An Energy-Efficient Capacitance-Controlled Oscillator-based Sensor Interface for MEMS sensors Jelle Van Rethy and Georges Gielen KU Leuven, ESAT-MICAS Kasteelpark Arenberg 10, 3001 Leuven, Belgium E-mail:
[email protected]
Abstract—This paper presents the optimization and implementation of an area- and energy-efficient capacitancecontrolled oscillator-based sensor interface, which outputs a period-modulated signal. This time-based output signal can easily be digitized with a reset counter, which benefits from firstorder quantization noise shaping and oversampling. The circuit is prototyped in 130-nm CMOS technology and takes only 0.05 mm2 . The performance is validated with both an external variable capacitor and a bare-die MEMS capacitive pressure sensor. The chip consumes 371 μW from a 1.2-V supply voltage and achieves 10.5-b resolution with 10-kHz input bandwidth for an input capacitance ranging from 3.7 to 13.7 pF. For both the external capacitor and the MEMS sensor, measurements show an improved energy efficiency compared to prior period modulationbased sensor interfaces. Index Terms—Energy efficient, capacitance-controlled oscillator, time-based sensing, period modulation, MEMS sensor
I. I NTRODUCTION Capacitive sensors are widely used as sensing elements in low-power applications. Apart from the sensor, the sensor interface circuit is what separates the physical from the digital world and is as important as the sensor itself. Traditional amplitude-based conditioning circuits convert the physical quantity to an electrical voltage and are since long the preferred readout circuits to interface sensors. However, the scaling of CMOS technologies and the constant search for improved energy efficiency, drives the search for new topologies and techniques, of which time-based interfacing is a primary choice. In addition, the tendency is to miniaturize and integrate as much as possible, explaining the popularity of MEMS sensors and integrated solutions. In time-based sensor interfaces, the physical quantity is first converted to the time domain. This can be done by converting the sensor capacitance to a period-modulated time signal [1]–[3] (Fig. 1 (a)). This time-modulated signal can then easily be digitized using a simple counter (Fig. 1 (b)) [3], [4]. Since the bandwidth of sensor applications is typically in the range of Hz to kHz, oversampling is exploited to increase the resolution. This paper presents an area- and energy-efficient capacitive sensor interface which is based on period modulation by integrating a capacitive MEMS sensor in a capacitance-controlled oscillator (CCO) (Fig. 1 (b)). The CCO is optimized towards optimal performance regarding power, tuning range and phase noise. The period-modulated signal is then quantized using a
c 978-1-4799-0280-4/13/$31.00 2013 IEEE
Fig. 1. (a) Block diagram of a period-modulation(PM)-based capacitive sensor interface. (b) Block diagram of the presented PM-based interface with a capacitance-controlled oscillator and counter-based period-to-digital converter.
simple reset counter, which benefits from first-order quantization noise shaping and oversampling. The paper is organized as follows. In section II, the integration of a capacitive sensor in a ring oscillator and the periodto-digital conversion are discussed. Next, the implementation of the CCO is discussed in section III. The circuit has been prototyped in UMC130 CMOS technology. Finally, in section IV, the measurements with an external variable capacitor and a capacitive MEMS pressure sensor are discussed and compared to the state of the art. Section V concludes this paper. II. O SCILLATOR -BASED S ENSOR I NTERFACE A. Capacitance-Controlled Oscillator The focus of this paper is on the integration of a capacitive sensor in a differential ring oscillator integrated in CMOS technology. The period T of an N-stage ring oscillator (Fig. 2) is based on the number of cells N and on the delay td of each cell. The delay td in general is dependent on the current I charging a load capacitor C, resulting in a voltage swing VS . In Fig. 2, all stages are loaded with a capacitor CL , while the first stage is loaded with the capacitive sensor CS . For an N-stage ring oscillator, the period is then defined by: CL · VS (CS,0 + ΔCS ) · VS + (N − 1) (1) T =2 I I with CS,0 the nominal capacitance and ΔCS the measuranddependent variation of the capacitive sensor. By inserting a
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Fig. 2.
Standard block diagram of a relaxation ring oscillator.
Fig. 4.
Schematic of the implemented 6-stage coupled sawtooth CCO.
B. Period-to-digital converter
Fig. 3. Block diagram of the period-to-digital converter and operation principle.
capacitive sensor as load of one delay cell, we can control the period as a function of the sensor capacitance in a linear way, resulting in a Capacitance-Controlled Oscillator (CCO). To optimize the performance of the CCO for use in the time-based interface, the following performance parameters are optimized: 1) Normalized Tuning Range: Based on Eq. (1), CS,0 will result in the free-running period T0 and a ΔCS change will result in a change in period ΔT . The Normalized Tuning Range (N T R) normalizes ΔT to T0 and results in Eq. (2) if the sensor is excited maximally: NTR =
ΔT ΔCS /CS,0 = T0 1 + (N − 1)CL /CS,0
(2)
The factor ΔCS /CS,0 is known as the sensitivity of the sensor itself. If CL is taken equal to CS,0 , the sensor sensitivity to the N T R is degraded with the number of stages N . To improve the N T R, the ratio CL /CS,0 in the denominator of Eq. (2) should be as small as possible (CL < CS,0 ), without degrading the performance of the oscillator. 2) Phase noise: Probably the most important performance parameter is the phase noise. Phase noise corresponds to jitter in the time domain and is thus equivalent to what amplitude noise is in the amplitude domain. It is shown in [4] that phase noise has an important role in oscillator-based quantizers, since it contributes to the white noise floor in the spectrum of the digital output (see section IV). In ring oscillators, it is interesting that the phase noise is independent of the number of stages N for the same free-running frequency f0 [6]. In addition, single-ended ring oscillators are very susceptible to supply and substrate noise and this can have a huge impact on the phase noise performance [6]. For this reason a differential structure is used in this implementation.
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Period-modulated signals can easily be digitized by using a simple (reset) counter and decimator [3], [4]. The operation principle is depicted in Fig. 3. The reset counter counts the number of rising edges of the CCO in one period of the CLK. The resulting digital number D is then decimated to increase the resolution. It is interesting to note that the quantization noise is first-order noise-shaped [4]. The quantization resolution Q is dependent on the sampling frequency fCLK and on the frequency tuning range ΔfCCO of the CCO, and can be calculated as: log2 (ΔfCCO /fCLK ). To have 1-b resolution Q, the sampling frequency fCLK should be chosen equal to ΔfCCO /2. The SQNR is then approximated by [4]: SQN R [dB] = 6.02 · Q − 3.41 + 30 log(OSR)
(3)
with OSR = fCLK /(2fin ) and fin the input bandwidth. In practice, phase noise (jitter) of the CCO will limit the noise floor in the digital output spectrum at low frequencies, as will be clear from the measured results in section IV. III. I MPLEMENTATION OF THE CCO The implemented CCO is a 6-stage coupled sawtooth oscillator with differential delay cells (Fig. 4), which is known for its good phase noise performance [7], [8]. In this oscillator, the oscillation period only depends on the charging of a capacitor to a certain defined threshold Vref in each stage. The discharging of stage n is triggered by the signal of stage n+2, and if the discharging is fast enough, it does not contribute to the period [7]. Therefore, one cycle through the loop equals one period of the oscillation signal and is in our 6-stage design equal to (Fig. 4): Vref · CL Vref · CS +5· (4) T = IB /2 IB The bias current of the sensor delay cell is divided by 2 to increase the sensitivity of the sensor stage. In order to improve the (1/f ) noise performance, Vref is generated by forcing the bias current IB through a resistor R [8]. In that way the oscillation period can be written as: R · IB · CL R · IB · CS +5· T = = 2·R ·CS +5·R ·CL (5) IB /2 IB
2013 IEEE Asian Solid-State Circuits Conference (A-SSCC)
Period [ns]
350 300 250 200 150
4
6
8 10 Input capacitance [pF]
12
14
4
6
8 10 Input capacitance [pF]
12
14
140 Jitter [ps]
120 100 80 60 40
Fig. 6. Measured period and cycle-to-cycle jitter of the CCO as a function of the input capacitance.
Fig. 5. (a) Microphotograph of the prototyped chip in UMC130 CMOS technology. The active area is 313 μm x 160 μm. (b) Microphotograph of the Microfab E1.3N MEMS pressure sensor wirebonded to the chip.
which means that the oscillation period is independent of the bias current IB , and that the noise of the bias current generator is canceled naturally [8]. The bias voltage Vbias is generated through an on-chip bias network. In the implementation, CL is chosen to be 1.5 pF. According to Eq. (2), for a CS,0 = 8 pF, the N T R is then equal to 0.51 · ΔCS /CS,0 . By choosing the bias current in the sensor stage equal to IB /2, the N T R in this implementation is increased to: N T R = 0.69 · ΔCS /CS,0
(6)
This is an improvement of 4x compared to the case in which all delay cells would be equal and CL = CS,0 . The simulated power consumption of the CCO is 354.6 μW at VDD = 1.2 V and the phase noise is simulated to be −104.2 dBc/Hz at 100-kHz offset and f0 is 4.64 MHz. IV. M EASUREMENT RESULTS The sensor interface has been prototyped in UMC130 CMOS technology and takes only 0.05 mm2 (Fig. 5 (a)). Measurements have been performed with an external variable capacitor connected to the CCO to evaluate the overall performance of the interface. In addition, the performance is evaluated with a real capacitive MEMS pressure sensor [9], which is wirebonded directly to the die (Fig. 5 (b)). The period-to-digital conversion is done off chip, similarly as in [1]–[3]. However, since the period-to-digital converter only involves a 2-b reset counter (Fig. 3), the power consumption in this case is negligible in nanometer CMOS. A. External variable capacitor Fig. 6 shows the measured period and cycle-to-cycle jitter performance of the CCO as a function of the input capacitance. For a sensor with nominal value CS,0 = 8 pF and a variation
power spectral density [dBfs]
0
Limit cycles
Bandwidth = 10 kHz
−20 −40
Integrated noise −60 −80 −100 2
10
3
10
4
10 Frequency [Hz]
5
10
Fig. 7. Measured spectrum of the digital output of the sensor interface with a variable capacitor at the input. A DC input is applied, explaining the limit cycles. fCLK of the period-to-digital converter is 1.7MHz.
ΔCS = ±1 pF, the measured N T R is then 14.7%, which is lower than the calculated 17.1% (Eq. (6)), which is due to extra parasitic capacitances from the connection between the external capacitor and the CCO chip. The measured jitter performance corresponds to −102.28 dBc/Hz at 100-kHz offset from f0 = 4.59 MHz (cycle-to-cycle jitter σc can be linked to 1/f 2 phase noise through the formula L(Δfx ) = σc2 .f03 /Δfx2 [5]). This measured result is only slightly worse than the simulated value (−104.2 dBc/Hz). In Fig. 7, the measured spectrum of the 1-b digitized output (with fCLK frequency equal to 1.7 MHz (ΔfCCO = 3.4 MHz)) clearly shows the noise-shaped quantization noise and white noise floor due to the phase noise. The spectrum is measured with a DC input and therefore multiple limit cycles pop up (Fig. 7). By integrating the noise in a bandwidth of 10 kHz, the SNR can be calculated to be equal to 64.68 dB, or 10.5-b resolution. This is under the assumption that the input range is from 3.7 to 13.7 pF. The power consumption of the CCO at VDD = 1.2 V is measured to be 371 μW. B. Capacitive MEMS pressure sensor To validate the performance of the CCO with a real sensor, a capacitive MEMS pressure sensor from Microfab [9] is directly
2013 IEEE Asian Solid-State Circuits Conference (A-SSCC)
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TABLE I P ERFORMANCE S UMMARY AND C OMPARISON
Period [ns]
210 208 206 204 202 1000
1200
1400 1600 Pressure [mbar]
1800
2000
1200
1400 1600 Pressure [mbar]
1800
2000
Jitter [ps]
95 90 85 80 1000
Fig. 8. Measured period and cycle-to-cycle jitter of the CCO as a function of the applied pressure for a capacitive MEMS pressure sensor die wirebonded to the sensor interface die.
power spectral density [dBfs]
0 −10
Limit cycles
Bandwidth = 3 kHz
−20 −30
Integrated noise
−40 −50 −60 −70 −80 2 10
3
10 Frequency [Hz]
4
10
Fig. 9. Measured spectrum of the 1-b digital output of the sensor interface with a capacitive MEMS pressure sensor. A DC input is applied, explaining the limit cycle. fCLK of the period-to-digital converter is 103 kHz.
wirebonded to the chip (Fig. 5 (b)). The pressure is applied and measured in a contained chamber with the Druck DPI 600. Fig. 8 plots the measured period and cycle-to-cycle jitter as a function of the applied pressure, ranging from 1 to 2 bar. The variation in capacitance is then between 6 and 6.6 pF [9], which theoretically results in an N T R of 6.57% (Eq. (6)). The measured N T R is slightly lower at 4.85%. The nonlinear behavior is due to the sensor characteristic [9]. The measured jitter performance corresponds to −100.4 dBc/Hz at 100-kHz offset from f0 = 4.90 MHz. Due to the limited tuning range, the sample frequency fCLK of the period-todigital converter is only 103 kHz to have 1-b quantization. The measured spectrum of the 1-b digitized output is depicted in Fig. 9 for a DC input. For a bandwidth of 3 kHz, the SNR is equal to 43.9 dB, or 7-b resolution, and is limited by the small sensor sensitivity. Table I summarizes and compares the performance of our design to current state-of-the-art PM-based sensor interfaces. In none of them the power consumption of the period-to-digital converter is incorporated. The reported FoMN is calculated as follows: Power FoMN = (7) (Resolution−20 log(ΔCS )/6.02) 2 · Bandwidth · 2
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Type Techn. [μm] Area [mm2 ] Resolution [bit] Power [mW] Conv. time [ms] Supply [V] Input range [pF] FoMN [pJ/(pF-conv)]
[1] JSSC ’08 PM 0.7 2.6 16 7 100 5 0-4.7 50209
[2] ISIE ’10 PM 0.7 3 20 5 1000 5 0-5.8 27661
[3] JSSC ’12 PM 0.35 0.51 15 0.211 7.6 3.3 0-6.8 333
[This work] Var. Pres. cap. sens. PM PM 0.13 0.13 0.05 0.05 10.5 7 0.371 0.371 0.05 0.167 1.2 1.2 3.7-13.7 6-6.6 133 290
and normalizes the energy consumption to the resolution per 1 pF ΔCS sensor input variation, and is expressed in pJ/(pFconversion). The table shows an improved area and energy efficiency (FoMN ) compared to previous state-of-the-art period modulation(PM)-based sensor interfaces. V. C ONCLUSIONS This paper has described the optimization of a capacitancecontrolled oscillator used as a period modulator in a timebased sensor interface. The circuit has been prototyped in 130nm CMOS technology and validates the use of on-chip ring oscillators as an interfacing element for external capacitive sensors. The prototyped sensor interface only takes 0.05 mm2 . The circuit performance has been measured with both an external variable capacitor and a bare-die MEMS capacitive pressure sensor. The chip consumes 371 μW from a 1.2-V supply voltage and achieves 10.5-b resolution with 10-kHz input bandwidth with an input capacitance ranging from 3.7 to 13.7 pF. Measurements with both the external capacitor and the MEMS pressure sensor show an improved energy efficiency compared to prior period modulation-based sensor interfaces. ACKNOWLEDGMENT The work of J. Van Rethy is funded by FWO Vlaanderen. R EFERENCES [1] A. Heidary and G. C. Meijer, “Features and design constraints for an optimized sc front-end circuit for capacitive sensors with a wide dynamic range,” IEEE J. of Solid-State Circuits, vol. 43, no. 7, pp. 1609–1616, 2008. [2] A. Heidary, S. Heidary Shalmany, and G. Meijer, “A flexible lowpower high-resolution integrated interface for capacitive sensors,” in IEEE Intern. Symp. on Industr. Electr. (ISIE), pp. 3347–3350, 2010. [3] Z. Tan, S. H. Shalmany, G. C. Meijer, and M. A. Pertijs, “An energyefficient 15-bit capacitive-sensor interface based on period modulation,” IEEE J. of Solid-State Circuits, vol. 47, no. 7, pp. 1703–1711, 2012. [4] J. Kim, et al., “Analysis and design of voltage-controlled oscillator based analog-to-digital converter,” IEEE Trans. on Circuits and Systems-I: Regular Papers, vol. 57, no. 1, pp. 18–30, 2010. [5] R. Poore, “Phase noise and jitter,” Agilent EEsof EDA, 2001. [6] A. Hajimiri, et al., “Jitter and phase noise in ring oscillators,” IEEE J. of Solid-State Circuits, vol. 34, no. 6, pp. 790–804, 1999. [7] S. Gierkink and E. van Tuij, “A coupled sawtooth oscillator combining low jitter with high control linearity,” IEEE J. of Solid-State Circuits, vol. 37, no. 6, pp. 702–710, 2002. [8] J. Frambach, “Electronic circuit with low noise delay circuit,” Nov. 2 2011. EP Patent 1,966,889. [9] Microfab Pressure sensor Die E1.3N [Online] Available: http://www.microfab.de/mems/pressuresensors/pressuresensordie/
2013 IEEE Asian Solid-State Circuits Conference (A-SSCC)
