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micromachines
Article
A 0.026 mm2 Time Domain CMOS Temperature
Sensor with Simple Current Source
Sangwoo Park and Sangjin Byun *
Division of Electronics and Electrical Engineering, Dongguk University, Seoul 04620, Korea; psw7478@naver.com
* Correspondence: sjbyun@dongguk.edu; Tel.: +82-2-2260-3331
Received: 1 September 2020; Accepted: 25 September 2020; Published: 28 September 2020
Abstract: This paper presents a time domain CMOS temperature sensor with a simple current source.
This sensor chip only occupies a small active die area of 0.026 mm2 because it adopts a simple current
source consisting of an n-type poly resistor and a PMOS transistor and a simple current controlled
oscillator consisting of three current starved inverter delay cells. Although this current source is
based on a simple architecture, it has better temperature linearity than the conventional approach
that generates a temperature-dependent current through a poly resistor using a feedback loop.
This temperature sensor is designed in a 0.18 µm 1P6M CMOS process. In the post-layout simulations,
the temperature error was measured within a range from −1.0 to +0.7 ◦ C over the temperature range
of 0 to 100 ◦ C after two point calibration was carried out at 20 and 80 ◦ C, respectively. The temperature
resolution was set as 0.32 ◦ C and the temperature to digital conversion rate was 50 kHz. The energy
efficiency is 1.4 nJ/sample and the supply voltage sensitivity is 0.077 ◦ C/mV at 27 ◦ C while the supply
voltage varies from 1.65 to 1.95 V.
Keywords: temperature sensor; time domain; threshold voltage; poly resistor; temperature error;
CMOS integrated circuits
1. Introduction
Due to their small form factor, low power consumption, low cost and convenient digital interface
capability, integrated temperature sensor chips have been widely used for thermal monitoring in
various smart applications such as the smart farm, smart factory, smart health, and so on. Integrated
temperature sensor chips can be implemented in various ways depending on the sensing element which
is generally chosen from the threshold voltage, mobility, resistance or thermal voltage; the measured
signal type, which is generally chosen from the voltage, current, frequency, or delay time; and the
overall architecture which is basically determined by the chosen sensing element and the measured
signal type [1–30].
Among the possible architectures, a time domain architecture based on frequency or delay time is
promising because it can benefit from the recent trend that time resolution is being increased while
voltage resolution is being decreased as the CMOS channel length and the supply voltage are scaled
down. By measuring time domain signals such as the clock frequency, clock period or delay time,
an efficient estimate of the current temperature can be obtained [1–20]. The sensing element can be
chosen from the mobility, threshold voltage or resistance. Depending on the choice, the temperature
linearity of a time domain CMOS temperature sensor is fundamentally limited by the temperature
linearity of the chosen sensing element. In this paper, we present a time domain CMOS temperature
sensor with the sensing element dependent on both the resistance of an n-type poly resistor and the
threshold voltage of a PMOS transistor at the same time. By adopting this simple current source as a
sensing element, we gain the ability to multiply two different types of temperature characteristics of
Micromachines 2020, 11, 899; doi:10.3390/mi11100899 www.mdpi.com/journal/micromachinesMicromachines 2020, 11, 899 2 of 10
Micromachines 2020, 11, x 2 of 10
the resistance of an n-type poly resistor and the threshold voltage of a PMOS transistor by each other
the resistance of an n-type poly resistor and the threshold voltage of a PMOS transistor by each other
and improve the temperature linearity of the temperature sensor.
and improve the temperature linearity of the temperature sensor.
This paper is organized as follows. In Section 2, we explain how this simple current source can
This paper is organized as follows. In Section 2, we explain how this simple current source can
have better temperature linearity than the conventional approach. Section 3 describes the architecture
have better temperature linearity than the conventional approach. Section 3 describes the architecture
and schematics of the implemented time domain CMOS temperature sensor adopting the simple
and schematics of the implemented time domain CMOS temperature sensor adopting the simple
current source. Section 4 shows the simulation results and the performance comparison with the
current source. Section 4 shows the simulation results and the performance comparison with the
previous works found in literature. Finally, the conclusion is given in Section 5.
previous works found in literature. Finally, the conclusion is given in Section 5.
2. Temperature Linearity of the Sensing Element
2. Temperature Linearity of the Sensing Element
Figure 1 shows the conventional current source based on a single n-type poly resistor [1,8,9,13].
Figure
It consists of 1multiple
shows the conventional current
diode-connected source based
PMOS transistors on a single
between n-type
VDD and thepoly resistor
ground, [1,8,9,13].
a differential
It consists
input of multiple diode-connected
to a single-ended output amplifier, PMOS transistors
an n-type between
poly resistor and Va DD and transistor.
PMOS the ground, a differential
Since multiple
input to a single-ended output amplifier, an n-type poly resistor and a PMOS
diode-connected PMOS transistors generate a reference voltage, VREF , it is applied across the n-type transistor. Since
multiple
poly diode-connected
resistor, RN (T), through PMOS transistors
the feedback generate
loop a reference
consisting voltage, VREF
of the differential , it is applied
amplifier and theacross
PMOS the
n-type poly resistor, R N(T), through the feedback loop consisting of the differential amplifier and the
transistor as shown in the below figure. The reference current, I(T), becomes exactly proportional to
VPMOS transistor as shown in the below figure. The reference current, I(T), becomes exactly
REF and inversely proportional to RN (T) as follows. This current source has been used because its
proportionallinearity
temperature to VREF and
can inversely proportional
be made dependent on to RN(T)
only thatasoffollows. This current
the resistor; then thesource hasand
analysis been used
design
because its temperature linearity can be made dependent
become simpler than for the other types of current sources. on only that of the resistor; then the analysis
and design become simpler than for the other types of current sources.
V
I(T) = V REF (1)
I(T) = RN (T) (1)
R (T)
Figure 1. The conventional approach for generating a temperature-dependent current through a poly
Figure using
resistor 1. The aconventional approach for generating a temperature-dependent current through a poly
feedback loop.
resistor using a feedback loop.
Figure 2 shows the temperature-dependent variation and temperature linearity error of RN (T)
and 1/RFigure
N (T),2respectively,
shows the temperature-dependent variation
where RN (T) is the resistance andn-type
of the temperature linearity
poly resistor. In error
these of RN(T)
figures,
andvalues
the 1/RN(T),
of Rrespectively,
(T) and 1/R where
(T) R
wereN (T) is the
normalized resistance
with of
respectthe
to n-type
the poly
values resistor.
measured In
at 25 ◦ C and
these figures,
the
N N
the values of R (T) and 1/R (T) were normalized with respect to the values measured
temperature linearity error is defined as the temperature deviation, which is measured in C, from the
N N
◦
at 25 °C and
the temperature
linear fit of RN (T)linearity errorSince
or 1/RN (T). is defined
RN (T)asisthe temperature
convex downward deviation,
whereaswhich
1/RNis(T)
measured
is convex inupward,
°C, from
the linear
they can befitmodeled
of RN(T)asor 1/RN(T). Since RN(T) is convex downward whereas 1/RN(T) is convex upward,
they can be modeled as
RN (T) = RN (25) × 1 − a(T − 25) + b(T − 25)2
h i
(2)
R (T) = R (25) × 1 − a(T − 25) + b(T − 25) (2)
and
and
1 1 h 2
i
= × 1 + α ( T − 25 ) − β ( T − 25 ) (3)
RN (1T) 1( )
= RN 25 × 1 + (T − 25) − (T − 25) (3)
R (T) R (25)
where a, b, α and β are positive first and second order temperature coefficients of RN(T) and 1/RN(T),
respectively. Here, RN(25) is the resistance of the n-type poly resistor measured at 25 °C. As shown inMicromachines 2020, 11, 899 3 of 10
where a, b, α and β are positive first and second order temperature coefficients of RN (T) and 1/RN (T),
Micromachines 2020, 11, x 3 of 10
respectively. Here, RN (25) is the resistance of the n-type poly resistor measured at 25 ◦ C. As shown in
Figure 2, the temperature linearity error varies from −2.60 to +2.87 ◦ C and from −0.79 to +0.83 ◦ C for
Figure 2, the temperature linearity error varies from −2.60 to +2.87 °C and from −0.79 to +0.83 °C for
R (T) and 1/R (T), respectively, over the temperature range of 0 to 100 ◦ C. This shows that 1/R (T) is
RNN(T) and 1/RNN(T), respectively, over the temperature range of 0 to 100 °C. This shows that 1/RNN(T) is
more linear against temperature variation than R (T) if they are implemented by using this CMOS
more linear against temperature variation than RNN(T) if they are implemented by using this CMOS
technology. Thus, in this work, we have chosen 1/R (T) as the sensing element and consequently I(T)
technology. Thus, in this work, we have chosen 1/RNN(T) as the sensing element and consequently I(T)
of (1) is now expressed as
of (1) is now expressed as
VVREF
25)2
h i
I(T)
I(T) =
= ×× 11++(T
α(T−−25)
25)−− (T
β(T− − 25) (4)(4)
RRN(25)
(25)
when
whenthe theconventional
conventionalcurrent
currentsource
sourceofof
Figure
Figure1 is1 used. Since
is used. the the
Since temperature linearity
temperature errorerror
linearity of I(T)
of
isI(T)
limited by that of 1/R (T) as implied in (4), we can expect that the temperature linearity
is limited by that of 1/RN (T) as implied in (4), we can expect that the temperature linearity
N of the
of
temperature
the temperaturesensor willwill
sensor varyvary
from −0.79
from to +0.83
−0.79 to +0.83 °C ◦ifC there is is
if there not
notany
anyother
otherkind
kindofof additional
additional
nonlinearity
nonlinearity source.
source.
(a)
(b)
Figure 2.
Figure Thetemperature-dependent
2. The temperature-dependent variation
variation and
and temperature
temperature linearity
linearity error
error of R
of (a) (a) RNand
N(T) (T) and
(b)
(b) 1/R
1/RN(T).N (T).
Figure 33 shows
Figure shows thethe simple
simple current
current source
source adopted
adopted alternatively
alternatively in in this
this time
time domain
domain CMOS
CMOS
temperaturesensor.
temperature sensor. AsAsshown
shownin inthe
thefigure,
figure,ititjust
justconsists
consistsof
ofan n-typepoly
ann-type polyresistor,
resistor, of
of which
which the
the
resistance value is R (T), and a single diode-connected PMOS transistor. Since I(T) flows
resistance value is RNN(T), and a single diode-connected PMOS transistor. Since I(T) flows through the through the
n-type poly resistor and PMOS transistor, we can obtain the equation of I(T) by equating
n-type poly resistor and PMOS transistor, we can obtain the equation of I(T) by equating two current two current
equationsof
equations of the n-type poly
the n-type poly resistor
resistor and
and the
the PMOS
PMOS transistor
transistor as
as follows.
follows.
1 W VDD − VSG (T)
I(T) = µ(T)COX (VSG (T) − VTH (T))2 = (5)
2 L RN (T)Micromachines 2020, 11, 899 4 of 10
Micromachines 2020, 11, x 4 of 10
Figure 3. The simple current source for generating a temperature-dependent current through a poly
Figure 3. The simple current source for generating a temperature-dependent current through a poly
resistor, with better temperature linearity.
resistor, with better temperature linearity.
Then, VSG (T) is solved as
1 W V − V (T)
VSG (T) = VTH (T)= 2 (T)C L V (T) −−V (T) 1W =
I(T) (5)
µ(T)COX L RN (T) R (T)
(6)
r 2
Then, VSG(T) is solved as + VDD − VTH (T) + 1
W − (VDD − VTH (T))2
µ(T)COX L RN (T)
1
V (T) = V (T) −
Since the PMOS transistor operates W in the vicinity of the threshold voltage for low power
(T)C R (T)
consumption in this work, VSG (T) can be Lsimplified to VTH (T) and thus we obtain
(6)
1
+ V − (T)
VDD − VTH (T) − V − V (T)
I(TV) ≈ + W (7)
R(T)C
N ( T ) L
R (T)
whereSince the PMOS transistor operates in the vicinity of the threshold voltage for low power
consumption in this work, VSG(T) V
can (T)simplified
THbe = VTH (25to
) −VγTH(T
(T) 25). thus we obtain
− and (8)
V of −
Here, γ is the positive temperature coefficient (T)
theV threshold voltage of the PMOS transistor and
I(T) ≈ ◦ (7)
R (T)
VTH (25) is the threshold voltage measured at 25 C. I(T) can be finally obtained in quadratic equation
form by substituting 1/RN (T) of (3) and VTH (T) of (8) into (7), as follows:
where
VDD −VTH (T) (T)
VDDV−VTH (25=)+V (25)
γ(T−25 ) − γ(T − 25).
× 1 + α(T − 25) − β(T − 25)2 (8)
h i
I(T) RN ( T )
= RN (25)
(9)
Here, γ is the positive temperature
V −V (25)coefficient of the threshold voltage
h 2
i of the PMOS transistor
≈ DDR (TH × 1 + A ( T − 25 ) − B ( T − 25 )
and VTH(25) is the threshold voltage N 25) measured at 25 °C. I(T) can be finally obtained in quadratic
equation form by substituting 1/RN(T) of (3) and VTH(T) of (8) into (7), as follows:
where
γ
V − V (T) V − V (25) A=+ α+γ(T − 25) (10)
I(T) = VDD − V×TH1(25 + )(T − 25) − (T − 25)
R (T) R (25)
and
αγ
V − V B(25) = β− . (11)
× V1 DD
+ A(T
− V− TH25)
(25)− B(T − 25) (9)
R (25)
Now let us compare (9) with (4) and observe the relative increase and decrease of A and B in
where
(10) and (11), respectively. We can see that A > α and B < β and that the temperature linearity of
this simple current source has been fairly γ the amount of the improved temperature
A =improved
α+ and (10)
linearity error is determined by α, β, γ and VDDV-VTH V (25)
− (25) as indicated in (10) and (11). Contrary to
the
andconventional approach shown in Figure 1, the reference current, I(T), of (9) depends on both the
resistance of an n-type poly resistor and the threshold voltage
αγ of a PMOS transistor at the same time and
the temperature linearity error has beenBsuccessfully
=β− .
V − V (25)as shown in Figure 4. The temperature
reduced (11)
linearity error of I(T) now varies from −0.40 to +0.38 C over the temperature range of 0 to 100 C.
◦ ◦
Now let us compare (9) with (4) and observe the relative increase and decrease of A and B in (10)
and (11), respectively. We can see that A > α and B < β and that the temperature linearity of this simple
current source has been fairly improved and the amount of the improved temperature linearity error
is determined by α, β, γ and VDD-VTH(25) as indicated in (10) and (11). Contrary to the conventional
approach shown in Figure 1, the reference current, I(T), of (9) depends on both the resistance of an n-Micromachines 2020, 11, x 5 of 10
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type poly resistor and the threshold voltage of a PMOS transistor at the same time and the
type poly resistor and the threshold voltage of a PMOS transistor at the same time and the
temperature linearity error has been successfully reduced as shown in Figure 4. The temperature
temperature linearity error has been successfully reduced as shown in Figure 4. The temperature
linearity error
Micromachines 2020,of
11,I(T)
899 now varies from −0.40 to +0.38 °C over the temperature range of 0 to 100 5°C.
of 10
linearity error of I(T) now varies from −0.40 to +0.38 °C over the temperature range of 0 to 100 °C.
Figure 4. The temperature-dependent variation and temperature linearity error of I(T).
Figure 4.
Figure Thetemperature-dependent
4. The temperature-dependent variation
variation and
and temperature
temperature linearity
linearity error
error of
of I(T).
3.3.Implementation
3.
Implementation
Implementation
3.1.Architecture
3.1. Architecture
3.1. Architecture
Figure55shows
Figure shows the
the architecture
architecture of the implemented
implemented time
timedomain
domainCMOS
CMOStemperature
temperaturesensor.
sensor.It
Figure 5 shows the architecture of the implemented time domain CMOS temperature sensor. It
Itconsists
consistsofofthe
thesimple
simplecurrent
current source,
source, aa three
three stage current controlled
controlled oscillator
oscillator(CCO),
(CCO),an
an11b
11bbinary
binary
consists of the simple current source, a three stage current controlled oscillator (CCO), an 11b binary
counterand
counter andan anadditional
additionaldigital
digitallogic.
logic.
counter and an additional digital logic.
Figure5.5.The
Figure Thearchitecture.
architecture.
Figure 5. The architecture.
The current source generates the temperature-dependent reference current, I(T), with improved
The current source generates the temperature-dependent reference current, I(T), with improved
The current
temperature source
linearity generates
which is fedthe temperature-dependent
to the CCO. The CCO generates reference current,
the clock I(T),oscillating
signal with improvedat the
temperature linearity which is fed to the CCO. The CCO generates the clock signal oscillating at the
temperature
frequency of linearity
f(T) whichwhich is fed
is linear to the
with I(T).CCO. The CCO
The logic circuitgenerates
generatesthe
theclock
ENABLEsignalpulse
oscillating
whoseat the
pulse
frequency of f(T) which is linear with I(T). The logic circuit generates the ENABLE pulse whose pulse
frequency of f(T)
width equals onewhich is linear1/f
clock period, with
REF ,I(T).
of theThe logic circuit
external reference generates the ENABLE
clock, CLK pulse whose
REF . As shown pulse
in the timing
width equals one clock period, 1/f REF, of the external reference clock, CLKREF. As shown in the timing
width
diagramequals one clock
of Figure 6, theperiod, 1/fREF, of
rising edges ofthe
theclock
external reference
signal, CLKCCO clock, CLKREF.from
, generated As shown in the
the CCO timing
is counted
diagram of Figure 6, the rising edges of the clock signal, CLKCCO, generated from the CCO is counted
diagram
by the 11bof Figure
binary6,counter
the rising
foredges
the timeof the clock signal,
duration of 1/fREFCLKtoCCOgenerate
, generated
thefrom the CCO
11b digital is counted
output code,
by the 11b binary counter for the time duration of 1/f REF to generate the 11b digital output code,
by the 11b binary
DATA[10:0]. counter for isthe
The DATA[10:0] thetime duration
quantized of 1/fvalue
digital REF toof
generate the 11b digital
the temperature output
estimation code,
function,
DATA[10:0]. The DATA[10:0] is the quantized digital value of the temperature estimation function,
DATA[10:0].
X(T), which isThe DATA[10:0]
defined as is the quantized digital value of the temperature estimation function,
X(T), which is defined as 1
X(T), which is defined as fREF
X(T) = 11 (12)
1
f(fT)
X(T) =f (12)
X(T) = 1 (12)
1
f(T)
f(T)Micromachines 2020, 11, 899 6 of 10
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Figure
Figure6.6.The
Thetiming
timingdiagram.
diagram.
Figure 6. The timing diagram.
InInthis
thispaper,
paper,in inregard
regard to to
thethedetailed definition
detailed of the
definition of temperature
the temperature estimation function,
estimation we
function,
introduced Inand
we introduced explained
thisand
paper,
explainedthe 12
in regard types
theto
12the of operational
detailed
types principles
definition
of operational of and thethe
the temperature
principles and corresponding
estimation temperature
function,
corresponding we
temperature
introduced
estimation
estimation and explained
functions
functions ofofthe the 12
thetime
time types of
domain
domain operational
CMOS
CMOS principlessensors
temperature
temperature and the from
sensors corresponding
fromour temperature
ourprevious
previous work
work[1].[1].
Finally,estimation
Finally,the
theSTART functions
STARTsignal of the
signalenables time
enablesthe domain
the11b CMOS
11bbinary temperature
binarycounter
counterand sensors
andthe from
theadditional our
additionallogicprevious
logiccircuitwork
circuit [1]. the
totostart
start the
Finally, the START
operation signal enables the 11b binary counter and the additional logic circuit to start the
operationofofthis
thistime
timedomain
domainCMOS CMOStemperature
temperaturesensor.
sensor.
operation of this time domain CMOS temperature sensor.
3.2.Circuits
3.2. Circuits
3.2. Circuits
Figure
Figure 7 7shows
Figure shows
7 shows theschematic
the schematic
the schematic ofofthe
ofthe simple
simple
the currentsource
simplecurrent
current source
source and
and and the
the the CCO.
CCO.
CCO. InInInthe
the thecurrent
current
current source,
source,
source,
theresistance
the resistance ofofthe
the resistance the n-type
of n-type
the poly
poly
n-type resistor,
resistor,
poly resistor,RRNRN (T), has
(T), hasbeen
N(T),has
beendesigned
been designed
designed tototo
bebebe externally
externally
externally tuned
tuned
tuned by
by thebythe
the
external
external 3b3bdigital
external digital control
control
3b digital word,
word,
control word, FREQ_CTRL[2:0].
FREQ_CTRL[2:0].
FREQ_CTRL[2:0].We Weadded
We addedthese
added these
these extra
extra
extra 3b3b3b digital
digital
digital codes
codes
codes forrough
for for
rough rough
compensation
compensation
compensation of the
of ofprobable
the probable severe
the probable severeprocess
severe processvariation
process of RNof
variation
variation (T),
of RNNwhich
R (T), which
(T), rarelyrarely
which happens. If theIfresistance
rarelyhappens.
happens. If the
the
resistance
of the n-type
resistance of the of
poly the n-type
resistor,
n-type poly resistor,
polyRresistor, R
N (T), is shifted (T),
RN(T), is
N is shifted
tooshifted
much tootoo
from much from
its typical
much its
from its typical
value value
at the
typical at
worst
value the worst
at case corner,
the worst
case case power
the corner,
total corner, the total
consumption
the total power power ofconsumption ofofthethetotal
the total temperature
consumption totaltemperature
temperature
sensor will sensor
be will
willbetoo
affected
sensor affected
be much.too
affected much.
Thus,
too this 3b
much.
Thus, thistuning
3b rough digital tuning by FREQ_CTRL[2:0] is only necessary for robust operation and
Thus, this 3b rough digital tuning by FREQ_CTRL[2:0] is only necessary for robust operationpower
rough digital by FREQ_CTRL[2:0] is only necessary for robust operation and consistent and
consistent power consumption and should be carried out before we execute the two point calibration.
consumption
consistent power and should be and
consumption carried
shouldoutbe before
carried weout
execute
beforethe two point
we execute thecalibration. Of course,
two point calibration.
Of course, if the resistance of the n-type poly resistor can be accurately controlled during fabrication
if course,
Of the resistance of the n-type
if the resistance of thepoly resistor
n-type polycan be accurately
resistor controlledcontrolled
can be accurately during fabrication within the
during fabrication
within the capability of normal two point calibration, FREQ_CTRL[2:0] needs not be additionally
capability
within of normal of
the capability
implemented. twonormal
point calibration, FREQ_CTRL[2:0]
two point calibration, needs not beneeds
FREQ_CTRL[2:0] additionally
not be implemented.
additionally
implemented.
Figure
Figure 7. The
7. The schematicofofthe
schematic thecurrent
current source
source(left
(leftside) and
side) thethe
and CCO (right
CCO side).
(right side).
The The temperature-dependent referencecurrent,
temperature-dependent
Figure 7. The schematicreference
current, I(T),
of the current source I(T), is delivered
(leftisside)
deliveredto each
and thetoCCO
current
each starved inverter
current
(right side).starved inverter
type delay cell inside the CCO through two DC bias voltages, VBIASP and VBIASN, respectively. By
type delay cell inside the CCO through two DC bias voltages, VBIASP and VBIASN , respectively.
supplying the almost equivalent currents to the PMOS and the NMOS paths of the current starved
By supplying
The the almost equivalent
temperature-dependent currents to the I(T),
PMOS and the NMOS paths of the current starved
inverters, the low to high and reference
high to low current,
propagation isdelay
delivered
times oftoeach
each current
delay cell starved inverter
can be made
inverters,
type almost equal to each other. Because the propagation delay time, τ(T), of each delay cell is representedmade
delay the
cell low to
inside high
the and
CCO high
throughto low
two propagation
DC bias delay
voltages, times
V of
BIASP each
and V delay
BIASN , cell can be
respectively. By
almost
as equal
supplying the to each other.
almost Because
equivalent the propagation
currents to the PMOS delayand time,
theτ(T),
NMOS of each delay
paths cellcurrent
of the is represented
starvedas
inverters, the low to high and high to low propagation delay times of each delay cell can be made
V C
τ(T) = DD
almost equal to each other. Because the propagation × time, τ(T), of each delay cell is represented
delay (13)
2 I(T)
asMicromachines 2020, 11, x 7 of 10
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τ(T) = × (13)
2 I(T)
the clock frequency, f(T), of
frequency, f(T), of the
the CCO
CCO can
can also
also be
be expressed
expressed as
as
1 1 I(T)
f(T) = 1 × 1 = I(T) (14)
f T = τ(T)× 2N = N × V × C
( ) (14)
τ(T) 2N N × VDD × C
where N is the number of total delay cells of the CCO, and f(T) is linear with I(T). Finally, the
where N is theestimation
temperature number offunction,
total delay cellsof
X(T), ofthe
thetemperature
CCO, and f(T)sensor
is linear
canwith I(T). Finally, the
be represented as temperature
estimation function, X(T), of the temperature sensor can be represented as
V − V (25)
X(T) = × 1h + A(T − 25) − B(T − 25) i (15)
f × NV×
DDV− V× TH 25R) (25)
C(× 2
X(T) = × 1 + A(T − 25) − B(T − 25) (15)
from (9), (12) and (14). fREF × N × VDD × C × RN (25)
from (9), (12) and (14).
4. Performance
4. Performance
The time domain CMOS temperature sensor was implemented in a 0.18 μm 1P6M CMOS process
with The
a general VTH. Figure
time domain CMOS 8 shows the diesensor
temperature photowas andimplemented
the active dieinarea a 0.18is 0.026
µm 1P6M mm2.CMOSTo theprocess
best of
our knowledge, the die area of 0.026 mm
with a general VTH . Figure 8 shows the die photo and the active die area is 0.026 mm . To the time
2 is the smallest among the previously published 2 best
domain CMOS temperature
of our knowledge, the die area sensors implemented
of 0.026 mm2 is the 0.18 μm CMOS
insmallest among technology.
the previously Figure 9 showstime
published the
simulated temperature error over the temperature range of 0 to
domain CMOS temperature sensors implemented in 0.18 µm CMOS technology. Figure 9 shows the100 °C after one point and two point
calibrations are carriederror
simulated temperature out,over
respectively.
the temperatureFor the process
range of 0 tocorners,
100 ◦ C TT, afterFF,oneSS,pointFS,andandtwo SF,point
the
temperature error varies from −2.33 to +1.99 °C after one point calibration at
calibrations are carried out, respectively. For the process corners, TT, FF, SS, FS, and SF, the temperature 50 °C and from −0.96 to
+0.66 °C after two point calibration at 20 and 80 °C, respectively. The
error varies from −2.33 to +1.99 C after one point calibration at 50 C and from −0.96 to +0.66 C
◦ ◦ temperature error of the time
◦
domain
after twoCMOS temperature
point calibration at sensor
20 and is 80measured as being
◦ C, respectively. Thesomewhat
temperature larger
errorthan the time
of the temperature
domain
linearity error of I(T) only, because the temperature linearity error
CMOS temperature sensor is measured as being somewhat larger than the temperature linearity of the load capacitance, C, error
may
also
of I(T) only, because the temperature linearity error of the load capacitance, C, may also affect the
affect the temperature estimation function, X(T), as can be seen from (15). Additionally, the
quantization error at the
temperature estimation 11b digital
function, X(T),output
as can becode,
seenDATA[10:0], the residue the
from (15). Additionally, process variation
quantization error
error at
after two point calibration, the approximation error of I(T) made for the derivation
the 11b digital output code, DATA[10:0], the residue process variation error after two point calibration, of (7), the charge
sharing effect within
the approximation theofdelay
error cell and
I(T) made for the transistor mismatch
the derivation effect between
of (7), the charge current
sharing effect mirrors
within may
the delay
also be the
cell and the sources
transistor ofmismatch
additionaleffectcontributions to the mirrors
between current increasemay of the
alsototal
be thetemperature
sources of error. The
additional
temperature error of Figure 9b has been measured greater than the temperature
contributions to the increase of the total temperature error. The temperature error of Figure 9b has been error of Figure 4. The
temperature
measured greater resolution
than the was set as 0.32error
temperature °C and the temperature
of Figure to digital
4. The temperature conversion
resolution wasrate,
set aswhich
0.32 ◦isC
exactly equal to f REF in this design, is about 50 kHz. The energy efficiency
and the temperature to digital conversion rate, which is exactly equal to fREF in this design, is about is 1.4 nJ/sample and most
of
50 the
kHz.power consumption
The energy is dissipated
efficiency by the current
is 1.4 nJ/sample and most source.
of theAs shown
power in Figure 10,is the
consumption supply
dissipated
voltage sensitivity
by the current is measured
source. As shown as inlow as 0.077
Figure °C/mV
10, the at 27voltage
supply °C while VDD varies
sensitivity from 1.65 to
is measured as 1.95
low V. as
Table 1
◦ compares the
◦ performances of this temperature sensor with
0.077 C/mV at 27 C while VDD varies from 1.65 to 1.95 V. Table 1 compares the performances of those of the previous works in
literature. The previous works are all time domain CMOS temperature
this temperature sensor with those of the previous works in literature. The previous works are all sensors which were
implemented
time domain CMOS in CMOS processes
temperature with which
sensors the samewereminimum
implemented channel
in CMOS length of 0.18with
processes μm,the forsame
fair
performance comparison with this work. Compared to the previous
minimum channel length of 0.18 µm, for fair performance comparison with this work. Compared to works, we can see that this
temperature
the previous sensor
works,occupies
we can see a relatively small die areasensor
that this temperature and has relatively
occupies small temperature
a relatively small die area errorandas
shown in Table 1.
has relatively small temperature error as shown in Table 1.
Figure 8. The die photo.
Figure 8. The die photo.Micromachines 2020,11,
Micromachines2020, 11,899
x 88of
of10
10
Micromachines 2020, 11, x 8 of 10
error [ºC]
error [ºC]
3
3
2
2 FF
FF
1 FS
1 SF FS
SF
TT
0 TT
0
SS
SS
-1
-1
-2
-2
-3
-3 0 10 20 30 40 50 60 70 80 90 100
0 10 20 30 40 50 60 70 80 90 100
temperature [ºC]
temperature [ºC]
(a)
(a)
(b)
(b)
Figure 9. The temperature error after (a) one point calibration at 50 °C and (b) two point calibration
Thetemperature
Figure9.9.The
Figure temperature error
error after (a) one point
point calibration
calibrationat 50◦°C
at50 C and
and(b)
(b)two
twopoint
pointcalibration
calibrationat
at 20 and 80 °C, carried out against the different process corners, TT, FF, FS
SS,and
FS and SF.
and8080◦ C,
at2020and °C,carried
carriedout
outagainst
againstthe
thedifferent
differentprocess
processcorners, TT,
corners, FF,FF,
TT, SS,
SS, FS SF.SF.
and
Figure 10.The
Figure10. TheVVDD
DD sensitivity
sensitivity when
when V
VDD is swept
DD is swept from
from 1.65
1.65 to
to 1.95
1.95 V.
V.
Figure 10. The VDD sensitivity when VDD is swept from 1.65 to 1.95 V.Micromachines 2020, 11, 899 9 of 10
Table 1. The performance summary.
Reference [1] [7] [8] [9] [14] This Work
CMOS technology 0.18 µm 0.18 µm 0.18 µm 0.18 µm 0.18 µm 0.18 µm
Die area 0.432 mm2 0.074 mm2 0.05 mm2 0.09 mm2 0.19 mm2 0.026 mm2
Supply voltage 1.8 V 0.8 V 1.0 V 1.2 V 1.2 V 1.8 V
Temperature range 0–100 ◦ C −20–80 ◦ C 0–100 ◦ C 0–100 ◦ C −40–85 ◦ C 0–100 ◦ C
Resolution 0.49 ◦ C 0.145 ◦ C 0.3 ◦ C 0.3 ◦ C 0.18 ◦ C 0.32 ◦ C
Accuracy −1.6–0.6 ◦ C −0.9–1.2 ◦ C −1.6–3.0 ◦ C −1.4–1.5 ◦ C −1.0–1.0 ◦ C −1.0–0.7 ◦ C
Conversion rate 25 kHz 1.2 Hz 100 Hz 33.3 Hz 1kHz 50 kHz
Energy efficiency 7.2 nJ/sample 8.9 nJ/sample 2.2 nJ/sample 2.2 nJ/sample 66.5 nJ/sample 1.4 nJ/sample
VDD sensitivity 0.085 ◦ C/mV 0.0038 ◦ C/mV - 0.014 ◦ C/mV - 0.077 ◦ C/mV
5. Conclusions
We implemented a time domain CMOS temperature sensor alternatively adopting a simple
current source consisting of an n-type poly resistor, a PMOS transistor and a simple three stage CCO.
Although the current source is based on a simple architecture, it can generate a temperature-dependent
reference current, I(T), which has better temperature linearity than the conventional approach because
it can multiply two different temperature characteristics of the resistance of an n-type poly resistor
and the threshold voltage of a PMOS transistor by each other. Consequently, we have successfully
implemented a temperature sensor with a small die area and a small temperature error.
Author Contributions: Conceptualization, S.B.; design, S.P.; validation, S.P.; writing, S.B. and S.P.; supervision,
S.B.; funding acquisition, S.B. All authors have read and agreed to the published version of the manuscript.
Funding: This research was supported by the Basic Science Research Program through the National Research
Foundation of Korea (NRF), funded by the Ministry of Education (NRF-2017R1D1A1B03028325).
Acknowledgments: The authors would like to thank the IC Design Education Center (IDEC), Daejeon, South Korea,
for supporting the MPW and EDA tools.
Conflicts of Interest: The authors declare no conflict of interest.
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