A 1 V 92 dB SNDR 10 kHz Bandwidth Second-Order Asynchronous Delta-Sigma Modulator for Biomedical Signal Processing

sensors Letter A1V92dBSNDR 10 kHz Bandwidth Second-Order Asynchronous Delta-Sigma Modulator for Biomedical Signal Processing Vilém Kledrowetz * , Lukáš Fujcik , Roman Prokop and Jiˇrí Háze Department of Microelectronics, Brno University of Technology (BUT), Technická 3058/10, 61600 Brno, Czech Republic; [email protected] (L.F.); [email protected] (R.P.); [email protected] (J.H.) *Correspondence: [email protected]; Tel.: +420-541-146-101 Received: 30 June 2020; Accepted: 23 July 2020; Published: 25 July 2020   Abstract: In this paper, a second-order asynchronous delta-sigma modulator (ADSM) is proposed based on the active-RCintegrators. The ADSM is implemented in the 0.18 µ m CMOS Logic or Mixed-Signal/RF, General Purpose process from the Taiwan Semiconductor Manufacturing Company with a center frequency of 848 kHz at a supply voltage of 1 V with a 92 dB peak signal-to-noise and distortion ratio ( SNDR ), which corresponds to 15 bit resolution. These parameters were achieved in all the endogenous bioelectric signals bandwidth of 10 kHz. The ADSM dissipated 295 µ W and had an area of 0.54 mm 2 . The proposed ADSM with a high resolution, wide bandwidth, and rail-to-rail input voltage range provides the universal solution for endogenous bioelectric signal processing. Keywords: asynchronous delta-sigma modulator (ADSM); center frequency; operational amplifier; biomedical signals; biosensors 1. Introduction Biomedical electronics have acquired significant attention in healthcare, with a focus on the development of biosensors that enable online monitoring, detection, prevention, and personalized medicine for a variety of chronic and acute diseases. Especially in the last few years, there has been growing interest in the design of biomedical wireless sensors [ 1 – 3 ]. Biomedical signals can be subdivided into two major classes: (1) endogenous signals that arise from natural physiological processes and are measured within or on living creatures (e.g., (EOG), electroencephalogram (EEG), electrocardiogram (ECG or EKG), electromyogram (EMG), temperature, blood glucose, etc.) and (2) exogenous signals applied from the outside (generally noninvasively) to measure internal structures and parameters. Endogenous bioelectric signals are invariably small, ranging from single microvolts to over 100 mV. Their bandwidths range from DC to perhaps 10 kHz at most [ 4 – 7 ]. The voltage and frequency ranges of some common biopotential signals are shown in Figure 1. A general biomedical system consists of an energy source, a differential amplifier, analog-to-digital conversion (ADC), digital signal preprocessing, and a communication subsystem. The ADC is one of the key building blocks, which enables converting analog signals from biomedical sensors to a digital format that can be easily processed and analyzed. For the design of the ADC, many authors choose the SARarchitecture due to its suitability for low-power and low-voltage requirements [ 8 – 11 ]. Recently, delta-sigma ( ∆Σ ) ADC has been gaining more and more popularity. Compared to other conversion techniques, ∆Σ ADCs cover the widest conversion region of the resolution-versus-bandwidth plane, providing the most efficient solution to digitize diverse types of signals in many different applications such as biomedical ones [ 12 ]. There exist two basic types of ∆Σ modulators: discrete-time (DTDSM) and continuous-time (CTDSM). The DTDSM is more Sensors 2020,20, 4137; doi:10.3390/s20154137 www.mdpi.com/journal/sensors Sensors 2020,20, 4137 2 of 13 attractive for high-resolution applications due to its higher linearity and accuracy. On the other hand , less stringent amplifier speed specifications are required in CTDSM due to the absence of switches in the active-RC integrator, allowing achieving a higher speed of operation and lower power consumption. The asynchronous ∆Σ modulator (ADSM) can be considered as a special type of CTDSM. ADSM is simple , does not require any clocking, matches well with mainstream CMOS technology, and can operate at low current and supply voltages [ 13 – 15 ]. A comparison between DTDSM, CTDSM, and ADSM is shown in Table 1. 10−1 100101102103104 10−5 10−4 10−3 10−2 10−1 Frequency (Hz) Voltage (V) EOG (electrooculogram) EEG (electroencephalogram) EEG (electrocardiogram) DC potential EMG (electromyogram) AAP (axon action potential) Figure 1. Voltage and frequency ranges of some common biopotential signals. Table 1. Comparison between DTDSM, CTDSM, and ADSM. DTDSM CTDSM ADSM + Synchronous system + Synchronous system + Immunity to clock jitter + High resolution + Implicit antialiasing filter + Implicit antialiasing filter + Highly linear SC integrator + Higher sampling frequency + Simple circuit + Accurately defined integrator + Relaxed operational amplifier + Relaxed OpAmp gains and transfer function speed requirements speed requirements + Low sensitivity to clock jitter + Higher conversion speed + Higher conversion speed and excess loop delay + Low power + Low power + Low sensitivity to DAC settling time + Do not require a clock - Low conversion speed - Sensitivity to clock jitter - Complex decoding scheme - Required pre-antialiasing filter - Excess loop delay - Lack of noise shaping - Required non-overlapping - Lower resolution - Lower resolution clock generator In several publications, DTDSMs are used for biomedical signal processing [ 1 , 16 , 17 ]. There also exists solutions utilizing ADSM [ 18 – 20 ]. These ADSM are distinguished by very low power consumption in the order of tens of nanowatts. However, their bandwidth is very low in the order of tens of Hertz. The proposed ADSM covers the full bandwidth of endogenous bioelectric signals up to 10 kHz. The differential input range equals VDDA with a 0.5 V reference level ( VCM ). The proposed ADSM with high resolution, wide bandwidth, and rail-to-rail input voltage range provides the universal solution for endogenous bioelectric signal processing. The circuit not only offers an alternative to the developed CTDSMs and DTDSMs, but it also fills the gap between published ADSMs, which do not allow processing the full spectrum of biomedical signals according to Figure 1except for those with a very high bandwidth in the order of MHz. An important parameter of ADSM is the center frequency, the calculation of which is part of this work. The following sections provide the details of our approach. Sensors 2020,20, 4137 3 of 13 2. Asynchronous Delta-Sigma Modulator There are two major types of architecture for ∆Σ modulators. The first one is the single-loop and the second the multi-loop architecture. Multi-loop architectures are commonly denoted as cascade or MASH (multi-stage noise shaping). A major drawback of MASH modulators is that precise matching of the analog and digital signal processing paths is required to avoid large errors (quantization noise leakage) caused by integrator gain coefficient variations. Because RC integrators are used in this design, where variations of about 20% in the RC time constant can be expected, the single-loop architecture was chosen in this work. Its stronger ability to achieve high SNDR since it does not suffer from matching errors, which severely affect MASH modulators, is the major advantage in the design. The block diagram of the second-order ADSM based on the cascade of integrators with distributed feedback (CIFB) topology is shown in Figure 2. C1 R1 VCM R2 C2 R3 VCM R4 VCM VIN(t) I1(t) VOUTP(t) +VREF -VREF VOUTN(t) VY1(t) VY2(t) VDDA VSSA VDDA VSSA I3(t) I4(t) I2(t) Figure 2. Simplified schematic of the second-order ADSM with the CIFB topology. The circuit consists of two integrators and a binary quantizer with hysteresis. The output VOUTP (or VOUTN ) is a pulse width modulated square wave of period TPER with a pulse width TPW . The duty cycle d is proportional to the amplitude of the input signal (Equation (1)). Moreover, the period TPER of the asynchronous modulator output signal is modulated by the normalized input voltage VIN (Equation (2)) [21]. d=VIN +1 2=TPW TPER (1) and: f0 fc =1−V2 IN and |v|<1 (2) where f0 is the output carrier frequency, fc is the maximum value of f0 , namely the center frequency, and |VIN|<1 is the normalized input amplitude. The center frequency of ADSMs determines the carrier-to-bandwidth ratio ( CBR =fc/( 2 B) , where B is the input signal bandwidth), which is the ratio between the center frequency and the signal bandwidth. This ratio is equal to the oversampling ratio ( OSR ) in synchronous delta-sigma modulators. It determines the minimal center frequency required for a certain conversion accuracy. The critical condition can occur when VIN is close to the full scale. The output frequency will decrease, and the high-frequency distortions around the center frequency shift to the low-frequency region. Consequently, distortions can leak into the baseband and adversely affect the modulator linearity for large input amplitudes. Therefore, the center frequency should be set far away from the baseband to avoid these components shifting into the signal baseband, and a high order filter is required to attenuate these out-band components. In order to achieve a high center frequency without degeneration of the linearity, the second-order topology was chosen. To calculate the center frequency of the proposed ADSM, the integrators’ output voltages are expressed as: VY1(t) = −I1(t) C1 +I2(t) C1t+VCM (3) Sensors 2020,20, 4137 4 of 13 VY2(t) = −I3(t) C2 +I4(t) C2t+VCM (4) where I1(t),I2(t),I3(t), and I4(t)can be expressed as: I1(t) = VIN(t)−VCM R1 (5) I2(t) = VREF(t)−VCM R2 (6) I3(t) = VY1(t)−VCM R3 (7) I4(t) = VREF(t)−VCM R4 (8) In order to find the center frequency, the timing diagram in Figure 3is considered, which corresponds to the schematic in Figure 2. t VIN VDDA VSSA VCM t VY1 VY1(mean) ∆VY1 VY2 VOUTN VCM t +VH -VH VCM t VREF -VREF VCM T1T2T1T2 Figure 3. Timing diagram of the asynchronous sigma delta modulator with a constant input. The duty cycle of the ADSM is given by the ratio of rising ( SRE )-to-falling edge ( SFE ) speed. To facilitate the equations, a symmetrical power supply is considered ( VDDAs =VDDA −VCM , VCM =0V , VSSAs =VSSA −VCM , VREF =VDDAs =|VSSAs| ; |VHL −VCM|=VHH −VCM =VH ). During the T1period, the output voltage of the first integrator VY1rises with speed, given by: SRE1=dVY1 dt =I1+I2 C1 =VIN R2+VREFR1 R1R2C1 (9) and the falling edge during T2: SFE1=dVY1 dt =I1+I2 C1 =VIN R2−VREFR1 R1R2C1 (10) The first integrator output voltage swing is in the range of: ∆VY1=VY1(mean)±|VH|I2 I4 (11) where VHis the comparator threshold voltage. Sensors 2020,20, 4137 5 of 13 In order to find VY1(mean) , we calculate I3(mean) . The duty cycle of the second integrator output VY2 is the same as the first one. From Equations (9) and (10), the value of I3(mean) is calculated to meet the duty cycle requirements. I3(mean)=VY1(mean) R3 =−VIN R2 R1R4 (12) For period T1, we can write: T1=2VHR1R4C2 R1VREF −VIN R2 (13) T2=2VHR1R4C2 R1VREF +VIN R2 (14) The entire period can be expressed as: TPER =T1+T2(15) When a zero input is applied VIN = 0, the output of the ADSM is a square wave with a duty cycle of 50%. By defining TCas the period of the output signal, it can be calculated as: TC=TPER =2T1=2T2=4VHR4C2 VREF (16) Similar to the conventional synchronous CTDSMs, propagation delay is also an issue in ADSMs. The delay of the comparator increases the effective value of hysteresis and negligibly affects the center frequency of the ADSM. Therefore, the impact of the comparator delay, τ , on the center frequency of the proposed ADSM can be given by: TC=TPER =2T1=2T2=1 fC =4VHR4C2 VREF +τ(17) Equation (17) shows that the center frequency fC of the modulator will decrease for a higher delay of the comparator, which degenerates the input bandwidth and linearity of the modulator [20]. 3. Transistor Level Realization In this section, the transistor level implementation of the ADSM will be described. Figure 4 illustrates the circuit diagram of the proposed ADSM. The implemented architecture is fully differential to minimize even-order harmonics, as well as common-mode noise. C1 C1 R1 VCM R2 R2 VINP VOUTP VOUTN R1 VINN C2 C2 R3 VCM R4 R4 R3 Figure 4. Proposed second-order asynchronous delta–sigma modulator. 3.1. Active-RC Integrator In the proposed design, the active-RC integrators were used due to simplicity, high linearity, parasitic insensitivity, as well as the overall power consumption. The ideal transfer function of the active-RC integrator is given by: Int(s) = 1 sRC =ki fs s(18) Sensors 2020,20, 4137 6 of 13 where fsis the sampling frequency and kiis the scaling coefficient. The parameters of the resistors and capacitors were designed to achieve a high center frequency according to Equation (16). The lower limit for R and C is defined by matching consideration and maximum charging current in the case of R . The upper limit for R is set by the allowed thermal noise level, which itself is fixed by the overall dynamic range requirements. Finding optimal R and C was also confirmed by behavioral simulations in MATLAB/Simulink, as well as variations of about 20% in the RC time constant. The R and C values were R1 = 650 k Ω , R2 = R4 = 500 k Ω , R3 = 357 k Ω , VH = 90 mV , C1 = C2 = 2 pF, and IR = 1 µ A. It can be calculated from Equation (16) that fC = 1.39 MHz, and from Equation (11), VY1(mean) = (0 ± 90) mV. The validity of these results was verified in MATLAB/Simulink and is shown in Figure 5. −0.1 0 0.1 VY2 (V) −0.1 0 0.1 VY1 (V) 103104105106107 −150 −100 −50 0 Frequency (Hz) Power spectral density (dB) 12 12.5 13 13.5 −0.5 0 0.5 Time (µs) VOUTN (V) (a) (b) f C = 1.39 MHz 0.36 0.36 Figure 5. MATLAB model simulation results: ( a ) timing diagram and ( b ) frequency spectrum of the ADSM for VIN = 0 V. As will be seen later, nonidealities such as input parasitic capacitances of the operational amplifier and the delay of the comparator negligibly affect the center frequency of the modulator. 3.2. Class AB Fully Differential Operational Amplifier The integrators in the ADSM were each implemented using the two-stage, Class A/AB operational amplifier topology shown in Figure 6. This topology combines a simple differential pair as the first stage with a Class A/AB second stage, wherein push-pull operation is implemented using current mirrors [22]. The slew-rate is limited only by the first stage. SR =I5 CC1+CG6+CG13 (19) The minimum value of the operational amplifier slew-rate can be determined from the falling edge speed of VY2 ( SFE2 ) according to Figure 3. The input parasitic capacitance of the comparator (Ccomp) should be included in the calculations. Thus, |SFE2|=dVY2 dt =I3+I4 C2+Ccomp =VY1R4+VREFR3 R3R4(C2+Ccomp)(20) The use of PMOS input transistors makes it possible to avoid the body effect. The compensation network is comprised of capacitor CCand resistor RM, which cancels the right half plane zero. Sensors 2020,20, 4137 7 of 13 VDDA VINP VINN VOUTP VOUTN VCM IBIAS M1 M3 M6 M8M9M11 M19 M15 M17 RM CCCC RM RCM RCM M18 M16 M13 M7 M14 M10 M12 M4 M5 M2 Figure 6. Circuit schematic of the two-stage Class A/AB operational amplifier. For the detection of the common-mode output voltage, two equal resistors were used (RCM =500 kΩ) . The voltage between the two resistors is subtracted from the desired common-mode output voltage, VCM , and scaled by the one-stage differential amplifier that consists of source-coupled pair M 15 –M 16 , diode-connected loads M 17 and M 18 , and tail current source M 19 . The main reason for using this solution is that the input to the common-mode sense amplifier (gate of M 15 ) is almost constant. Therefore, this CMFB solution does not limit the operational amplifier output voltage swing. Table 2sums up the simulated parameters of the operational amplifier used in the integrators. Table 2. Simulated parameters for the operational amplifier (CL= 3 pF). Parameter Condition Value Hysteresis |VTH|=|VTL|90 mV Time delay CL=3pF 50 ns Slew-rate CL=3pF 42 V/µs Power consumption duty cycle = 50% 5 µW Input capacitance 0.4 pF IBIAS 2.5 µA 3.3. Comparator with Hysteresis The schematic of a comparator using the internal positive feedback circuit is given in Figure 7. The comparator consists of a differential pair (M 1 –M 2 ) with output inverters in order to to achieve reasonable voltage swings, output resistance, and differential output. A second, smaller differential pair, M 6 –M 7 , unbalances the input differential pair. The inputs of the second differential pair are tied to the output signals in such a way as to introduce positive feedback and, hence, hysteresis. VDDA M1 M3M4 M5 M17 M8 M6M7 M9M11 M13 M15 M10 M12 M14 M16 M2 VINP IBIAS VOUTP VOUTN VINN Figure 7. Comparator with hysteresis using an unbalanced differential pair. Sensors 2020,20, 4137 8 of 13 If M 1 and M 2 are operating in strong inversion, the amount of hysteresis VTH −VTL can be calculated using [23]: VTH −VTL =2(√ID3+ID11 −√ID3−ID11) pµCOX(W/L)1 (21) If M1and M2are operating in weak inversion, VTH −VTL =4nUTtanh−1(ID11/ID3)(22) Assume that the gate of M 1 ( VINP ) is tied to VDDA . With the input of M 2 ( VINN ) much less than VDDA , M 1 is off and M 2 on, and VOUTP is at VDDA and VOUTN at VSSA , thus turning on M 7 and turning off M 4 and M 6 . In this state, no current flows through the differential pairs. As the voltage at the VINP input decreases toward the threshold point (Equations (21) or (22)), some of ID5 begins to flow through M 1 and M 3 , and simultaneously, some of the hysteresis bias current ID8 begins to flow through M 4 . This continues until the point where the current through M 1 equals the current ID8 . Just beyond this point, the comparator switches its state. Figure 8shows the voltage transfer characteristic of the comparator. The hysteresis bias current ID8 was 6.8 µ A, and the input bias current ID5 was 10 µ A. The output high-to-low threshold, VTL , was simulated as − 90 mV. The output low-to-high threshold, VTH , was simulated as +90 mV. The amount of hysteresis was 180 mV. Simulated parameters of the comparator circuit are given in Table 3. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 −0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 VINP (V) VOUTP (V) VTH=VCM + 0.0932 VTL=VCM - 0.0912 +VREF -VREF Figure 8. Simulated DC transfer characteristic of the comparator. Table 3. Simulated parameters for the comparator. Parameter Condition Value Hysteresis |VTH|=|VTL|90 mV Time delay CL=3 pF 50 ns Slew-rate CL=3 pF 42 V/µs Power consumption duty cycle = 50% 5 µW Input capacitance 0.4 pF IBIAS 2.5 µA According to parameters mentioned in Tables 2and 3, the center frequency was recalculated to fC=857 kHz. 4. Simulation Results The ADSM was designed utilizing the 0.18 µ m CMOS Logic or Mixed-Signal/RF, General Purpose process from the Taiwan Semiconductor Manufacturing Company. The circuit was designed for VDD =1V and IBIAS = 2.5 µ A. After completion of the layout design, its parasitic extraction was Sensors 2020,20, 4137 9 of 13 performed to find the parasitic resistances and capacitances corresponding to the designed devices and interconnects. After parasitic extraction, all simulations were performed using the Spectre simulator on the Cadence platform. The layout of the ADSM is shown in Figure 9. The layout size is 350 ×155 µm . R1, R2, C1 Operational amplifier1 Operational amplifier2 Comparator R3, R4, C2 Figure 9. Layout of the proposed ADSM. The ADSM output bitstream can be recovered by applying an ideal low pass filter with a cut-off frequency at the signal bandwidth. When ADSMs are used in A/D data conversion, a decoding circuit is required. The simplest one is the sample and hold circuit with a high sampling frequency. The time domain waveforms of the output signal VOUTN for VIN = 0 V and the corresponding frequency spectrum are shown in Figure 10. The limit cycle frequency of the post-layout model of the ADSM was equal to 848 kHz and was very close to the calculated value in Section 3.3 ( fC= 857 kHz). The small difference was caused by the parasitic capacitances and resistances extracted from the layout. 1 2 3 4 5 −1 −0.5 0 0.5 1 Time (µs) VOUTN (V) 103104105106107 −200 −150 −100 −50 0 Frequency (Hz) Power spectral density (dB) fC = 848 kHz 0.56 0.56 (a) (b) Figure 10. Post-layout simulation results: ( a ) timing diagram and ( b ) frequency spectrum of the ADSM for VIN = 0 V. Figure 11 shows the simulated spectrum of the ADSM for a sinusoidal input signal with an amplitude of (a) 100 mV (20% modulation depth) and (b) 500 mV (100% modulation depth). The corresponding spectra were obtained by applying a signal at fIN ≤fBandwidth/ 3 to include at least the second and third harmonic inside the band of interest. Due to this reason, the input frequency was set to 3.125 kHz, and then the third harmonic component was located in the 10 kHz bandwidth. The achieved SNDR was (a) 91.84 dB and (b) 78.13 dB. In the second case, the significant SNDR reduction was caused by higher harmonic tones.