim-ic.com).
14 ADS1278 datasheet (www.ti.com).
15 VRE3025 datasheet (www.cirrus.com).
14
FIGURE CAPTIONS
FIG. 1. Drawing of glucose sensor. Light from LED1 is transmitted directly through the fluid chamber
to the photodiodes and light from LED2 goes around the fluid chamber.
FIG. 2. Transimpedance amplifier schematic.
FIG. 3. Schematic of transimpedance amplifier noise model.
FIG. 4. Expected SNR vs. RT for 250 samples averaged per data point.
FIG. 5. Chart of IR photodiode I-V characteristic curves with load line. Dark current and I-V curve for
10 nA of photocurrent are shown with load lines using zero and negative bias.
FIG. 6. Block diagram of the DAU.
FIG. 7. Schematic of one photodiode channel using low noise metal film resistors.
FIG. 8. Method for recording experimental data. Samples are recorded at Sn and data points are
calculated at Dn.
FIG. 9. Channel voltage vs. time for channel 1. 2000 data points or 33.3 minutes of data are shown.
FIG. 10. Chart of SNR vs. channel for all 32 channels.
FIG. 11. Experimental and expected SNR vs RT. A plot of thermal noise is shown for comparison.
15
FIGURES
FIG. 1. Drawing of glucose sensor. Light from LED1 is transmitted directly through the fluid chamber
to the photodiodes and light from LED2 goes around the fluid chamber.
16
FIG. 2. Transimpedance amplifier schematic.
17
FIG. 3. Schematic of transimpedance amplifier noise model.
18
FIG. 4. Expected SNR vs. RT for 250 samples averaged per data point.
19
FIG. 5. Chart of IR photodiode I-V characteristic curves with load line. Dark current and I-V curve for
10 nA of photocurrent are shown with load lines using zero and negative bias.
20
FIG. 6. (Color online) Block diagram of the DAU.
21
FIG. 7. Schematic of one photodiode channel using low noise metal film resistors.
22
FIG. 8. Method for recording experimental data. Samples are recorded at Sn and data points are
calculated at Dn.
23
FIG. 9. Channel voltage vs. time for channel 1. 2000 data points or 33.3 minutes of data are shown.
24
FIG. 10. Chart of SNR vs. channel for all 32 channels.
25
FIG. 11. Experimental and expected SNR vs RT. A plot of thermal noise is shown for comparison.
26
