Wide Input Range 1.7µW 1.2kS/s Resistive Sensor Interface Circuit with 1 cycle/sample Logarithmic Sub-Ranging
Myungjoon Choi, Junhua Gu, David Blaauw, Dennis Sylvester
University of Michigan, Ann Arbor, MI, myungjun@umich.edu
Abstract
A wide input range 1.7µW, 1.2kS/s resistive sensor interface circuit
fabricated in 0.18µm CMOS is presented. This circuit consumes 6.6×
lower power and 31.8× less energy than previous state-of-the-art
work, considering the worst-case cycle count required for correct
conversion. The proposed design uses a logarithmic subrange detector
based on comparator metastability to convert an input resistance
ranging from 10kΩ to 10MΩ in 1 cycle/sample.
Introduction
Resistive sensing is widely used in chemical [1], gas [2], and
pressure sensing [3], with applications in implantable and
point-of-care diagnostics among others. Sensor interface circuits for
these systems are challenging due to the wide input resistance (RIN)
range (kΩ to MΩ) and µW power constraint to achieve long battery
life. In a resistance-to-digital converter (RDC), RIN is first converted
to a voltage VIN, then measured by an ADC (Fig. 1). The resistance to
voltage conversion is performed by connecting the input resistor to a
fixed current source. However, accommodating a high RIN range
results in one of two issues: the ADC input voltage will saturate at
high RIN or an extremely high resolution ADC is required to sense low
RIN that produce very small voltages. Hence, a common approach is to
divide the RIN range into sub-ranges and apply different currents for
each sub-range using a current DAC (I-DAC) [1,5,6]. This technique
greatly increases accuracy across the total RIN range (Fig. 1).
A key challenge in sub-ranging RDCs is finding the correct
sub-range. Typically, the RDC starts with an arbitrary sub-range,
performs a complete conversion (including ADC step), and examines
the resulting code. If this code is out of range, the sub-range is changed
(±1 step) and the process repeats until the correct sub-range is found
[1,4]. This requires worst-case N iterations to obtain the correct code for
2N-1 sub-ranges, increasing energy and slowing the sampling rate.
To address this issue, we propose a new sub-ranging RDC that
finds the correct sub-range within 1 sampling cycle using a novel
logarithmic converter. We also note that the energy consumed by the
I-DAC is a major portion of total energy consumption. This work
minimizes I-DAC energy by dynamically adjusting its on-time
according to the sub-range setting, whereas previous RDCs enable the
I-DAC for the worst-case stabilization time. In addition, a switched
capacitor (SC) amplifier is inserted prior to the ADC; it improves
ADC resolution and reduces energy via shorter VIN settling time. The
proposed design consumes 1.7µW. It reduces energy per conversion
by 31.8× compared to current state-of-the-art RDCs [1,2,4] and
achieves 1000× RIN range with 0.21% measurement error.
Logarithmic Sub-Range Detector
Fig. 2 shows the logarithmic sub-range detector. The full RIN range
is divided into sub-ranges that increase in geometric fashion. Hence,
the correct sub-range is found by taking the log of RIN. To implement
this log function, we use the intrinsic behavior of a comparator
operating near its metastable point. RIN is first converted to VIN by the
I-DAC, sampled on CSAMPLE and shifted up by VREF to position both VL
and VR at the metastable point. At this point, φ2 switches are opened
and a cross-coupled inverter pair starts to resolve VL and VR. If VIN is
large, VL (VR) resolves to 1.2V (0V) quickly, while this resolution time
increases exponentially as VIN becomes smaller. The subsequent
inverter chains and XOR output 0 and stop the counter when VR
becomes lower than VDDL/2 (mathematical analysis in Fig. 2). The
proposed log converter determines the correct sub-range in one
comparison, enabling 1 cycle/sample operation. To remove the effect
of charge injection, the voltage transfer circuit uses bottom-plate
sampling and the SC structure uses stray-capacitance insensitive
topology. Auto-zeroing is also adopted for offset cancellation,
resulting in offset of σ=0.24mV (40× smaller than without
auto-zeroing, simulation). Across process corners, comparator gain is
one-point calibrated to maintain a consistent code range.
Resistance to Digital Conversion
After the correct sub-range is found for a particular RIN, the
corresponding I-DAC current is selected and VIN is generated from the
resulting IR drop (Fig. 3). VIN is transferred to VOUT+ and VOUT- (with
opposite sensitivities to VCM) via two SC amplifiers and then digitized
by a 10-bit SAR ADC. The SC amplifiers are used for three reasons:
1) they perform pseudo-differential sampling to cancel out
common-mode voltage; 2) they increase usable ADC output range by
SC amplifier gain and thus enhance resolution by 1.98×; 3) they
decouple the large capacitor DAC (CDAC+, CDAC-) from the RIN. If the
large CDAC is used as the sampling capacitor, the I-DAC must remain
on for a longer time due to the large RC time constant. By sampling
with the smaller CSAMPLE+,- (1pF) and charging CDAC+,- (9.3pF) in a
different phase, energy is reduced by 7.7× compared to an approach
where CDAC+,- is used as the sampling capacitors.
Fig. 4 shows the flow chart of the RDC conversion process. First, a
300nA current (IINITIAL) is applied to the unknown RIN and the resulting
IINITIAL×RIN is sampled. This IINITIAL is chosen to map the entire RIN
range (10kΩ – 10MΩ) to the log converter’s operating range. The log
converter then produces a counter value that is compared to 4 threshold
values to determine 4 coarse sub-ranges. According to the coarse
sub-range, a second current (6.4µA, 1.6µA, 0.4µA, or 0.1µA) is
activated on the I-DAC resulting in an ICOARSE×RIN spanning
50−800mV in each coarse sub-range. The same procedure repeats to
divide each coarse sub-range into 5 fine sub-ranges, yielding 14
possible sub-ranges. Sub-ranges overlap to guarantee correct
conversion for the entire RIN range. Each of the 14 fine sub-ranges
specifies an I-DAC setting that ensures IFINE×RIN lies in the SC
amplifier operating range. This voltage is then pseudo-differentially
sampled and converted into a digital code by the 10b SAR ADC. Also,
each fine sub-range specifies a sampling time, minimizing I-DAC
activation time and reducing worst-case power consumption by 21%.
Finally, recall that in the proposed RDC, sub-range determination is
performed every conversion cycle, in contrast to traditional RDCs that
can require multiple cycles to determine the correct sub-range.
Measurement Results
Fig. 5 shows measured log converter counter values at different VIN.
Because the converter is based on metastability, it is susceptible to
noise and hence ±1σ curves are shown. Each sub-range overlaps with
its adjacent sub-ranges to provide error tolerance and ensure the
probability of a sub-ranging failure (i.e., RIN falls outside a correct
sub-range) to be < 3.2σ probability for sub-range 1 and < 5σ
probability for sub-ranges 2 − 4. The worst-case measurement error is
0.21%. Off-chip 0.01% precision resistors are used to measure
accuracy and the resistor bottom node voltage is swept with a
sourcemeter to obtain additional equivalent resistances. The error
pattern reflects repeated error behavior in each sub-range. A 10b ADC
with SC amplifier shows DNL of +0.37/-0.56LSB and INL of +0.93/
-1.48LSB. The SC amplifier slightly degrades INL but improves
resolution by 1.98×, resulting in better accuracy overall. At the
minimum input resistance, the circuit consumes its maximum 1.7µW
at a sampling rate of 1.2kS/s. Power consumption is 6.6× smaller than
the state-of-the-art work in [4]. Table 1 compares the RDC with prior
work showing large resistive range and similar conversion rate while
worst-case energy/conversion is reduced by ~31.8×. A resistive CdS
light sensor was successfully measured with the RDC (Fig. 6). Total
design area is 1.5×0.82mm2 in 0.18µm CMOS (Fig. 7).
References
[1] Taeg Sang Cho, et al., JSSC, Feb. 2009.
[2] Grassi, M., et al., JSSC, Mar. 2007.
[3] Rong Wu, et al., ISSCC, 2011.
[4] Hyunsoo Ha, et al., CICC, 2012.
[5] Xiaoyi Mu, et al., ISCAS, 2011.
[6] A. Lombardi, et al., Sensors and Actuators B 142, 2009.
Previous
Sample
UP or DOWN (±1 step)
VIN = II-DAC × RIN
MULTI-STEP control signal
RIN
y = log(VIN)
VIN
R to V
Converter
Scale
2VIN
VREF
ADC
Digital
code
Switched
Cap. Amp.
Logarithmic
Sub-range Detector
× 1 cycle/sample
Φ1
Φ1Φ1
Φ2'
VR
VREF+VIN
VREF
Counter
Φ1
VDDL = 0.6V
VREF VREF
Stray-capacitance
insensitive / Autozeroing voltage
transfer
(VIN → VIN + VREF)
CLK
Logarithmic voltage
to time converter
based on
metastability
Count
duration of
metastable
state
Detect end of
metastable
state
VL
Stop Counter
& Read Code
VDDL/2
VR
Simulated
50
100
150
Time (µs)
200
250
TT
FF
FS
SF
SS
300
250
200
150
100
Simulated
1
10
VIN (mV)
100
VR(t)–VL(t) = (VR,initial–VL,initial) × exp(αt), with α = gm/C – 1/RC
Counter records when, VR(t)-VL(t) = -VDDL , count×clock period = α-1(log(VDDL)-log(VL,initial–VR,initial))
Fig. 2. A logarithmic voltage-to-time converter based on comparator metastability resolution time, and its transient voltage behavior and sub-ranging
code output vs. VIN.
Φ1
CSAMPLEΦ1
VCM
Φ1'
Φ2
Φ2'
Φ2
VOUTΦ1
0.0
-0.5
-1.0
-1.5
Simulated
0.0
0.2
0.4
0.6
VIN(V)
0.8
1.0
ADC Output Code
VOUT+ - VOUT- (V)
0.5
VOUT- (= VREF2+VCM –VIN)
VDDH
CDACVCM
GND
800
400
50
0.4
0.2
0.0
-0.2
-0.4
-0.6
200 300 400 500 600 700 800 900
40
30
20
10
0
100
10
0.20
0.15
0.10
0.05
0.00
-0.05
-0.10
-0.15
-0.20
VIN (mV)
Code
1.0
0.5
0.0
-0.5
-1.0
-1.5
200 300 400 500 600 700 800 900
Code
100
10
1,000
10,000
Input Resistance (kΩ)
100
300
1000
100
90
80
70
60
50
40
30
20
10
Illuminance (Lux)
Room light condition
0
1000
2000
3000
Time (ms)
0.0
0.2
0.4
0.6
0.8
VIN(V)
5000
This
work
CICC
2012 [4]
Technology (µm)
Required number
of cycle (worst case)
0.18
0.13
0.5
1
4
N/A
Supply (V)
1.2/0.6
10k – 10M
1,000
1.2
< 0.21
0.5
23k – 4.6M
200
1
1.42
45.2
N/A
87.4
> 60**
N/A
1.7
11.3
66
32
6,000
10,000
Input Range (Ω)
Conv. Rate (kS/s)
Meas. Error (%)
Measured
0
4000
Fig. 6. Conversion result measured with off-the-shelf CdS light sensor.
< 0.32
ISCAS
JSSC
2011 [5] 2009 [1]
JSSC
2007 [2]
Sensors and
Actuators B
142 2009 [6]
0.18
0.35
0.35
5
6, (5 cycles with
coarse ADC)
3.3
1.2/0.5
60k – 10M 10k – 9M
166.7
900
1.83
N/A
< 1.32
N/A
3.3
100 – 20M
200,000
0.1
< 0.14
1.0
1.2
Fig. 3. (a) A switched capacitor amplifier that pseudo-differentially samples
input and (b) improvement of ADC resolution by SC amplifier gain.
8
N/A
10k – 2G
200,000
N/A
< 2.7
* Assumes a worst case cycle count and minimum input resistance.
** Coarse ADC power is not reported, thus extra energy needed for finding sub-range is not included.
0.42mV/code
200
(b)
60
Max. R / Min. R
VOUT-
1.15mV/code
0.58mV/code
600
1.2
70
Energy/conversion (nJ)
(worst case)*
Power (µW)
CSAMPLE/CT = 3
CSAMPLE/CT = 2
CSAMPLE/CT = 1
1000
Average
Average ± 1σ
TABLE I. Performance summary and comparison.
ADC
CT
(a)
CSAMPLE/CT = 3
CSAMPLE/CT = 2
CSAMPLE/CT = 1
1.0
Φ1
SAR ADC
VOUT+ (= VREF1–VCM +VIN)
VCM
Φ1
VREF2
1.5
CDAC+
VOUT+
GND
VOUT+
VCM
VREF1
VIN
VDDH
CT
Φ1 Φ1
Φ2'
GND
Φ1
Φ2
Φ1'
RIN
VDDH
Φ2
CSAMPLE+
VIN
Pseudo-Differentially sample & amplify VIN
Fig. 5. Measured results of a sub-ranging, DNL & INL of 10b ADC
with SC amplifier, and measurement error for input resistance range.
50
0
Similar to ICOARSE search,
Choose 1 of 14 IFINE based on Code & RC
lly
ua d
ad an
gr h
or by
ns ed
Se ver
co
0
Sub-ranging code
VIN = 100mVVIN = 10mV VIN = 1mV
Start
Comparison
Voltage(V)
Φ1', Φ2' are delayed versions of Φ1, Φ2, respectively.
1.2
1.0
0.8
0.6
0.4
0.2
0.0
RC = 4
ICOARSE = 0.1µA
Code value?
10b
SAR
ADC
80
Sub-ranging code
Φ2
Φ2 V
L
RC = 3
ICOARSE = 0.4µA
Logarithmically convert VIN to sub-ranging code
IFINE×RIN
Pseudo Differential
Sampling
90
Meas. Error (%)
VIN
Φ1
RC = 2
ICOARSE = 1.6µA
Fig. 4. Conversion process flow chart of 1 sample. RIN is logarithmically
compressed, sub-ranged, then converted by 10b ADC.
Sub-ranging
code
VREF
= 0.6V
Coarse Sub
range(RC) = 1
ICOARSE = 6.4µA
Next
Sample
Measured Resistance (Ω)
VDDH = 1.2V
Φ2
CSAMPLE
Φ2
Logarithmic
Sub-range
search
Proposed Approach
Fig. 1. An overview of N cycles/sample conventional RDC and a proposed 1
cycle/sample RDC with logarithmic sub-range detector.
Φ1'
ICOARSE×RIN
Sampling
I-DAC control code
RIN
Conventional System
3 < Code < 14 ?
Code value?
44 < Code < 61?
14 < Code < 44 ?
Code > 61?
100k
Current DAC
(I-DAC)
Logarithmically convert VIN to sub-ranging code
Logarithmic
Sub-range
search
DNL (LSB)
control
signal
..
Digital code
IINITIAL×RIN
Sampling
INL (LSB)
Yes
Conversion Process Flow
* 2N-1 = Number of total sub-ranges
30k
RIN
× N cycles/sample*
No
In
range?
ADC
10k
R to V
VIN
Converter
RIN
Flow IINITIAL(0.3µA) and Sample
Scan for testing
FSM
Sub-ranging
circuit
I-DAC
Decap
SAR
ADC
Fig. 7. Microphotograph (1.5 × 0.82mm2).