Delft University of Technology

A CMOS Readout Circuit for Resistive Transducers Based on Algorithmic Resistance and

Power Measurement

Cai, Zeyu; Rueda Guerrero, Luis E.; Louwerse, Alexander Mattheus Robert; Suy, Hilco; van Veldhoven,

Robert; Makinwa, Kofi; Pertijs, Michiel

DOI

10.1109/jsen.2017.2764161

Publication date

2017

Document Version

Accepted author manuscript

Published in

IEEE Sensors Journal

Citation (APA)

Cai, Z., Rueda Guerrero, L. E., Louwerse, A. M. R., Suy, H., van Veldhoven, R., Makinwa, K. A. A., &

Pertijs, M. A. P. (2017). A CMOS Readout Circuit for Resistive Transducers Based on Algorithmic

Resistance and Power Measurement. IEEE Sensors Journal, 17(23), 7917-7927.

https://doi.org/10.1109/jsen.2017.2764161

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1

Abstract— This paper reports a readout circuit capable of

accurately measuring not only the resistance of a resistive

transducer, but also the power dissipated in it, which is a critical

parameter in thermal flow sensors or thermal-conductivity

sensors. A front-end circuit, integrated in a standard CMOS

technology, sets the voltage drop across the transducer, and senses

the resulting current via an on-chip reference resistor. The

voltages across the transducer and the reference resistor are

digitized by a time-multiplexed high-resolution analog-to-digital

converter (ADC) and post-processed to calculate resistance and

power dissipation. To obtain accurate resistance and power

readings, a voltage reference and a temperature-compensated

reference resistor are required. An accurate voltage reference is

constructed algorithmically, without relying on precision analog

signal processing, by using the ADC to successively digitize the

base-emitter voltages of an on-chip bipolar transistor biased at

several different current levels, and then combining the results to

obtain the equivalent of a precision curvature-corrected bandgap

reference with a temperature coefficient of 18 ppm/°C, which is

close to the state-of-the-art. We show that the same ADC readings

can be used to determine die temperature, with an absolute

inaccuracy of ±0.25°C (5 samples, min-max) after a 1-point trim.

This information is used to compensate for the temperature

dependence of the on-chip polysilicon reference resistor,

effectively providing a temperature-compensated resistance

reference. With this approach, the resistance and power

dissipation of a 100 transducer have been measured with an

inaccuracy of less than ±0.55 and ±0.8%, respectively, from

–40°C to 125°C.

Index Terms— resistive transducer; bandgap reference;

temperature measurement; power measurement; algorithmic

readout

This work was supported by NXP Semiconductors, The Netherlands, and

ams AG, The Netherlands.

Zeyu Cai is with Delft University of Technology and NXP

Semiconductors, The Netherlands (email: z.cai@nxp.com).

Luis E. Rueda G. is with Universidad Industrial de Santander, Colombia

(email: luis.rueda@correo.uis.edu.co).

Alexander Louwerse, Kofi Makinwa and Michiel Pertijs are with the

Electronic Instrumentation Laboratory, Delft University of Technology, Delft

2628 CD, The Netherlands (e-mail: M.A.P.Pertijs@tudelft.nl).

Hilco Suy is with ams, BL Environmental Sensors, Eindhoven, The

Netherlands.

Robert van Veldhoven is with NXP Semiconductors, Eindhoven, The

Netherlands.

I. INTRODUCTION

ESIS

T

IVE

TRANSDUCERS can be used to measure

various physical parameters, such as temperature, flow,

pressure, gas concentration and gas composition [1-7]. In

many resistive-sensor systems, e.g. thermal sensors or thermal

flow sensors [3, 4, 7], readout of the transducer’s resistance is

not sufficient for an accurate measurement. This is because the

transducer’s power dissipation also needs to be either stabilized

or accurately measured. However, most integrated readout

circuits for resistive transducers only measure resistance,

without measuring or stabilizing power dissipation [1, 2, 5, 6].

Accurate stabilization or measurement of the power

dissipated in a resistive transducer is challenging, because it

relies on a stable power reference, which is typically derived

from a voltage reference and a resistance reference. As a result,

the previously-reported constant power circuits, based on

translinear loops or other feedback loops, still rely on the

accuracy of external voltage and current (or resistance)

references. The stability reported for prior constant-power

circuits in CMOS technology is typically not better than 1%,

and is reported over load variations only, without addressing

temperature dependency [8-10]. For instance, [8] presents a

power control circuit using discrete resistors and monolithic

ICs achieving less than 2.2% power errors. Using translinear

loop in CMOS, [9] reports power errors from 1% to 3%. This

level of stability is insufficient for demanding applications,

such as the readout of thermal-conductivity-based resistive CO

2

sensors [3, 4]. In many applications, the variations of power

dissipation are not only caused by load changes but also by the

variations of ambient temperature due to the temperature

dependence of the resistor. In addition, the system is preferred

to be self-contained, and thus any external voltage, current or

reference references are to be circumvented.

Instead of stabilizing the dissipated power, an alternative is

to directly measure the power dissipation in the transducer

along with its resistance, the impact of which can then be

evaluated in obtaining the final measurement results. However,

to accurately measure power dissipation, an accurate power

reference is still needed, inherently requiring accurate voltage

and resistance references that should be insensitive to process

variations and temperature drift.

In standard CMOS, bandgap voltage references are the

best-in-class voltage references. They combine a voltage that is

proportional to absolute temperature (PTAT) with a voltage

A CMOS Readout Circuit for Resistive

Transducers Based on Algorithmic Resistance

and Power Measurement

Zeyu Cai, Member, IEEE, Luis E. Rueda G., Alexander Louwerse, Hilco Suy, Robert van Veldhoven,

Senior Member, IEEE, Kofi Makinwa, Fellow, IEEE, and Michiel Pertijs, Senior Member, IEEE

R

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2

that is complementary to absolute temperature (CTAT), both

generated using the parasitic BJTs available in any CMOS

process, to obtain a temperature-independent reference voltage

[11]. Using precision circuit design techniques as well as

appropriate calibration and correction schemes, bandgap

references can achieve high accuracy over a wide temperature

range with low chip-to-chip variations [12-15]. For instance, in

[14] a temperature dependency of 5-12 ppm/°C over the

temperature range of -40°C to 125°C has been achieved after a

single room-temperature trim that compensates for the process

spread of the BJTs. A key factor limiting the accuracy of most

existing bandgap references are the errors introduced by the

analog circuit that combines the PTAT and CTAT voltages

(e.g., offset and gain errors), since these errors typically cannot

be removed by a single trim [15]. Alternatively, the PTAT and

CTAT voltages can also be combined in the charge domain by a

switched-capacitor integrator, and it has been experimentally

proven that the accuracy of a bandgap voltage thus synthesized

can be very high [16]. In addition, accurate voltage

measurements with algorithmic curvature correction have also

been proposed, resulting in 12-bit accuracy over the

temperature range of -40°C to 125°C [17].

Compared with voltage references, on-chip resistance

references are even more difficult to realize, as resistors in IC

technology are subject to significant process variation and

temperature drift. Especially the latter results in errors which

cannot be easily removed by calibration and trimming.

Polysilicon resistors are relatively stable over temperature, but

still exhibit a temperature dependence typically from ±0.1%/°C

to ±1%/°C [15, 18-20]. Several circuit techniques have been

reported to achieve a near-zero temperature coefficient of

resistance (TCR), which typically involve combining resistors

and/or linear MOSFETs with positive and negative temperature

coefficients [18-20]. However, such combinations will be

process-dependent, typically resulting in a residual temperature

dependence of at least 100 ppm/°C. In consequence, the

accuracy of reported on-chip power references [8-10] is much

lower than that of voltage references [12-15].

Switched-capacitor resistors have been investigated in

literature as a substitute for resistors in systems that require a

stable resistance reference, such as current references [21] or

resistor-based temperature sensors [2]. However, this approach

requires stable capacitors and a stable clock. The latter is

typically an off-chip quartz crystal, since on-chip oscillators

typically exhibit temperature dependences of about 30 ppm/°C

[22, 23], i.e. several times higher than that of the voltage

reference. This makes this solution less attractive from a cost

point of view.

In this paper, we present a circuit capable of accurately

measuring resistance and power dissipation without relying on

off-chip references. It operates algorithmically, by successively

digitizing the voltage drop across the transducer (V

load

), the

voltage drop across an on-chip reference resistor carrying the

same current (V

ref

), and the base-emitter voltages of a single

BJT (V

be

) biased at different current levels, and then processing

the results in the digital domain. The ratio of V

load

and V

ref

provides information about the transducer resistance R

load

relative to the reference resistance R

ref

. Rather than using an

analog bandgap reference circuit, the reference voltage needed

to calculate the power dissipation is obtained by combining the

digitized base-emitter voltages to construct an equivalent

reference voltage in the digital domain. To obtain the

temperature information required to compensate for the

temperature dependence of R

ref

, the same digitized

based-emitter voltages are used to construct an equivalent

PTAT voltage in the digital domain, which, combined with the

reference voltage, provides accurate information about the die

temperature. The precision of the circuit is determined by the

BJT and its bias circuit, and by the linearity and resolution of

the ADC. It is independent of the analog reference voltage of

the ADC, which, as we will show, cancels out. As will be

detailed later in this paper, the main target of this work is to

design a complete measurement system that processes the

signals as much as possible in the digital domain, and thus

circumvents the errors due to analog signal processing.

Experimental results obtained using a CMOS front-end

prototype combined with an off-chip high-resolution ADC

show that the proposed architecture works as expected. The

digitally-constructed temperature sensor achieves an

inaccuracy of ±0.25°C (min-max) across the temperature range

of –40°C to 125°C after a 1-point trim, and the

digitally-constructed bandgap reference achieves a temperature

dependence of 18 ppm/°C, which are both close to the

state-of-the-art. The inaccuracy of power measurements (load

variations and temperature variations across the mentioned

range) is better than ±0.8% after a single-temperature

individual trim. Prior works [8-10] report comparable levels of

accuracy, but do not address temperature variation, and rely on

stable external voltage and/or current references.

The paper is organized as follows. In Section II, details of the

measurement principle are presented. Section III is devoted to

the circuit implementation of the readout circuit. Experimental

results and discussions are presented in Section IV, and the

paper is concluded in Section V.

II. O

PERATING PRINCIPLE

A. Algorithmic resistance and power measurement

Measuring resistance and/or power involves both voltage

and current measurements. As shown in Fig. 1, the transducer

R

load

is biased at a desired voltage V

bias

by an opamp circuit,

while a reference resistor R

ref

is included in the same branch as

the transducer in order to measure the resulting current. The

voltages across the transducer and across the reference resistor

are measured sequentially by a multiplexed precision ADC,

giving two digital outputs:

1

load

ref

V

V

(1)

2

iload

ref

V

V

(2)

where V

ref

is the reference voltage of the ADC. This needs to be

a low-noise voltage that is stable during the measurement, but

does not have to be accurate, as it will eventually be replaced by

an accurate reference voltage constructed in the digital domain,

as will be discussed below.

This is the author's version of an article that has been published in this journal. Changes were made to this version by the publisher prior to publication.

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3

From these results, the transducer’s resistance and power

dissipation can be calculated:

1

2

load load

load ref ref

load iload

VV

R

RR

IV

(3)

2

12

ref

iload

load load load load

ref ref

V

V

PVI V

RR

(4)

These results depend on the ADC’s reference voltage V

ref

and

on accurate knowledge of the value of R

ref

.

As detailed below,

to eliminate the dependence on V

ref

, we algorithmically

construct an accurate bandgap voltage reference, by digitizing

several base-emitter voltages. We use the temperature

information contained in these base-emitter voltages to

compensate for the temperature dependency of R

ref

.

B. Algorithmic bandgap voltage reference

To obtain an accurate bandgap voltage reference, we use the

same ADC to digitize the base-emitter voltage V

be

of a single

BJT that is successively biased at two different collector

currents I

1

and I

2

¸as shown in Fig. 2:

1,2

1,2

ln

be

S

I

nkT

V

qI

(5)

in which n is the BJT’s non-ideality factor, k is Boltzmann’s

constant, q is the electron charge, T is absolute temperature, and

I

S

is the BJT’s saturation current (I

S

<< I

1,2

) [24]. Note that this

is a simplified expression; the impact of non-idealities of the

BJT will be discussed in Section II-D. These base-emitter

voltages are approximately linear functions of temperature,

with an extrapolated value at 0 K that is equal to the bandgap

voltage of Silicon of about 1.2 V, and a negative temperature

coefficient of about 2 mV/K that depends on the current level,

as illustrated in Fig. 3 [24]. The difference of the two

base-emitter voltages is a PTAT voltage that depends, to first

order, only on the current ratio p = I

1

/ I

2

:

12

ln

be be be

kT

VVV p

q

(6)

In a conventional bandgap reference, a

temperature-independent reference voltage is obtained by

adding a scaled V

be

to V

be

:

11122bg be be be be

VV VaV aV

, (7)

where a

1

= 1 + , a

2

= – , and the optimal coefficient is

subject to tolerances on the BJT’s saturation current and the

bias current, and can be found based on a single-temperature

calibration [15].

Rather than generating a bandgap reference voltage in the

analog domain, we successively digitize V

be1,2

in two additional

conversions, giving:

12

34

,

be be

ref ref

VV

VV

, (8)

These results are then combined digitally to obtain the

equivalent of (7):

13 24bg ref

VVa a

(9)

which allows us to express the (inaccurate) analog reference of

the ADC V

ref

in terms of the (accurate) bandgap reference V

bg

.

Note that the coefficients a

1

and a

2

in (9) can in principle be

defined with arbitrary precision, which is not possible in a

conventional analog implementation.

The voltage drop across the transducer can now be found

independently of V

ref

by combining (1) and (9):

1

13 2 4

load bg

VV

aa

(10)

Similarly, the power dissipated in the transducer can be found

by combining (4) and (9):

2

12

2

13 24

bg

load

ref

V

P

R

aa

(11)

C.

Algorithmic temperature measurement

Expressions (3) and (11) still depend on R

ref

, which will

generally be subject to process tolerances and temperature drift:

Fig. 1. Transducer front-end for resistance and power measurement.

V

bias

V

load

V

iload

R

ref

R

load

MUX ADC

V

load

V

iload

V

ref

µ

1

µ

2

V

dd

V

ss

Fig. 2. BJT front-end for algorithmic voltage measurement.

I

1

I

2

V

be1

V

be2

MUX ADC

V

be1

V

be2

V

ref

µ

3

µ

4

V

dd

V

ss

V

dd

Fig. 3. Temperature dependency of the key voltages for constructing a

bandgap reference.

Temperature (°C)

V (V)

∆V

be

V

be

V

PTAT

= α·∆V

be

V

bg

= V

be +

α·∆V

be

-273 -55 125 330

0

1.2

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4

00

1

ref ref Rref

RR TT

(12)

where R

ref0

is the value of R

ref

at temperature T

0

and

Rref

is the

resistor’s TCR. The tolerances of R

ref0

can be compensated for

by a single-temperature calibration, which is done by replacing

the transducer by an off-chip precision resistor in the

calibration setup.

To compensate for the resistor’s temperature drift,

information about the die temperature T is needed. Fortunately,

this can readily be obtained from the PTAT voltage given by

(6):

34

34

13 24

ln ln

ln

ref

be

bg

qV

qV

T

kp kp

qV

aakp

(13)

where the relation (9) between V

ref

and V

bg

is again used to

obtain an expression independent of V

ref

. The result only

depends on the current ratio p, the bandgap scale factors a

1,2

,

the bandgap voltage V

bg

and physical constants k and q. The

temperature reading thus obtained is substituted into (12) to

calculate the value of R

ref

so as to obtain a

temperature-compensated resistance and power measurement.

D.

Compensation for BJT non-idealities

As mentioned, expression (5) for the base-emitter voltage

ignores various non-idealities of the BJT [15]. First of all, the

non-linear temperature dependence of I

S

will lead to a (slightly)

non-linear temperature dependence of V

be

, which leads to a

small non-linear temperature dependence of the bandgap

reference voltage, also referred to as curvature [24]. Rather than

applying analog curvature-correction techniques, in our

algorithmic approach, we will use the temperature information

obtained using (13) to correct for this curvature in the digital

domain.

Second, the transistor’s finite current gain causes the

collector current to deviate from the bias current, which is

applied to the transistor’s emitter. We assume the transistor is

operated at current levels at which the current gain is only a

weak function of the current level, so that this effect leads to

small gain error in the bias current that can be compensated for

using an appropriate bias circuit [25], as will be shown in

Section III-B.

Further non-idealities associated with the BJT can be

captured by replacing (5) by

ln

leak

be s

S

pI I

nkT

VpIR

qI

(14)

where the transistor is assumed to be biased at a multiple p of a

bias current I, and in which I

leak

accounts for leakage currents

(including the transistor’s own saturation current), and R

s

accounts for the voltage drop across the BJT’s emitter (series)

resistance, as illustrated in Fig. 4. Leakage current and series

resistance lead to errors in the bandgap reference and the

temperature measurement that cannot be corrected based on a

single-temperature calibration [14]. The conventional approach

to dealing with this is to choose the current level and transistor

size such that these errors are sufficiently small.

Our algorithmic approach offers the unique possibility to

correct for leakage and series resistance by combining more

than two base-emitter voltages digitally. Equation (14) can be

rewritten as:

,,

ln( / )

ln( )

leak S

be be ideal be ideal s

pI I

VV V pIR

p

(15)

where V

be,ideal

and V

be,ideal

are the ideal voltages given by (5)

and (6). From base-emitter voltages measured at a minimum of

four different values of p, V

be,ideal

and V

be,ideal

can be found by

curve fitting to (15). These values can then be used, as before,

to construct the voltage reference and measure temperature,

without errors due to series resistance or leakage current.

III.

CIRCUIT IMPLEMENTATION

The block diagram of the readout circuit is shown in Fig. 5.

The on-chip circuits, including the transducer front-end for

resistance and power measurement, the BJT front-end for the

construction of the algorithmic voltage reference and

temperature sensor, and the multiplexer to select the desired

voltage for measurement, have been designed and fabricated in

a 0.16 µm CMOS technology.

Fig. 4. (a) BJT front-end with series resistance R

s

and leakage current I

leak

;

(b) temperature errors due to I

leak

; (c) temperature errors due to R

s

.

I

1

= I I

2

= p·I

I

leak

V

BE

R

S

0 0.01 0.02 0.03 0.04 0.05

Error [°C]

0

2

4

6

8

10

12

T = 125°C

T = 27°C

T = -40°C

Ɛ = I

leak

/I

V

Rs

=R

s

·I [mV]

0 0.02 0.04 0.06 0.08 0.1

Error [°C]

0

0.5

1

1.5

2

2.5

3

Fig. 5. Block diagram of the entire readout circuit (on-chip and off-chip).

Transducer

front-end

V

be(p)

BJT

front-end

V

load

V

iload

MUX

V

out

1

µ

3

µ

4

ADC

V

ref

µ

1

µ

2

On-chip Off-chip

Shift register

Ctrl

This is the author's version of an article that has been published in this journal. Changes were made to this version by the publisher prior to publication.

The final version of record is available at http://dx.doi.org/10.1109/JSEN.2017.2764161