1 V Tunable High-Quality Universal Filter Using Multiple-Input Operational Transconductance Amplifiers
Abstract
This paper presents a new multiple-input single-output voltage-mode universal filter employing four multiple-input operational transconductance amplifiers (MI-OTAs) and three grounded capacitors suitable for low-voltage low-frequency applications. The quality factor (Q) of the filter functions can be tuned by both the capacitance ratio and the transconductance ratio. The multiple inputs of the OTA are realized using the bulk-driven multiple-input MOS transistor technique. The MI-OTA-based filter can also offer many filtering functions without additional circuitry requirements, such as an inverting amplifier to generate an inverted input signal. The proposed filter can simultaneously realize low-pass, high-pass, band-pass, band-stop, and all-pass responses, covering both non-inverting and inverting transfer functions in a single topology. The natural frequency and the quality factors of all the filtering functions can be controlled independently. The natural frequency can also be electronically controlled by tuning the transconductances of the OTAs. The proposed filter uses a 1 V supply voltage, consumes 120 mu W of power for a 5 mu A setting current, offers 40 dB of dynamic range and has a third intermodulation distortion of -43.6 dB. The performances of the proposed circuit were simulated using a 0.18 mu m TSMC CMOS process in the Cadence Virtuoso System Design Platform to confirm the performance of the topology.
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Citation: Kumngern, M.; Khateb, F.; Kulej, T.; Knobnob, B. 1 V Tunable High-Quality Universal Filter Using Multiple-Input Operational Transconductance Amplifiers. Sensors 2024,24, 3013. https://doi.org/10.3390/ s24103013 Academic Editor: Pak Kwong Chan Received: 22 April 2024 Revised: 4 May 2024 Accepted: 6 May 2024 Published: 9 May 2024 Copyright: © 2024 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). sensors Article 1 V Tunable High-Quality Universal Filter Using Multiple-Input Operational Transconductance Amplifiers Montree Kumngern 1, Fabian Khateb 2,3,4,* , Tomasz Kulej 5and Boonying Knobnob 6 1Department of Telecommunications Engineering, School of Engineering, King Mongkut’s Institute of Technology Ladkrabang, Bangkok 10520, Thailand; montr[email protected] 2Department of Microelectronics, Brno University of Technology, Technická10, 601 90 Brno, Czech Republic 3Faculty of Biomedical Engineering, Czech Technical University in Prague, nám. Sítná3105, 272 01 Kladno, Czech Republic 4 Department of Electrical Engineering, Brno University of Defence, Kounicova 65, 662 10 Brno, Czech Republic 5Department of Electrical Engineering, Czestochowa University of Technology, 42-201 Czestochowa, Poland; [email protected] 6Faculty of Engineering, Rajamangala University of Technology Thanyaburi, Pathum Thani 12110, Thailand; [email protected] *Correspondence: [email protected] Abstract: This paper presents a new multiple-input single-output voltage-mode universal filter employing four multiple-input operational transconductance amplifiers (MI-OTAs) and three grounded capacitors suitable for low-voltage low-frequency applications. The quality factor (Q) of the filter functions can be tuned by both the capacitance ratio and the transconductance ratio. The multiple inputs of the OTA are realized using the bulk-driven multiple-input MOS transistor technique. The MI-OTA-based filter can also offer many filtering functions without additional circuitry requirements, such as an inverting amplifier to generate an inverted input signal. The proposed filter can simultaneously realize low-pass, high-pass, band-pass, band-stop, and all-pass responses, covering both non-inverting and inverting transfer functions in a single topology. The natural frequency and the quality factors of all the filtering functions can be controlled independently. The natural frequency can also be electronically controlled by tuning the transconductances of the OTAs. The proposed filter uses a 1 V supply voltage, consumes 120 µ W of power for a 5 µ A setting current, offers 40 dB of dynamic range and has a third intermodulation distortion of − 43.6 dB. The performances of the proposed circuit were simulated using a 0.18 µ m TSMC CMOS process in the Cadence Virtuoso System Design Platform to confirm the performance of the topology. Keywords: universal filter; voltage-mode circuit; operational transconductance amplifier 1. Introduction An operational transconductance amplifier (OTA) is a voltage-controlled current source that offers numerous advantages in circuit design, such as providing electronic tuning capability, easy implementation of the OTA structure, and the powerful ability to realize various applications. In addition, OTA-based circuits are usually absent from resistor requirements, making them suitable for integrated circuit (IC) implementation [ 1 , 2 ]. Biquad filters are very useful blocks for applications in measurement, communication, and control systems. From the general form of second-order filter functions [ 3 ], there are five frequency responses that are possible to obtain, namely low-pass filter (LPF), high-pass filter (HPF), band-pass filter (BPF), band-stop filter (BSF), and all-pass filter (APF). These are the so-called five standard filtering functions. A biquad filter can be used to realize high-order filters by cascading multiple first-order and second-order sections, as used in phase-lock loops (PLL) for loop filtering (usually an LP filter), FM stereo demodulators (usually LP and BP filters), and crossover networks in three-way high fidelity (usually LP, Sensors 2024,24, 3013. https://doi.org/10.3390/s24103013 https://www.mdpi.com/journal/sensors
Sensors 2024,24, 3013 2 of 16 BP, and HP filters) [ 3 ]. A filter that can provide several second-order filters in a single topology is classified as a universal filter. There are many universal filters available in the literature using varying active devices, such as second-generation current conveyors (CCIIs) [ 4 – 6 ] and current feedback operational amplifiers (CFOAs) [ 7 – 9 ]. Unfortunately, these filters lack electronic tuning capabilities, which is important when parameters such as the natural frequency and quality factor deviate by process–voltage–temperature (PVT) variations. Some universal filters that offer the possibility of electronic tuning and minimal active elements have been introduced by using the voltage differencing inverting buffered amplifier (VDIBA) [ 10 , 11 ] and inverters [ 12 ]. However, these filters supply the input signals through capacitors, and therefore, an additional buffer circuit is required, and these capacitors become floating. This work is focused on a universal filter with electronic tuning capability that utilizes an operational transconductance amplifier (OTA) as the active element. There are many universal filters using OTAs as active elements available in the literature; for example, see [ 13 – 49 ]. The circuits in [ 13 – 16 ] are current-mode filters, the circuits in [ 17 – 35 ] are voltage-mode filters, and the circuits in [ 35 – 42 ] are mixed-mode filters. Considering the input and output terminals, the circuits in [ 17 – 22 , 39 ] are single-input multiple-output (SIMO) filters, the circuits in [ 15 , 16 , 23 – 29 , 40 , 41 ] are multiple-input single-output (MISO) filters, and the circuits in [ 13 , 14 , 30 – 38 , 42 ] are multiple-input multiple-output (MIMO) filters. Compared with SIMO filters, MISO and MIMO filters usually employ fewer active devices because the variant filtering functions of these filters can be obtained by appropriately selecting the input and/or output terminals. This work is focused on utilizing the MISO filter so that parameters such as the natural frequency and the quality factor can be electronically and independently controlled. Considering the MIMO and MISO filters in [13–16,23–38,40–42], these filters suffer from some drawbacks: (i) They require additional circuits at the input, such as a SIMO current follower circuit [13–16]. (ii) They use a floating capacitor or floating resistor [23,28,31,32]. (iii) They do not provide the non-inverting and inverting transfer functions of LP, HP, BP, BS, and AP filters [23–38,40,41]. (iv) They do not provide independent tunable control of the natural frequency and the quality factor [23–25,27,29–33,38,40,41]. (v) They require inverted input signals to obtain some transfer functions [24,31,37,38]. It should be noted that these universal filters are not designed for low-voltage lowpower signal-processing applications. Nowadays, low-voltage low-power filters are required for biomedical applications, such as biosensors [ 3 ]. Universal filters using OTAs operating with a low supply voltage and with low power consumption are available in the literature [ 42 – 47 ]. However, these configurations cannot benefit from independent and electronic control of the quality factor and the natural frequency and cannot provide a high-quality (high-Q) filter. In modern applications, high-Qfilters are strictly desirable for processing weak signals, such as the detection, measurement, and quantification of biomedical signals [ 48 , 49 ]. The bio-signal has the attributes of a low amplitude and a low frequency (≤10 kHz). This paper presents a low-voltage low-power universal biquadratic filter that allows the natural frequency and quality factor to be independently and electronically controlled. A high-Qfilter can also be obtained. The filter is realized using multiple-input operational transconductance amplifiers (MI-OTAs). In the filter’s input differential stage, the MI-OTAs are realized using the multiple-input MOS transistor technique (MI-MOST), which obtains a minimal differential pair and minimal power consumption. Using an MI-OTA-based filter shows that both the non-inverting and the inverting transfer functions of LP, HP, BP, BS, and AP filters can be obtained without inverted input signals. The proposed filter uses a 1 V supply voltage and 120 µ W of power consumption for a 5 µ A setting current. The filter was designed and simulated in the Cadence Virtuoso environment using 0.18 µ m TSMC CMOS technology.
Sensors 2024,24, 3013 3 of 16 2. Circuit Description 2.1. Multiple-Input OTA The multiple-input OTA is used to realize the filter application. Its circuit symbol is shown in Figure 1. Ideally, the transfer characteristic of this OTA is given by the following equation: Io=gm(V+1+V+2+. . . +V+n−V−1−V−2−. . . −V−n)(1) where Io is the output current, and gm is the small-signal transconductance. Note that the circuit in the general case has nnon-inverting and ninverting inputs; thus, its input voltage can be considered as the difference of two sums of voltages applied to the non-inverting V+1,...,+nand inverting V−1,...,−ninputs, respectively. Sensors2024,24,xFORPEERREVIEW3of16 current.ThefilterwasdesignedandsimulatedintheCadenceVirtuosoenvironmentusing0.18µmTSMCCMOStechnology. 2.CircuitDescription 2.1.Multiple‐InputOTA Themultiple-inputOTAisusedtorealizethefilterapplication.Itscircuitsymbolis showninFigure1.Ideally,thetransfercharacteristicofthisOTAisgivenbythefollowing equation:𝐼𝑔𝑉𝑉⋯𝑉𝑉𝑉⋯𝑉(1) where𝐼istheoutputcurrent,and𝑔isthesmall-signaltransconductance.Notethat thecircuitinthegeneralcasehasnnon-invertingandninvertinginputs;thus,itsinput voltagecanbeconsideredasthedifferenceoftwosumsofvoltagesappliedtothenoninverting𝑉,…,andinverting𝑉,…,inputs,respectively. g m o V +1 V +2 V -1 V -2 I o Figure1.ElectricalsymboloftheMI-OTA. Thetransistor-levelschematicoftheOTAproposedinthisworkwithn=3isshown inFigure2.ThecircuitconsistsofanOTAwithfolded-cascodetopologywithalinearized inputstageconsistingofthetransistorsM1–M2andM1SD,M2SD,andbiasedbythecurrent sinksM3andM4.ThetransistorsM13–M18wereusedforbiasing.Themultipleinputswere realizedinasimplewaybyaddingacapacitivevoltagedividertothetransistorsM1and M2,thuscreatingamultiple-inputdevice,asshowninFigure3.TheinputcapacitorsCBi werebypassedbylargeRMOSiresistances,whichwererealizedasananti-parallelconnectionofMOStransistorsoperatinginacutoffregion.Thelargeresistancesprovidedthe DCbiasingoftheM1andM2gates. M 13 M 2 M 14 M 12 V SS M 1 M 4 M 3 M 10 M 18 V DD M 5 M 16 M 17 M 7 M 8 M 15 M 6 I set V B1 V B1 M 2SD M 1SD o V B2 V B1 V B2 M 11 M 9 V B1 V +1 V +2 V +3 V -1 V -2 V -3 Figure2.CMOSrealizationoftheMI-OTAusingtheMIBD-MOSTtechnique. Thelinearizationtechniqueusedinthisworkissimilartothetechniquewithgatedriveninputstagesoperatinginstronginversionintroducedin[50].However,inthis work,thebulk-drivendevicesoperatinginweakinversionwereappliedtotheproposed structure.Operationinweakinversiongenerallyleadstoanarrowerlinearrange Figure 1. Electrical symbol of the MI-OTA. The transistor-level schematic of the OTA proposed in this work with n= 3 is shown in Figure 2. The circuit consists of an OTA with folded-cascode topology with a linearized input stage consisting of the transistors M 1 –M 2 and M 1SD , M 2SD , and biased by the current sinks M 3 and M 4 . The transistors M 13 –M 18 were used for biasing. The multiple inputs were realized in a simple way by adding a capacitive voltage divider to the transistors M 1 and M 2 , thus creating a multiple-input device, as shown in Figure 3. The input capacitors C Bi were bypassed by large R MOSi resistances, which were realized as an anti-parallel connection of MOS transistors operating in a cutoff region. The large resistances provided the DC biasing of the M1and M2gates. Sensors2024,24,xFORPEERREVIEW3of16 current.ThefilterwasdesignedandsimulatedintheCadenceVirtuosoenvironmentusing0.18µmTSMCCMOStechnology. 2.CircuitDescription 2.1.Multiple‐InputOTA Themultiple-inputOTAisusedtorealizethefilterapplication.Itscircuitsymbolis showninFigure1.Ideally,thetransfercharacteristicofthisOTAisgivenbythefollowing equation:𝐼𝑔𝑉𝑉⋯𝑉𝑉𝑉⋯𝑉(1) where𝐼istheoutputcurrent,and𝑔isthesmall-signaltransconductance.Notethat thecircuitinthegeneralcasehasnnon-invertingandninvertinginputs;thus,itsinput voltagecanbeconsideredasthedifferenceoftwosumsofvoltagesappliedtothenoninverting𝑉,…,andinverting𝑉,…,inputs,respectively. g m o V +1 V +2 V -1 V -2 I o Figure1.ElectricalsymboloftheMI-OTA. Thetransistor-levelschematicoftheOTAproposedinthisworkwithn=3isshown inFigure2.ThecircuitconsistsofanOTAwithfolded-cascodetopologywithalinearized inputstageconsistingofthetransistorsM1–M2andM1SD,M2SD,andbiasedbythecurrent sinksM3andM4.ThetransistorsM13–M18wereusedforbiasing.Themultipleinputswere realizedinasimplewaybyaddingacapacitivevoltagedividertothetransistorsM1and M2,thuscreatingamultiple-inputdevice,asshowninFigure3.TheinputcapacitorsCBi werebypassedbylargeRMOSiresistances,whichwererealizedasananti-parallelconnectionofMOStransistorsoperatinginacutoffregion.Thelargeresistancesprovidedthe DCbiasingoftheM1andM2gates. M 13 M 2 M 14 M 12 V SS M 1 M 4 M 3 M 10 M 18 V DD M 5 M 16 M 17 M 7 M 8 M 15 M 6 I set V B1 V B1 M 2SD M 1SD o V B2 V B1 V B2 M 11 M 9 V B1 V +1 V +2 V +3 V -1 V -2 V -3 Figure2.CMOSrealizationoftheMI-OTAusingtheMIBD-MOSTtechnique. Thelinearizationtechniqueusedinthisworkissimilartothetechniquewithgatedriveninputstagesoperatinginstronginversionintroducedin[50].However,inthis work,thebulk-drivendevicesoperatinginweakinversionwereappliedtotheproposed structure.Operationinweakinversiongenerallyleadstoanarrowerlinearrange Figure 2. CMOS realization of the MI-OTA using the MIBD-MOST technique. Sensors2024,24,xFORPEERREVIEW4of16 comparedtothestronginversionversionofthecircuit.Onthecontrary,theuseofbulkdriventerminalsextendsthelinearrangecomparedtothegate-drivenrealization.Moreover,theinputcapacitivedividerfurtherextendsthelinearrange.TheresultistherelativelylargelinearrangeoftheOTA,evenforweaklyinverteddevicesbiasedwithvery lowcurrents.Asimilarinputstagewasfirstdescribedandverifiedexperimentallyin [51,52].TheM1SDandM2SDtransistorsoperateinatrioderegion,introducingnegative feedbacktotheinputpairM1andM2.Controllingtheircharacteristicsbythesignalsseen atthegatesofthemaintransistorsofthepairM1andM2furtherimprovesthelinearityof theinputstage[51]. R MOS = M R M R (a) (b) S G D V n V 1 MM V 1 V n C B1 C Bn R MOS1 R MOSn B S G D B (c) Figure3.TheMIBD-MOSTtechnique:(a)symbol,(b)realization,and(c)RMOSrealization. AssumingthatallthecapacitancesCBiareidentical,thesmall-signaltransconductanceoftheOTAisgivenby: 𝑔𝜂𝑛4𝑘 4𝑘1∙𝐼 𝑛𝑈(2) where𝜂𝑔,/𝑔,isthebulktogatetransconductanceratioattheoperatingpoint, nisthenumberofinputterminals,npisthesubthresholdslopefactorforthep-channel transistors,UTisthethermalpotential,Isetisthebiasingcurrentandkistheratioofaspect ratiosofthetriode-regiontransistorsM1SD,M2SDandthemaintransistorsoftheinputpair M1andM2: 𝑘𝑊/𝐿, 𝑊/𝐿, (3) Notethatthebestlinearityperformanceisobtainedfork=0.5[51].Insuchacase,the circuittransconductancecanbeexpressedas: 𝑔23𝜂𝑛∙𝐼 𝑛𝑈(4) Theuseofaninputcapacitivedividerandbulk-drivendevicesextendsthelinear rangeoftheOTA,butontheotherhand,itincreasestheinputnoiseanddecreasesthe voltagegain.Forinstance,with𝜂1/3and3inputs,thecircuittransconductanceislowered9timesascomparedtoagate-driveninputpair.Consequently,thelow-frequency voltagegainofthecircuitisdecreasedbyaround19dB.Tocounteractthiseffect,weappliedacascodehigh-impedanceoutputstage,composedofthetransistorsM5–M12.With theappliedoutputstage,thelow-frequencygainoftheOTAcanbeapproximatedas: 𝐴 ≅𝑔𝑔𝑟𝑟||𝑔𝑟𝑟 (5) Consequently,thisgainisimprovedbythefactorof𝑔𝑟(intrinsicvoltagegainof anMOStransistor),whichfortheappliedtechnologyandoperatingpointexceeds30dB. Aswasalreadymentioned,theappliedtechniqueincreasesthelinearrangeofthe OTA.Ontheotherhand,however,itincreasesitsinputnoiseduetosignalattenuation. Sincetheinputnoiseisincreasedinthesameproportion,thedynamicrange(DR)ofthe OTAremainsunchangedandisequaltotheDRoftheGDOTAwithasingledifferential inputandtheappliedlinearizationtechnique.Nevertheless,thelargerlinearrangeallows foravoidinghardnonlinearitiesforthelargevoltageswingsandVDD,asappliedinthe considereddesign. Figure 3. The MIBD-MOST technique: (a) symbol, (b) realization, and (c) RMOS realization. The linearization technique used in this work is similar to the technique with gatedriven input stages operating in strong inversion introduced in [ 50 ]. However, in this work,
Sensors 2024,24, 3013 4 of 16 the bulk-driven devices operating in weak inversion were applied to the proposed structure. Operation in weak inversion generally leads to a narrower linear range compared to the strong inversion version of the circuit. On the contrary, the use of bulk-driven terminals extends the linear range compared to the gate-driven realization. Moreover, the input capacitive divider further extends the linear range. The result is the relatively large linear range of the OTA, even for weakly inverted devices biased with very low currents. A similar input stage was first described and verified experimentally in [ 51 , 52 ]. The M 1SD and M 2SD transistors operate in a triode region, introducing negative feedback to the input pair M 1 and M 2 . Controlling their characteristics by the signals seen at the gates of the main transistors of the pair M1and M2further improves the linearity of the input stage [51]. Assuming that all the capacitances C Bi are identical, the small-signal transconductance of the OTA is given by: gm=η n·4k 4k+1·Iset npUT (2) where η=gmb1,2/gm1,2 is the bulk to gate transconductance ratio at the operating point, n is the number of input terminals, n p is the subthreshold slope factor for the p-channel transistors, U T is the thermal potential, I set is the biasing current and kis the ratio of aspect ratios of the triode-region transistors M 1SD , M 2SD and the main transistors of the input pair M1and M2: k=(W/L)1SD,2SD (W/L)1,2 (3) Note that the best linearity performance is obtained for k= 0.5 [ 51 ]. In such a case, the circuit transconductance can be expressed as: gm=2 3·η n·Iset npUT (4) The use of an input capacitive divider and bulk-driven devices extends the linear range of the OTA, but on the other hand, it increases the input noise and decreases the voltage gain. For instance, with η= 1 / 3 and 3 inputs, the circuit transconductance is lowered 9 times as compared to a gate-driven input pair. Consequently, the low-frequency voltage gain of the circuit is decreased by around 19 dB. To counteract this effect, we applied a cascode high-impedance output stage, composed of the transistors M 5 –M 12 . With the applied output stage, the low-frequency gain of the OTA can be approximated as: AV∼ =gm[(gm8rds8rds6)||(gm10rds10rds12)] (5) Consequently, this gain is improved by the factor of gmrds (intrinsic voltage gain of an MOS transistor), which for the applied technology and operating point exceeds 30 dB. As was already mentioned, the applied technique increases the linear range of the OTA. On the other hand, however, it increases its input noise due to signal attenuation. Since the input noise is increased in the same proportion, the dynamic range (DR) of the OTA remains unchanged and is equal to the DR of the GD OTA with a single differential input and the applied linearization technique. Nevertheless, the larger linear range allows for avoiding hard nonlinearities for the large voltage swings and V DD , as applied in the considered design. 2.2. Proposed Tunable High-Q Voltage-Mode Universal Filter Figure 4shows the proposed tunable high-Qvoltage-mode universal filter using OTAs. Figure 4a shows the proposed voltage-mode universal filter using conventional OTAs and Figure 4b shows the proposed voltage-mode universal filter using MI-OTAs. It should be noted from Figure 4a,b that the universal filter using MI-OTAs has a significantly reduced number of OTAs (10 OTAs vs. 4 MI-OTAs). The input terminals of the universal filter in Figure 4b are connected to the high-input impedance of the OTA; thus, the proposed
Sensors 2024,24, 3013 5 of 16 universal filter offers high input impedance, which is ideal for voltage-mode circuits. The output impedance can be given by 1/gm4. Sensors2024,24,xFORPEERREVIEW5of16 2.2.ProposedTunableHigh‐QVoltage‐ModeUniversalFilter Figure4showstheproposedtunablehigh-Qvoltage-modeuniversalfilterusing OTAs.Figure4ashowstheproposedvoltage-modeuniversalfilterusingconventional OTAsandFigure4bshowstheproposedvoltage-modeuniversalfilterusingMI-OTAs.It shouldbenotedfromFigure4a,bthattheuniversalfilterusingMI-OTAshasasignificantlyreducednumberofOTAs(10OTAsvs.4MI-OTAs).Theinputterminalsofthe universalfilterinFigure4bareconnectedtothehigh-inputimpedanceoftheOTA;thus, theproposeduniversalfilteroffershighinputimpedance,whichisidealforvoltage-mode circuits.Theoutputimpedancecanbegivenby1/𝑔. (a) (b) Figure4.Proposedtunablehigh-Qvoltage-modeuniversalfilterusing(a)conventionalOTAsand (b)MI-OTAs. Letting𝑔𝑔𝑔,𝑔𝑔𝑔,𝑔𝑔𝑔𝑔, 𝑔𝑔𝑔𝑔,andusingnodalanalysis,theoutputvoltageofFigure4a,b canbegivenby: 𝑉𝑔𝑔𝑉𝑉𝑠𝐶𝑔𝑉𝑉 𝑠𝐶𝐶𝑔 𝐶𝑉𝑉𝑉𝑉 𝐷𝑠𝑉 𝑉 𝐷𝑠 (6) where𝐷𝑠𝑠𝐶𝐶𝑠 𝑔𝑔. Figure 4. Proposed tunable high-Qvoltage-mode universal filter using (a) conventional OTAs and (b) MI-OTAs. Letting gm1a=gm1b=gm1 , gm2a=gm2b=gm2 , gm3a=gm3b=gm3c=gm3 , gm4a=gm4b=gm4c=gm4 , and using nodal analysis, the output voltage of Figure 4a,b can be given by: Vout = gm1gm2(Vin1−Vin2)+sC1gm2(Vin3−Vin4) +sC1C2gm3 C3(Vin5+Vin6−Vin7−Vin8) +D(s)(Vin9−Vin10) D(s)(6) where D(s)=s2C1C2+sC1C2gm3 C3+gm1gm2. The variant filtering functions are shown in Table 1. It should be noted that the variant non-inverting and inverting transfer functions of the LPF, BPF, HPF, BSF, and APF can be obtained without inverted input signal requirements. For the BPF, if the input signals are
Sensors 2024,24, 3013 6 of 16 V in3 and V in4 , varying the quality factor will increase the gain of the transfer functions. Conversely, if the input signals are V in5 or V in6 and V in7 or V in8 , varying the quality factor will not affect the gain of the transfer functions. Table 1. Obtaining the variant filtering functions of the proposed universal filter. Filtering Function Input LPF Non-inverting Vin1 Inverting Vin2 BPF Non-inverting Vin3 Inverting Vin4 Non-inverting Vin5or Vin6 Inverting Vin7or Vin8 HPF Non-inverting Vin2=Vin7=Vin9 Inverting Vin1=Vin5=Vin10 BSF Non-inverting Vin7=Vin9 Inverting Vin5=Vin10 APF Non-inverting Vin7=Vin8=Vin9 Inverting Vin5=Vin6=Vin10 Letting V in7 =V in8 =V in9 =V in ,V out =V AP+ , the transfer function of the non-inverting APF can be expressed as in (7), and letting V in5 =V in6 =V in10 =V in ,V out =V AP− , the transfer function of the inverting APF can be expressed as in (8). VAP+ Vin =s2C1C2−sC1C2gm3 C3+gm1gm2 s2C1C2+sC1C2gm3 C3+gm1gm2 (7) VAP− Vin =−s2C1C2+sC1C2gm3 C3−gm1gm2 s2C1C2+sC1C2gm3 C3+gm1gm2 (8) These transfer functions can be used to express the magnitudes and phase responses of APFs. The natural frequency (ωo) and the quality factor (Q) can be given by: ωo=rgm1gm2 C1C2 (9) Q=C3 gm3rgm1gm2 C1C2 (10) The parameter ωo can be controlled electronically by gm1 and gm2 and the parameter Qcan be controlled by C3 and/or gm3 . If C3 is used as a parameter, C1 and C2 could be constant ( C1 = C2 ), and if gm3 is used as a parameter, gm1 and gm2 could be constant ( gm1=gm2 ). Thus, the parameter Qcan be tuned by varying the values of the capacitance and resistance. 2.3. Effects of the Nonidealities of the MI-OTA Figure 5shows the nonideal model of the OTA [ 53 ]. There are three components that have been considered: (i) the input capacitances C + ,C − , and input resistances R + ,R − ; (ii) the output capacitance C o and output resistance R o (or conductance go ); and (iii) the frequency-dependent transconductance gm.
Sensors 2024,24, 3013 7 of 16 Sensors2024,24,xFORPEERREVIEW7of16 2.3.EffectsoftheNonidealitiesoftheMI‐OTA Figure5showsthenonidealmodeloftheOTA[53].Therearethreecomponentsthat havebeenconsidered:(i)theinputcapacitancesC+,C−,andinputresistancesR+,R−;(ii)the outputcapacitanceCoandoutputresistanceRo(orconductance𝑔);and(iii)thefrequency-dependenttransconductance𝑔. Figure5.NonidealstructureoftheOTA. Thefrequency-dependenceof𝑔(𝑔)canbeapproximated[54]as: 𝑔𝑔1𝑠𝜏 (11) where𝜏1𝜔 ⁄and𝜔denotesthesecondpoleoftheOTA. Thefirstconsiderationcanberewrittenbyusing(9)andthedenominatorof(6)as: 𝑠𝐶𝐶1𝑔𝜏 𝐶𝑔𝑔𝜏𝜏 𝐶𝐶 𝑠𝐶𝐶𝑔 𝐶1𝐶𝑔𝑔 𝐶𝐶𝑔 𝜏𝜏𝑔𝑔 (12) Itcanbeseenthattheparasiticpoles(𝜏)ofthei-thOTAaffectthefilterperformance. Theinfluenceoftheparasiticpolecanbeneglectedifthefollowingconditionsaremet: 𝑔𝜏 𝐶𝑔𝑔𝜏𝜏 𝐶𝐶≪1 𝐶𝑔𝑔 𝐶𝐶𝑔 𝜏𝜏≪1⎭ ⎬ ⎫ (13) Next,theparasiticcapacitancesandresistances(orconductance)havebeenconsideredbylettingthetransconductance𝑔beideal.ConsideringFigure4b,thevaluesofthe capacitorsC1,C2,andC3canberepresented,respectively,by𝐶,𝐶,and𝐶,where𝐶 𝐶𝐶𝐶,𝐶𝐶𝐶𝐶𝐶𝐶,and𝐶𝐶𝐶𝐶𝐶𝐶, where𝐶istheoutputcapacitanceofthej-th𝑔,and𝐶and𝐶aretheinputcapacitancesofthej-th𝑔(j=1,2,3,4). Whentheparasiticresistancesareconsidered,thecapacitors𝐶,𝐶,and𝐶areexpressed,respectively,by𝐶,𝐶,and𝐶,where𝐶𝐶//𝑅//𝑅,𝐶𝐶//𝑅// 𝑅//𝑅//𝑅,𝐶𝐶//𝑅//𝑅//𝑅//𝑅,whereRojistheoutputresistanceofthe j-th𝑔,R+jandR−jaretheinputresistancesofthej-th𝑔(j=1,2,3,4). Theparasiticeffectsonthenaturalfrequencyandthequalityfactoroftheproposed universalfiltercanbeavoidedbychoosing: 𝐶≫𝐶𝐶 𝐶≫𝐶𝐶𝐶𝐶 𝐶≫𝐶𝐶𝐶𝐶 (14) 3.SimulationResults TheproposedMI-OTAandthefilterapplicationweresimulatedintheCadenceVirtuosoSystemDesignPlatformusingthe0.18µmCMOStechnologyfromTSMC(Taiwan SemiconductorManufacturingCompany,Taiwan).TheaspectratiooftheMOS Figure 5. Nonideal structure of the OTA. The frequency-dependence of gm(gmn) can be approximated [54] as: gmn =gm(1−sτ)(11) where τ=1/ωpand ωpdenotes the second pole of the OTA. The first consideration can be rewritten by using (9) and the denominator of (6) as: s2C1C21−gm3τ3 C3+gm1gm2τ1τ2 C1C2 +sC1C2gm3 C31−C3gm1gm2 C1C2gm3(τ1−τ2)+gm1gm2 (12) It can be seen that the parasitic poles (τi) of the i-th OTA affect the filter performance. The influence of the parasitic pole can be neglected if the following conditions are met: gm3τ3 C3+gm1gm2τ1τ2 C1C2≪1 C3gm1gm2 C1C2gm3(τ1−τ2)≪1)(13) Next, the parasitic capacitances and resistances (or conductance) have been considered by letting the transconductance gm be ideal. Considering Figure 4b, the values of the capacitors C 1 , C 2 , and C 3 can be represented, respectively, by C′ 1 , C′ 2 , and C′ 3 , where C′ 1=C1+Co1+C+2 , C′ 2=C2+Co2+C−1+C+3+C+4 , and C′ 3=C3+Co3+ C+1+C−3+C−4 , where Coj is the output capacitance of the j-th gm , and C+j and C−j are the input capacitances of the j-th gm(j= 1, 2, 3, 4). When the parasitic resistances are considered, the capacitors C′ 1 , C′ 2 , and C′ 3 are expressed, respectively, by C′′ 1 , C′′ 2 , and C′′ 3 , where C′′ 1=C′ 1//Ro1//R+2 , C′′ 2=C′ 2//Ro2//R−1//R+3//R+4 , C′′ 3=C′ 3//Ro3//R+1//R−3//R−4 , where R oj is the output resistance of the j-th gm , R +j and R −j are the input resistances of the j-th gm (j = 1, 2, 3, 4). The parasitic effects on the natural frequency and the quality factor of the proposed universal filter can be avoided by choosing: C1≫(Co1+C+2) C2≫(Co2+C−1+C+3+C+4) C3≫(Co3+C+1+C−3+C−4) (14) 3. Simulation Results The proposed MI-OTA and the filter application were simulated in the Cadence Virtuoso System Design Platform using the 0.18 µ m CMOS technology from TSMC (Taiwan Semiconductor Manufacturing Company, Taiwan). The aspect ratio of the MOS transistors of the MI-OTA in Figure 1is listed in Table 2. The voltage supply was 1 V (VDD =−VSS = 0.5 V). The proposed MI-OTA consumed 30 µW for a 5 µA setting current.
Sensors 2024,24, 3013 8 of 16 Table 2. Parameters of the components of the MI-OTA. Transistor W/L (µm/µm) M1–M4, M13–M18 10/0.5 M1SD, M2SD 5/0.5 M5–M12 20/0.5 MR4/5 CB= 0.5 pF VB1 =−300 mV, VB2 = 200 mV The parasitic impedances of the MI-OTA are shown in Figure 6, where R +,− = 42 G Ω , C +,− = 0.25 pF for the input terminal, and R o = 32.4 M Ω ,C o = 52.8 fF for the output terminal. Sensors2024,24,xFORPEERREVIEW8of16 transistorsoftheMI-OTAinFigure1islistedinTable2.Thevoltagesupplywas1V(VDD =−VSS=0.5V).TheproposedMI-OTAconsumed30µWfora5µAsettingcurrent. Table2.ParametersofthecomponentsoftheMI-OTA. TransistorW/L(µm/µm) M1–M4 , M13–M1810/0.5 M1SD,M2SD5/0.5 M5–M1220/0.5 MR4/5 CB=0.5pF VB1=−300mV,VB2=200mV TheparasiticimpedancesoftheMI-OTAareshowninFigure6,whereR+,−=42GΩ, C+,−=0.25pFfortheinputterminal,andRo=32.4MΩ,Co=52.8fFfortheoutputterminal. ToobtainthedynamiccharacteristicoftheMI-OTA,asinewaveof1kHzwasapplied totheinputoftheOTA.TheextendedlinearityoftheMI-OTAwithvarioussettingcurrentsIset=(2.5,5,10,20)µAisshowninFigure7a.ThetransconductanceACcharacteristic oftheMI-OTAwithvarioussettingcurrentsIset=(2.5,5,10,20)µAisshowninFigure7b. Thetransconductancewas(2.9,4.9,7.9,12.6)µS,respectively.ThetransconductanceAC characteristicwithIset=5µAwasrepeatedfortheMonteCarlo(MC)analysiswith200 runsandprocess,voltage,andtemperature(PVT)corners,asshowninFigure8. Figure6.TheparasiticimpedancesoftheMI-OTA. (a)(b) Figure7.TheIoversusVin(a)andthetransconductanceACcharacteristic(b)withdifferentsetting currents. 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 1.E+0 1.E+1 1.E+2 1.E+3 1.E+4 1.E+5 1.E+6 Z+,−, Zo(dB) Frequency (Hz) Zo Z+,Z- -8 -6 -4 -2 0 2 4 6 8 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 Io(µA) Vin (V) Iset=2.5uA Iset=5uA Iset=10uA Iset=20uA 0 2 4 6 8 10 12 14 16 1.E+3 1.E+6 1.E+9 gm(µS) Frequency (Hz) Iset=2.5uA Iset=5uA Iset=10uA Iset=20uA Figure 6. The parasitic impedances of the MI-OTA. To obtain the dynamic characteristic of the MI-OTA, a sine wave of 1 kHz was applied to the input of the OTA. The extended linearity of the MI-OTA with various setting currents I set = (2.5, 5, 10, 20) µ A is shown in Figure 7a. The transconductance AC characteristic of the MI-OTA with various setting currents I set = (2.5, 5, 10, 20) µ A is shown in Figure 7b. The transconductance was (2.9, 4.9, 7.9, 12.6) µ S, respectively. The transconductance AC characteristic with I set = 5 µ A was repeated for the Monte Carlo (MC) analysis with 200 runs and process, voltage, and temperature (PVT) corners, as shown in Figure 8. Sensors2024,24,xFORPEERREVIEW8of16 transistorsoftheMI-OTAinFigure1islistedinTable2.Thevoltagesupplywas1V(VDD =−VSS=0.5V).TheproposedMI-OTAconsumed30µWfora5µAsettingcurrent. Table2.ParametersofthecomponentsoftheMI-OTA. TransistorW/L(µm/µm) M1–M4 , M13–M1810/0.5 M1SD,M2SD5/0.5 M5–M1220/0.5 MR4/5 CB=0.5pF VB1=−300mV,VB2=200mV TheparasiticimpedancesoftheMI-OTAareshowninFigure6,whereR+,−=42GΩ, C+,−=0.25pFfortheinputterminal,andRo=32.4MΩ,Co=52.8fFfortheoutputterminal. ToobtainthedynamiccharacteristicoftheMI-OTA,asinewaveof1kHzwasapplied totheinputoftheOTA.TheextendedlinearityoftheMI-OTAwithvarioussettingcurrentsIset=(2.5,5,10,20)µAisshowninFigure7a.ThetransconductanceACcharacteristic oftheMI-OTAwithvarioussettingcurrentsIset=(2.5,5,10,20)µAisshowninFigure7b. Thetransconductancewas(2.9,4.9,7.9,12.6)µS,respectively.ThetransconductanceAC characteristicwithIset=5µAwasrepeatedfortheMonteCarlo(MC)analysiswith200 runsandprocess,voltage,andtemperature(PVT)corners,asshowninFigure8. Figure6.TheparasiticimpedancesoftheMI-OTA. (a)(b) Figure7.TheIoversusVin(a)andthetransconductanceACcharacteristic(b)withdifferentsetting currents. 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 1.E+0 1.E+1 1.E+2 1.E+3 1.E+4 1.E+5 1.E+6 Z+,−, Zo(dB) Frequency (Hz) Zo Z+,Z- -8 -6 -4 -2 0 2 4 6 8 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 Io(µA) Vin (V) Iset=2.5uA Iset=5uA Iset=10uA Iset=20uA 0 2 4 6 8 10 12 14 16 1.E+3 1.E+6 1.E+9 gm(µS) Frequency (Hz) Iset=2.5uA Iset=5uA Iset=10uA Iset=20uA Figure 7. The I o versus V in (a) and the transconductance AC characteristic (b) with different setting currents.
Sensors 2024,24, 3013 9 of 16 Sensors2024,24,xFORPEERREVIEW9of16 (a)(b) (c)(d) Figure8.ThetransconductanceACcharacteristicoftheMI-OTA:(a)MC,(b)process,(c)voltage and(d)temperaturecorners. Theprocesscornersofthetransistorwerefast–fast,fast–slow,slow–fast,andslow– slow.FortheinputMIMcapacitorC B ,theywerefast–fastandslow–slow.Thevoltage cornerswereV DD ±10%,andthetemperaturecornerswere−30°Cand70°C.TheMC showedmin.4.5µSandmax.5.4µS.Theprocesscornersshowedmin.4.91µSandmax. 5µS.Thetemperaturecornersshowedmin.4.66µSandmax.5.36µS.Thevoltagecorners showedmin.4.94µSandmax.4.97µS.Allthetransconductancevariationswereinthe acceptablerange.ThefrequencyandphasecharacteristicsofthefilterwithI set1–4 =5µA andC 1–3 =100pFareshowninFigure9.Thecutofffrequencywas7.85kHz.Thesimulation oftheLPFwasrepeatedwithMCandPVTcornersanalyses,asshowninFigure10.While thecurvesforthePVToverlapped,fortheMC,thegainvariationatlowfrequencieswas intherangeof−3.1dBto1.6dBandthecutofffrequencyvariationwasintherangeof0.72 kHzto9.3kHz,whichcanberealignedbyadjustingthesettingcurrent. (a)(b) 0 1 2 3 4 5 6 1.E+3 1.E+6 1.E+9 gm(µS) Frequency (Hz) MC 0 1 2 3 4 5 6 1.E+3 1.E+6 1.E+9 gm(µS) Frequency (Hz) process corners 0 1 2 3 4 5 6 1.E+3 1.E+6 1.E+9 gm(µS) Frequency (Hz) Voltage corners 1V 0.9V 1.1V 0 1 2 3 4 5 6 1.E+3 1.E+6 1.E+9 gm(µS) Frequency (Hz) Temp. corners -30ºC 27ºC 70ºC -270 -225 -180 -135 -90 -45 0 -60 -50 -40 -30 -20 -10 0 10 1.E+2 1.E+3 1.E+4 1.E+5 1.E+6 Phase (º) Gain (dB) Frequency (Hz) LPF Gain Phase -90 -45 0 45 90 135 180 -60 -50 -40 -30 -20 -10 0 10 1.E+2 1.E+3 1.E+4 1.E+5 1.E+6 Phase (º) Gain (dB) Frequency (Hz) HPF Gain Phase Figure 8. The transconductance AC characteristic of the MI-OTA: (a) MC, (b) process, (c) voltage and (d) temperature corners. The process corners of the transistor were fast–fast, fast–slow, slow–fast, and slow– slow. For the input MIM capacitor C B , they were fast–fast and slow–slow. The voltage corners were V DD ± 10%, and the temperature corners were − 30 ◦ C and 70 ◦ C. The MC showed min. 4.5 µ S and max. 5.4 µ S. The process corners showed min. 4.91 µ S and max. 5 µ S. The temperature corners showed min. 4.66 µ S and max. 5.36 µ S. The voltage corners showed min. 4.94 µ S and max. 4.97 µ S. All the transconductance variations were in the acceptable range. The frequency and phase characteristics of the filter with I set1–4 = 5 µ A and C 1–3 = 100 pF are shown in Figure 9. The cutoff frequency was 7.85 kHz. The simulation of the LPF was repeated with MC and PVT corners analyses, as shown in Figure 10. While the curves for the PVT overlapped, for the MC, the gain variation at low frequencies was in the range of − 3.1 dB to 1.6 dB and the cutoff frequency variation was in the range of 0.72 kHz to 9.3 kHz, which can be realigned by adjusting the setting current. To demonstrate the tuning capability of the Q, Figure 11 shows the frequency characteristics of the BPF with: (a) I set1–4 = 5 µ A, C 1,2 = 100 pF and tuning C 3 = (25, 50, 100, 200, 400, 800) pF and (b) with I set1,2,4 = 5 µ A, C 1–3 = 100 pF and tuning I set3 = (0.3125, 0.625, 1.25, 2.5, 5, 10) µ A. To demonstrate the tuning capability of the ω , Figure 12 shows the frequency characteristics of the BPF with C 1–3 = 100 pF and tuning I set = I set1–4 = (0.3125, 0.625, 1.25, 2.5, 5, 10) µ A. The natural frequency was (0.767, 1.44, 2.63, 4.62, 7.85, 12.7) kHz, respectively.
Sensors 2024,24, 3013 16 of 16 43. Kumngern, M.; Khateb, F.; Kulej, T.; Psychalinos, C. Multiple-Input Universal Filter and Quadrature Oscillator Using MultipleInput Operational Transconductance Amplifiers. IEEE Access 2021,9, 56253–56263. [CrossRef] 44. Jaikla, W.; Khateb, F.; Kumngern, M.; Kulej, T.; Ranjan, R.K.; Suwanjan, P. 0.5 V Fully Differential Universal Filter Based on Multiple Input OTAs. IEEE Access 2020,8, 187832–187839. [CrossRef] 45. Namdari, A.; Dolatshahi, M. Design of a Low-Voltage and Low-Power, Reconfigurable Universal OTA-C Filter. Analog Integr. Circuits Signal Process. 2022,111, 169–188. [CrossRef] 46. Khateb, F.; Kumngern, M.; Kulej, T.; Akbari, M.; Stopjakova, V. 0.5 V, nW-Range Universal Filter Based on Multiple-Input Transconductor for Biosignals Processing. Sensors 2022,22, 8619. [CrossRef] 47. Namdari, A.; Dolatshahi, M.; Aghababaei Horestani, M. A New Ultra-Low-Power High-Order Universal OTA-C Filter Based on CMOS Double Inverters in the Subthreshold Region. Circuits Syst. Signal Process. Vol. 2023,42, 6379–6398. [CrossRef] 48. Tlelo-Coyotecatl, E.; Díaz-Sánchez, A.; Rocha-Pérez, J.M.; Vázquez-González, J.L.; Sánchez-Gaspariano, L.A.; Tlelo-Cuautle, E. Enhancing Q-Factor in a Biquadratic Bandpass Filter Implemented with Opamps. Technologies 2019,7, 64. [CrossRef] 49. Jendernalik, W.; Jakusz, J.; Blakiewicz, G. Low-Voltage Low-Power Filters with Independent ωo and Q Tuning for Electronic Cochlea Applications. Electronics 2022,11, 534. [CrossRef] 50. Krummenacher, F.; Joehl, N. A 4-MHz CMOS Continuous-Time Filter with On-Chip Automatic Tuning. IEEE J. Solid-State Circuits. 1988,23, 750–758. [CrossRef] 51. Khateb, F.; Kulej, T.; Akbari, M.; Tang, K.-T. A 0.5-V Multiple-Input Bulk-Driven OTA in 0.18µ m CMOS. IEEE Trans. Very Large Scale Integr. (VLSI) Syst. 2022,30, 1739–1747. [CrossRef] 52. Khateb, F.; Kulej, T.; Kumngern, M.; Psychalinos, C. Multiple-Input Bulk-Driven MOS Transistor for Low-Voltage Low-Frequency Applications. Circuits Syst. Signal Process. 2019,38, 2829–2845. [CrossRef] 53. Sun, Y.; Fidler, J.K. Synthesis and Performance Analysis of Universal Minimum Component Integrator-Based IFLF OTA-Grounded Capacitor Filter. IEE Proc.-Circuits Devices Syst. 1996,143, 107–114. [CrossRef] 54. Nevárez-Lozano, H.; Sánchez-Sinencio, E. Minimum Parasitic Effects Biquadratic OTA-C Filter Architectures. Analog Integr. Circuits Signal Process. 1991,1, 297–319. [CrossRef] Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.