A CMOS Low Pass Filter for SoC Lock-in-Based Measurement Devices

Abstract

This paper presents a fully integrated G_m–C low pass filter (LPF) based on a current steering G_m reduction-tuning technique, specifically designed to operate as the output stage of a SoC lock-in amplifier. To validate this proposal, a first-order and a second-order single-ended topology were integrated into a 1.8 V to 0.18 µm CMOS (Complementary Metal-Oxide-Semiconductor) process, showing experimentally a tuneable cutoff frequency that spanned five orders of magnitude, from tens of mHz to kHz, with a constant current consumption (below 3 µA/pole), compact size (<0.0140 mm²/pole), and a dynamic range better than 70 dB. Compared to state-of-the-art solutions, the proposed approach exhibited very competitive performances while simultaneously fully satisfying the demanding requirements of on-chip portable measurement systems in terms of highly efficient area and power. This is of special relevance, taking into account the current trend towards multichannel instruments to process sensor arrays, as the total area and power consumption will be proportional to the number of channels.

1. Introduction

Recent technological advances in the implementation of CMOS-based sensors has raised the interest of designing low-power compact electronic interfaces to be integrated in the same chip as the sensing element, so as to obtain miniaturized system-on-chip (SoC) portable devices with improved reliability and reduced fabrication costs. In this endeavor, there is one crucial front-end basic building block that possess significant challenges in being fully integrated with high performance, compact size, and low-power consumption—low-pass filters (LPFs) with very low cutoff frequencies.

Accordingly, in recent years, there has been significant research efforts towards the development of such LPFs, boosted mainly because of their application in biomedical systems [1,2,3,4], where it is necessary to low pass filter the signal over the frequencies of interest—typically in the 100 mHz to 1 kHz range—to remove noise before digitizing it for further processing. These LPFs are also widely used as DC (Direct Current) magnitude extractors; in this case, they are typically placed in the last stage of the sensor readout chain and require sub-Hz cutoff frequencies, such as in lock-in amplifiers (LIA), an extremely versatile instrument mostly used as a precision AC (Alternating Current) voltage and AC phase meter, or equivalently, as an impedance spectroscope [5,6,7,8,9,10,11,12,13], an application field that is the motivation of this work.

Lock-in amplifiers are based on a technique known as phase sensitive detection (PSD) that can extract the amplitude and phase of a signal even in a noisy environment operating at a known frequency f₀ [14,15,16,17]. In a single-phase LIA, the input signal V_in = a_s*sin(ωt) (sensor response) is typically amplified by a low-noise amplifier (LNA) A_s = A_LNA*a_s; then, a mixer or phase-sensitive detector controlled by a reference signal V_ref of the same frequency f₀ and aligned in phase (θ = 0) with V_in demodulates the input signal [18]. An output LPF, with a suitable corner frequency, extracts the DC component V_X of the resulting synchronously modulated signal, which is proportional to the input signal amplitude according to

$$V_X=\frac{V_{dd}}{2}+\frac{2A_{s}cos\left(\theta \right)}{\pi },$$

(1)

assuming that V_ref is a digital signal, V_dd is the system single supply, and V_dd/2 the common mode voltage.

To recover both amplitude and phase information, a dual-phase LIA with two branches—with two outputs V_X and V_Y, instead of one (Figure 1)—is needed. The input signal is respectively multiplied in both branches by quadrature reference signals V_ref (f_o) and V_ref (f_o, 90°), recovering after the corresponding LPF the DC outputs V_X and V_Y, proportional to the magnitude and phase or, equivalently, the real and imaginary components:

$$V_x=\frac{V_{dd}}{2}-\frac{2A_{s}cos\left(\theta \right)}{\pi },$$

(2)

$$V_y=\frac{V_{dd}}{2}-\frac{2A_{s}sin\left(\theta \right)}{\pi }.$$

(3)

Assuming that all the electronics prior to the filter present low noise performance, the accuracy in the recovery largely depends on the LPF cutoff frequency. In this sense, a LIA can be understood as a band-pass filter with central frequency f₀ and a very high quality factor Q = (f₀/f_c), where f_c is the bandwidth of the output low-pass filter. Hence, the smaller the LPF cutoff frequency, the better the noise rejection and the better the recovery accuracy, but a compromise arises with the related acquisition times.

Different integrated LIAs have been recently proposed for smart instrumentation applications [13,19,20,21] to exploit the advantages that render CMOS compatibility in terms of miniaturization. However, these LIAs maintain the LPF external use of off-chip resistors and capacitors [19,20,21] or, for fully integrated LIA solutions [13], the active filter area is rather large (it is the dominant element of the 3.6 mm² area of the implemented chip) for frequencies ~300 Hz. In particular, a previous author’s proposal [21] achieves very competitive capabilities in terms of area, power, and signal recovery, but the LPF is also kept external. Thus, the purpose of this work was to design an LPF suitable for this LIA architecture to achieve a fully integrated design. Accordingly, the design specifications were 1.8 V to 0.18 µm CMOS monolithic single-ended stage with two configurable cutoff frequencies of 0.5 and 5 Hz to bring flexibility to the system adjusting the speed-accuracy trade-off; input range from V_dd/2 = 0.9 V up to V_dd = 1.8 V, corresponding to the synchronous rectified signal range, assuming a single supply V_dd = 1.8 V and signals over a common-mode V_cm = V_dd/2; low noise, to preserve high dynamic range; compact size (<0.1 mm²) and minimum power consumption (<10 µW) with currents of the order of hundreds of nA to be reliably generated on-chip.

There is a vast amount of literature on integrated low pass filters with very low-cutoff frequencies, mainly based on G_m–C approach [22,23,24,25,26,27,28,29,30,31,32,33,34,35,36] and focused on biological signal processing. Therefore, besides not strictly presenting a tuneable frequency over our target sub-Hz to Hz range (5.4 kHz [22], from 2 kHz to 20 kHz [23]), some of them exhibit a power consumption rather high to be suitable to be integrated within multichannel systems ([24] consumes 75.9 µW, [25] from 59.5 µW to 90 µW, and [26] 105.3 µW including a buffer). Among those that are power-efficient, either area is jeopardized, restricting their use within portable devices (an area of 0.336 mm² is reported in [27], 0.2 mm² in [28,29] has an external 10 nF capacitor, [30] has an area of 1 mm², and an area of 0.24 mm² is reported in [31]), or dynamic range is jeopardized (34 dB [22] and 49.9 dB [32]), whereas others achieve such low power thanks to bias currents in the order of pA or a few nA, which are difficult to be reliably generated on-chip and are typically tuned to adjust the G_m and thus adjust the cut-off frequency (from 300 pA to 900 pA [33], from 90 pA to 430 pA [34], in [35] two bias currents are used ranging from 200 pA to 4 nA and from 1 nA to 20 nA respectively, and from 250 pA to 25 nA [36]), existing on the overall power-area-dynamic range trade-off that makes their design a real challenge.

Thus, a novel low pass filter is needed that satisfies all the needed specifications for its operation as a DC extractor in a portable multichannel LIA-based measurement system, enhancing the state-of-the-art power-area-dynamic range trade-off, so as to obtain a topology suitable for its use in the next generation of lock-in based-measurement devices for impedance sensor arrays.

To do so, we notice that in [1] an OpAmp active-RC low pass filter with a current steering technique (CST) that attenuates the current through the integrator in the feedback loop is proposed, reaching an f_c down to 0.25 Hz from a nominal target f_c of 18 Hz. It is a simpler structure compared to previously reported G_m–C techniques, but at the expense of a reduced input impedance. Thus, in this work, a G_m–C approach was adopted to attain a high impedance input node, which made the coupling between stages straightforward. The core of the V–I converter remained unaltered so that the bias point was not moved from its optimum value, whereas both G_m reduction and tuning were done in the transconductor output current transfer section, exploiting a current steering technique as the most suitable choice for effectively reducing the G_m, preserving a good overall performance trade-off. In this way, all the requirements of a SoC high performance solution can be simultaneously met, bringing about a very competitive solution.

Authors have reported preliminary simulation results of the basic integrator in [37]. This current paper offers a more in depth study and the complete experimental characterization of these structures. The paper is organized as follows: Section 2 describes the proposed G_m topology and the two derived low pass filters. The experimental results are summarized in Section 3, in Section 4 experimental measurements of the LPF applied to a lock-in amplifier are shown, and conclusions are drawn in Section 5.

2. Proposed G_m-C LPF

A single-input single-output LPF was required for our application (Figure 1). Therefore, a differential-input single-output G_m-C architecture in unity gain feedback configuration was adopted. The resulting closed-loop configuration maintained, without a specific G_m linearization technique, good linearity in the passband over all the input range while not degrading the noise [36], optimizing the dynamic range in this way. Note that for this scheme, when the input signal frequency is close to the filter cut-off frequency, there will be an important phase shift among both inputs of the transconductor, which will cause distortion. Therefore, it is not a general-purpose low-pass signal-processing filter, but a DC extractor for synchronously rectified signals operating at higher frequencies. Figure 2 shows the basic order-1 scheme and the corresponding transfer function, with a pole located at G_m/C [38]. The load capacitor value was set to 50 pF, considered the maximum practical on-chip capacitor.

Two structures were implemented: the basic integrator (order-1 filter, O1F) in Figure 2 and a second-order LPF (O2F).

2.1. Transconductor Architecture

The transconductor core was the classic mirrored Operational Transconductance Amplifier (OTA) (Figure 3a). Its overall transconductance was given by G_m = k*g_m1, with g_m1 the transconductance of the input differential pair M1 and k the gain factor of the current mirror. To keep an intrinsic reduced G_m value, the input pair was designed to have a small g_m1 ~µS with a bias current I_Bias = 0.5 µA while unity gain (k = 1) current mirrors were used. Thus, this scheme provided the same gain G_m = g_m1 as the classical differential pair, but uncoupled the input and output common-mode range at the cost of doubling the power consumption. Because the input voltage needs to swing from V_dd/2 to nearly V_dd for our target LIA application, a Negative-channel Metal-Oxide-Semiconductor (NMOS) input pair was used.

On the basis of this structure (Figure 3a), the idea was to keep constant the input V–I conversion gain (g_m) so that the input NMOS differential pair was biased with a constant bias current introduced through a 1:2 current mirror, and a current steering technique was introduced in the output current transfer section to reduce the overall G_m. This was achieved by replacing the conventional M2 current mirrors by current steering gain tuneable M2–M3 high swing cascode current mirrors, as shown in Figure 3b. Transistors M2 remained equal, but cascode transistors M3—both in the input and output branches—were split into identical transistors driven not by a constant V_C gate voltage but by complementary control voltages V_± = V_C ± V_gc [39], resulting in two output branches conveying complementary currents.

Because transistors M2 present the same drain to source voltage and gate to source voltage, the current mirror operated properly, rendering unity gain current I_out = I_in. The output current I_out was split into two complementary currents, I_O1 and I_O2, whose fractional value α_i (0 ≤ α_i ≤ 1) depended upon the differential control voltage V_gc:

$$\begin{array}{c}\begin{array}{c} I_{out}=I_{O1}+I_{O2,}\\ I_{O1}=\left(1-{\propto }_i\right)I_{in},\end{array}\\ I_{O2}= {\propto }_i{I}_{in}.\end{array}$$

(4)

Therefore, the transconductance gain for each output had complementary values:

$$\begin{array}{c} G_{m_{O1}} = \left(1-{\propto }_i\right)g_{m1}, \\ G_{m_{O2}} = {\propto }_i{g}_{m1}, \end{array}$$

(5)

with G_mo1 + G_mo2 = G_m = g_m1.

The simulated behavior of the DC current splitting over the control voltage variation is shown in Figure 4a, for V_gc > 0 (the figure is complementary for V_gc < 0). The tuning voltage variation V_gc ranged from 0 up to ≈200 mV, to keep the output offset bounded below ±1% and a DC gain error below 0.5 dB. Note that for V_gc = 0, I_O1 = I_O2 = I_Bias/2 = 250 nA; for V_gc > 0, I_O1 < I_O2; for V_gc < 0, I_O1 > I_O2 and the complementary division is obtained [39].

The simulated transconductance variation in both branches O1 and O2 is shown in Figure 4b. Initially, transistors M3_O1 and M3_O2 were in saturation, strong inversion, and I_O1 and I_O2 followed a linear relation with V_gc (up to ≈50 mV). Transistor M3_O2 remained in strong saturation over all V_gc variation, but for approximately V_gc > 50 mV, M3_O1 entered the weak inversion regime, and thus its current had an exponential relationship with V_gc and therefore the transconductance for O1 followed a linear dependence with V_gc in a logarithmic scale, as can be seen in Figure 4.

Figure 5 shows the capacitance variation of a MOS (Metal-Oxide-Semiconductor) capacitor over the output voltage, showing that from V_dd/2 to V_dd it had a constant 50 pF capacitance.

2.2. O1-Filter: O1F

The schematic of the basic unity gain integrator, named O1F, is shown in Figure 6a. Transistor sizes (in µm/µm) were M1 = 7.5/10, M2 = 10/4, M3 = 5/4, M4 = 1/4, MB = 2/10, and MB’ = 4/10. It had a 1.8 V supply voltage with a common mode V_cm = V_dd/2 = 0.9 V, V_C of the complementary control voltages at the gates was set to 1.2 V to maximize the input range, the bias current—externally generated—was set to 0.5 µA, with a total power consumption of 5.4 µW. The reason for using such lengths (L = 10 µm) was, on one hand, to reduce the input-referred noise at the differential input pair. On the other hand, in this way, a small W/L ratio can be achieved, making the input pair g_m smaller (g_m ≈ 10 µS) while operating in saturation with bias currents ~µA.

For the output stage, two conventional NMOS cascode current mirrors generated the complementary outputs O1 and O2.

Cascode current mirrors were chosen instead of high swing cascade, as an output voltage of 0.9 V was needed, and since the operating range for the application was from V_dd/2 to V_dd, an increase on the voltage range towards V_ss was not needed, and in this way an extra bias voltage was saved. Output O1 was selected as the integrator output, and output O2 is kept at V_dd/2 to preserve symmetry and assure linear current division in the output branches.

Figure 6b presents the microphotograph of the integrated O1F. The active area of the proposed G_m structure without the capacitor was 78.5 × 61.5 µm². As shown, both a MIM (Metal-Insulator-Metal) and a MOS capacitor were implemented so that a performance comparison can be made. A clear advantage of using a MOS capacitor instead of an MIM capacitor was the great save in area (a reduction of the 85%). Thus, the total active area with the MOS capacitor was 0.0140 mm².

2.3. O2-Filter: O2F

The second order filter, named O2F, was also a unity gain scheme based on [27] with a quality factor Q = 1/√2 given by C₂ = 0.5C₁, C₁ = 50 pF, both MOS capacitors. Figure 7a shows its structure as well as its quality factor and cutoff frequency, where each G_m structure was identical to the one reported in the previous subsection, again with a bias current of 0.5 µA, and thus the total power consumption was 9.9 µW. The microphotograph is shown in Figure 7b.

3. Experimental Results

To perform the experimental characterization of the two low pass filters, integrated in a single die (Figure 8), we designed a printed circuit board (PCB) (Figure 9). In Figure 10, the measurement setup is shown—both the experimental setup (Figure 10a) and the block diagram (Figure 10b)—for the characterization of the main parameters of the circuits: tunability, cutoff frequency range, V_in–V_out characteristic, quiescent current, and linearity.

3.1. Experimental Setup

The integrated die had five separated circuits, as can be seen in Figure 8, with the two integrated LPFs presented in this paper being the ones marked in green and blue, using a total of 18 pins (10 for O1F, 7 for O2F and V_ss) out of the 48 existing in the packaging used (48-DIL, Dual-In-Line). All of the circuits had a common ground, but they were biased through different input pins, as not all of them worked at the same supply voltage.

The PCB shown in Figure 9 was designed with a set of jumpers (front) and switches (rear) to select, either manually or automatically with a data acquisition card (DAQ) NI-USB 6008, the circuit to be characterized without compromising the other circuits in the die. For the switches, a low impedance NMOS transistor IRFML8244 (R_DS = 41 mΩ, drain-to-source resistance) with their gates connected to the digital outputs of the DAQ was used.

In addition, there were jumpers to connect the MIM or MOS capacitor and to shortcut V_in with V_out for the O1F so it could be tested as an OTA and as a filter.

One channel of a dual source measurement unit (SMU) Keithley 2636B set the voltage supply to the corresponding activated LPF, and the bias current was supplied to the circuit using the other channel. A second dual SMU was used to provide the control voltage V_gc and the input voltage V_in in the static characterization. A 34401A Agilent 6½ digital multimeter (DMM) was used to read the DC output voltage, V_out. For the dynamic characterization, an Agilent 3352A arbitrary waveform generator (AWG) provided the input voltage, and the transient input and output signals were read through a DPO4104 Tektronix oscilloscope. All the instrumentation was connected to a PC, having the measurement process automatized. Figure 10b shows in grey the instrumentation used for the static characterization and in green the instrumentation used for the dynamic characterization.

The complementary control voltages were provided with an SMU to keep a tight control of their values and study the dependence of the filters parameters with them. However, in order to provide a portable device, this solution was not realistic, and different approaches can be employed to substitute the SMUs either using commercial components such as a digital potentiometer [40], a digital-to-analog converter (DAC) [41,42], or with a microcontroller (µC) if it is used to generate the excitation signal or to read the filtered signals from the LPFs; otherwise, it is also possible to use a specific integrated circuit (IC) to generate these voltages [43,44].

First, the current steering performance was validated. For this, a replica transconductor was included in the die. The current flowing through each output branch, O1 and O2, was measured by connecting a load resistor. From these measurements, the transconductances, G_m,O1 and G_m,O2, and their dependency with V_gc, were derived and are shown in Figure 11, presenting a good matching with the simulation results (Figure 4b).

3.2. G_m-C LPF Cutoff Tunability

Figure 12 shows the filters cutoff frequencies by steeping V_gc in 10 mV steps. The cutoff frequency of the O1F implemented with a MOS capacitor could be tuned from 66 mHz (V_gc = 210 mV) up to 2.5 kHz (V_gc = 0 mV). On the other hand, with an MIM capacitor, the frequency range achieved was similar, from 66 mHz up to 1.2 kHz. Thus, MOS capacitor is the most suitable choice, as it rendered a comparable frequency range but with the advantage of significantly saving area. The cutoff frequency of the O2F could be tuned from 157 mHz (V_gc = 220 mV) up to 5.2 kHz (V_gc = 0 mV). Thus, the target frequencies of 0.5 and 5 Hz initially established were within the ranges of both filters.

Through simulation, it was verified that both target cutoff frequencies could be met even against PT-variations (V is assumed to be provided by a voltage Low Drop-Out (LDO) regulator [45]). Experimentally, to study the influence of the temperature over the cutoff frequency, a Fitoterm 22E thermal chamber from Aralab was used to sweep the temperature from −40 to 100 °C. Despite the dependence with the temperature, it was possible to correct the variation produced by T and achieve a constant f_c over all of the temperature range thanks to the tunability of the circuit. In Figure 13, it was shown that the V_gc tuning needed to keep the cutoff frequency constant at 5 Hz for both filters.

3.3. DC Input/Output Characteristics

Focusing on our two target cutoff frequencies, 0.5 Hz and 5 Hz, Figure 14 shows the static V_in–V_out integrator transfer characteristic. Figure 14a,b presents detailed measurements of the input/output characteristics of filters O1F and O2F, respectively, for both target cutoff frequencies. Figure 14c presents for O2F, f_c = 0.5 Hz, the oscilloscope caption of the output signal for a triangular input signal ranging from 0 to V_dd. These measurements were done following the setup for static behavior presented in Figure 10b, using the 34401A Agilent DMM to read the DC output voltage, and the 2602A Keithley SMU to generate and read the input voltage.

No major difference was appreciated by using an MIM or a MOS capacitor, but from Figure 5 it can be seen that for MOS capacitors the minimum DC output voltage to provide a 50 pF capacitance was ≈0.42 V. The linear input range was 0.43 V (0.45 V-MOS) to 1.65 V (f_c = 0.5 Hz), and 0.39 V (0.45 V-MOS) to 1.67 V (f_c = 5 Hz) for O1F (Figure 14a), whereas for O2F (Figure 14b), it ranged from 0.45 V to 1.65 V and 0.45 V to 1.67 V for f_c = 0.5 Hz and 5 Hz, respectively. Note that this will not affect the achieved dynamic range, as will be shown next.

3.4. Dynamic Range

The total harmonic distortion (THD) as a function of the peak-to-peak amplitude is shown in Figure 15. The setup measurement followed the green setup of Figure 10b, which corresponded with the setup for the dynamic behavior. A sinusoidal input signal at a frequency f_c/5 and with variable amplitude was generated with the 33522A Agilent AWG, whereas the DPO4104 Tektronix oscilloscope measured the output signal. The fast Fourier transform (FFT) of the output signal was recovered, computing the THD for each amplitude of the input signal.

For O1F, THD was below 1% at a frequency f_c/5 up to 210 mV_pp in the cases of f_c = 0.5 Hz and up to 162 mV_pp in the cases of f_c = 5 Hz (Figure 15a). For O2F, THD was below 1% at f_c/5, for amplitudes up to 305 mV_pp and 345 mV_pp for f_c = 0.5 Hz and 5 Hz, respectively (Figure 15b). The THD for the filter using a MIM capacitor presented similar values as with the MOS capacitor.

Figure 15c shows a detailed view of the frequency spectrum for one of the THD values shown in Figure 15a. It shows the input signal (in blue) with a 41 mV_pp amplitude and a 1 Hz frequency coupled with the 50 Hz line signal. The math function (in red) represents the FFT (fast Fourier transform) of the signal after being filtered by O1F with a 5 Hz cutoff frequency. From Figure 15c, after processing the FFT, the THD obtained was 0.65%, which corresponded with the O1F-5 Hz MIM-Cap. value of Figure 15a.

The rms (root mean square) noise was obtained through simulation (Figure 16) of the extracted views of each circuit over an integration band of 10 kHz. Values for cutoff frequencies of 0.5 and 5 Hz were, respecively: 13.3 and 16.3 µV_rms for O1F, and 19.2 and 19.9 µV_rms for O2F. Thus, the dynamic range was above 70 dB for both filters and cutoff frequencies.

4. LPF in a Lock-In Amplifier

The proposed circuits were tested, operating as the last processing element in a lock-in amplifier—a LPF responsible for obtaining the average value of a voltage signal provided by the previous stage, a synchronous rectifier. Figure 17 shows an example of a signal provided by a synchronous rectifier prior to being filtered to recover its DC component, showing a 200 mV_pp noise-free amplitude embedded in white noise with a signal-to-noise ratio (SNR) of 20 dB. The frequency of the input test signals was set to 70 kHz, in the range of the resonance frequencies of the microcantilever-based sensors used in volatile organic compounds (VOC) detection and identification [46]. For the sake of simplicity, we considered test signals as being provided by purely resistive systems, where the DC value followed Equation (2), being the phase shift θ = 0, and a single-phase LIA can recover the input data, whereas for signals provided by complex impedance devices (whose phase shift θ can be nonzero), a dual-phase LIA was needed to recover both amplitude and phase information, and thus two LPFs would be required to obtain the average values given in Equations (2) and (3).

Figure 18 shows the DC voltage values recovered for input signals with amplitude values (peak-to-peak) ranging from 150 µV to 5.75 mV, and an SNR > 20 dB. Signal was previously conditioned by a preamplifier with a gain G = 100. The LPF cutoff frequency was set to f_c = 5 Hz. Selecting a cutoff frequency 10 times lower (f_c = 0.5 Hz), the recovered amplitude would present a higher accuracy but at a much longer output stabilization time. Similarly, a higher f_c would provide a faster response but at a lower accuracy.

The proposed O1F filter presented a current consumption below 3 µA, a tuneable cutoff frequency spanning over five orders of magnitude, and an area of 0.0140 mm²; otherwise, the O2F filter provided a better average voltage estimation but at an increase of power and area consumption.

Table 1. LPF performance comparison with similar G_m-C works.

Parameter	O1F	O2F	[24] ‘14	[25] ‘15	[47] ‘15	[33] ‘18	[32] ‘18	[23] ‘18
Technology (µm)	0.18	0.18	0.6	0.35	0.13	0.35	0.18	0.35
Vsupply (V)	1.8	1.8	3.3	3.3	1.2	0.6	1	1.8
IBias (nA)	500	500	NA	NA	NA	1.5–4.5	NA	14.9–182.3
Power (µW)	5.4	9.9	75.9	59.5–90	450	9–27(10−4)	0.35	0.1–1.31
Order	1	2	2	9	3	4	5	2
Gain (dB)	<0.5	<0.5	≈0	18.8/21.1@fc	10	−2.77	−6/−8	0–12
Area (mm2)	0.0140	0.0264	0.17	0.9	0.08	0.168	0.12	0.12
T range (°C)	−40 to 100	−40 to 100	NA	NA	NA	NA	NA	NA
DC in/out range (V)	0.39(0.45 **)–1.65	0.45–1.65	NA	NA	NA	NA	NA	NA
fc (Hz)	0.066–2.5 k	0.157–5.2 k	2.5 k–10 k	31–8 k	375 k–590 k	101–272	50	2 k–20 k
noise (µVrms)	13.3; 16.3(a,b)	19.2; 19.9(a,b)	91.8; 60.7	93.3; 34.3(c)	342	46.6; 46.8	100	86.3; 84.3
Vpp@THD≤1%	0.22; 0.16(a)	0.305; 0.345(a)	4.13; 3.13	0.082; 0.031(d)	0.45	NA	NA	0.216; 0.294
DR (dB)	75.3; 70.9(a)	75; 75.7(a)	84–85.2	49.8–50.2	53.35	47	49.9	58.9; 61.8
NP (µ)	1.07	1.96	NA	3.34–5.05	NA	NA	0.292	0.02–0.3
Normalized Area	0.432	0.815	0.472	7.347	4.734	1.371	3.704	0.980
FoM1 (10−10)	1.838–3.051	1.743–1.608	NA	12–17.34	NA	NA	1.868	0.114–1.219
FoM2 (µ)	2.64*10−5–1.66	1.126 × 10−4–3.44	2.83–9.84	4.87–1.816 × 103	0.573 × 106–0.9 × 106	1.39 × 10−4–1.12 × 10−3	0.0415	0.11–10.4

* NA: not available, DR: dynamic range, NP: normalization of power, FoM: figures of merit; ** minimum linear range with MOS capacitor; ^(a) for f_c = 0.5 and 5 Hz, respectively; ^(b) simulated; ^(c) minimum noise values; ^(d) @THD < 5%.

shows a comparison with previously reported works covering similar tunability and frequency ranges to our proposals. Analyzing the figures of merit (FoMs) in the literature, we found that the main parameters that are involved are power, dynamic range (DR), order of the filter (n), bandwidth (BW), and area consumption. We included in the table two FoMs defined in [31,32], as they not only take into account all the previous parameters, but also normalize the power (NP) and the area (NA) consumption to the technology used, according to:

$$Fo{M}_1=\frac{NP}{n\ast DR}$$

(6)

$$Fo{M}_2=\frac{Power\ast BW\ast NA}{n\ast DR}$$

(7)

with NP = Power × [0.5/(V_dd − V_th)] × (1/V_dd) and NA = area(mm²)/Tech(µm²)², with V_th = 0.4 V for 0.18 µm CMOS technology and 0.6 V for 0.35 µm CMOS technology.

As Table 1 shows, both filters presented a significant enhancement in the dynamic range, whereas the target cutoff frequencies can be maintained for a range of temperatures from −40 °C to 100 °C. Both FoMs showed a good performance for all the frequency range compared with the other proposed filters, proving it was an efficient solution in terms of power and area consumption.

5. Conclusions

Two low pass filters with programmable cutoff frequencies were presented in this paper. They relied on a simple current steering technique to give tunability over a wide frequency range. The first order LPF with a 1.8 V voltage supply presented a five orders of magnitude f_c range, with a low power consumption and a high dynamic range. Similar results were achieved with the second proposed structure, a second order design, with a 1.8 V voltage supply, increasing the cutoff frequency range and slightly enhancing the dynamic range at the expense of an increase of the area and power consumption. Compared to state-of-the-art solutions, the proposed structure exhibited very competitive performances while meeting the critical requirements of battery-portable on-chip micro-instruments in terms of power and area efficiency, critical for its implementation in multichannel measurement instruments for impedance sensor arrays. Further reduction on the power consumption could be achieved by lowering the bias current used.

The recovered signals from Section 4 showed the validity of the proposed LPFs as DC magnitude extractors. Higher accuracy over the recovered signal was achieved with the second order filter, although a higher consumption in power and area was required. Thus, there was an accuracy power–area trade-off that was dependent on the order of the filter. Thanks to the implementation of a fully integrated low pass filter, we achieved a completely integrated lock-in amplifier, together with the previously authors proposal [21] for a multichannel measurement device.