The Self-Biasing Current Generator: A Useful Transconductance Cell

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The Self-Biasing Current Generator: A Useful Transconductance Cell | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Short Report The Self-Biasing Current Generator: A Useful Transconductance Cell Meysam Akbari This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4971100/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract This brief presents a bulk-driven transconductance cell using a basic self-biasing current generator circuit. The proposed cell employs two N-type and P-type current mirrors to form a positive feedback structure. The circuit is adaptively biased by diode-connected topologies of the current mirrors. The bulk terminals of the P-type transistors act as the input nodes to employ the proposed circuit as a transconductance cell. Thanks to its symmetrical self-biasing topology, a tailed double-output differential structure is achieved. An additional current source is also used to ensure the stability and adjust the amount of the produced transconductance. The circuit is simulated using a 0.18-µm CMOS technology to verify its operation. Electrical Engineering Transconductance cell Ultra-low-power Positive feedback Current generator Self-biasing Bulk-driven Figures Figure 1 Figure 2 Figure 3 I. INTRODUCTION TRANSCONDUCTANCE cells are widely used in analog and mixed-signal circuits such as operational transconductance amplifiers (OTA) [1], rail-to-rail circuits [2], tunable filters [3, 4], etc. Among all these circuits, the ultra-low-power (ULP) OTAs are widely used because of their capability of playing the role of many different functions. Recently, several OTAs have been enhanced based on the positive feedback topologies in [5, 6], which are suitable for ultra-low-voltage (ULV) applications. In this way, bulk terminals of the differential pair topology were used as the input nodes to provide a high input dynamic range. Nonetheless, due to a lower bulk transconductance than that of the gate terminal, designers face some disadvantages such as lower gain bandwidth (GBW), lower DC gain, lower slew rate (SR), larger input noise, and larger offset, which were carefully analyzed and reduced in [5–7]. II. PROPOSED TRANSCONDUCTANCE CELL Figure 1 (a) shows the basic idea of a conventional current generator circuit, which its performance can be improved by adding a resistance at the source terminal of transistor M4 [ 8 ]. This circuit forms a positive feedback loop and will be stable for a loop gain less than unity. This structure is very useful to design a transconductance cell with a self-biasing topology. Figure 1 (b) shows the proposed self-biasing transconductance cell [ 9 ]. As is seen, transistor M0 is added as the tail current to create a virtual ground at the source of M1-M2, which results in a special differential pair. Based on the analysis done in [ 9 ], having a tail current will increase the common-mode-rejection ratio (CMRR) of the structure. This circuit can only be converted to a bulk-driven transconductance cell because there is no more idle terminal to be used as the input node except bulks. Therefore, the bulk terminals of P-type transistors M1-M2 are used as the input nodes that offer a high input dynamic range. To stabilize the proposed structure, an adjustable current source, M5, should be paralleled with one of the non-diode-connected transistors M2-M3. Actually, without employing M5, the proposed structure provides an infinite output impedance casing an unstable behavior in the transient response. Eq. ( 1 ) expresses the impedance seen from both outputs where its amount is adjusted by the transconductance of M5, gm 5 , and the pole associated with output nodes can be moved by tuning V b2 . $${R_{out \pm }} \approx \frac{1}{{g{m_1}\left( {1 - \frac{{g{m_2}\left( {g{m_1} - g{m_5}} \right)}}{{g{m_1}g{m_4}}}} \right)}}$$ 1 where gm i represents the transconductance of the corresponding transistors, and ( gm 1 - gm 5 ) = gm 3 . Therefore, to achieve a finite positive impedance at the output, gm 5 should have a non-zero value. It is obvious that the proposed structure benefits from a high output impedance, which results in a higher transconductance and a larger DC gain in comparison with a conventional bulk-driven structure. In addition, the proposed cell provides a double-ended structure, while the output common mode voltages are controlled by its self-biasing topology without employing any common-mode feedback (CMFB) circuit. By employing two of the proposed cells, a self-biasing high-performance transconductance amplifier can easily be designed as a tunable high dynamic range circuit. III. SIMULATION RESULTS The proposed circuit was simulated in TSMC 0.18 µm CMOS technology @ 0.4 V driving a 2×2 pF capacitive load. The frequency response of the amplifier is shown in Fig. 2, while a DC gain and a gain bandwidth of 25 dB and 3 kHz were respectively achieved. To simulate the step response, a unity-gain capacitive buffer employed in [10] was used. In this way, a large differential step of 0.2V at 50 kHz was applied to the inputs. Fig. 3 shows the step response of the amplifier representing an average slew rate of 32 V/ms. Thanks to the use of the bulk-driven method, Fig. 3 also shows that a differential input/output voltage swing of 0.4V was achieved. Table 1 reports the main specifications of the proposed transconductance cell, while it consumes just 4 nW power. As a result, the proposed circuit can be very useful in configuring a high-performance bulk-driven transconductance amplifier, specially those that operate under sub-threshold supplies with a self-biasing topology. IV. CONCLUSION This brief re-configured a basic self-biasing current generator circuit as a high-performance transconductance cell. The proposed structure used the bulk terminals of P-type transistors as the input nodes to provide a high input dynamic range. To stabilize the circuit, an additional transistor was used as a shunt-current method to finite the output impedance. The circuit was designed and simulated in TSMC 0.18 µm CMOS technology under a supply voltage of 0.4 V. Simulation results showed a DC gain of 25 dB and an average slew rate of 32 V/ms for a capacitive load of 2×2 pF. References M. Akbari, S. M. Hussein, Y. Hashim and K. -T. Tang, "An Enhanced Input Differential Pair for Low-Voltage Bulk-Driven Amplifiers," in IEEE Transactions on Very Large Scale Integration (VLSI) Systems, vol. 29, no. 9, pp. 1601-1611, Sept. 2021. M. Akbari, S. M. Hussein, Y. Hashim, F. Khateb and K. -T. Tang, "A Rail-to-Rail Transconductance Amplifier Based on Current Generator Circuits," in IEEE Transactions on Very Large Scale Integration (VLSI) Systems, vol. 31, no. 10, pp. 1624-1628, Oct. 2023. E. Derogar, M. Akbari, and O. Hashemipour, “A self-biased transconductor with widely input linear range for Gm-C filters,” International Journal of Electronics Letters., 2020 Jan 2;8(1):70-82. M. Akbari, S. M. Hussein, Y. Hashim and K. -T. Tang, "An Adjustable Dual-Output Current Mode MOSFET-Only Filter," in IEEE Transactions on Circuits and Systems II: Express Briefs , vol. 68, no. 6, pp. 1817-1821, June 2021. M. Akbari, and O. Hashemipour, “A 63‐dB gain OTA operating in subthreshold with 20‐nW power consumption,” International Journal of Circuit Theory and Applications ., 2017 Jun;45(6):843-50. M. Akbari, S. M. Hussein, Y. Hashim, F. Khateb, T. Kulej and K. -T. Tang, "Implementation of a Multipath Fully Differential OTA in 0.18-μm CMOS Process," in IEEE Transactions on Very Large Scale Integration (VLSI) Systems, vol. 31, no. 1, pp. 147-151, Jan. 2023. M. Akbari, O. Hashemipour and F. Moradi, "Input Offset Estimation of CMOS Integrated Circuits in Weak Inversion," in IEEE Transactions on Very Large Scale Integration (VLSI) Systems , vol. 26, no. 9, pp. 1812-1816, Sept. 2018. S. Lee and E. Sánchez-Sinencio, "Current Reference Circuits: A Tutorial," in IEEE Transactions on Circuits and Systems II: Express Briefs , vol. 68, no. 3, pp. 830-836, March 2021. M. Akbari, S. M. Hussein, Y. Hashim and K. -T. Tang, "0.4-V Tail-Less Quasi-Two-Stage OTA Using a Novel Self-Biasing Transconductance Cell," in IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 69, no. 7, pp. 2805-2818, July 2022. M. Akbari, “Single-stage fully recycling folded cascode OTA for switched-capacitor circuits,” Electronics Letters ., 2015 Jun 4;51(13):977-9. Table Table 1: Specifications of the proposed transconductance cell. Additional Declarations The authors declare no competing interests. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4971100","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Short Report","associatedPublications":[],"authors":[{"id":344690974,"identity":"439c5a0a-9fee-4063-8dee-bf4a8992d738","order_by":0,"name":"Meysam Akbari","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAxklEQVRIiWNgGAWjYHACZmYgwcMPZIC5bERrkWwgVQuDwQGoFoJAt4H5sXFBzT0Z4xvJhw0YauwY+KQP4NdidoDNOHnGsWIesxtpyQkMx5IZ2PgSCGlhMD7Mw5YA1JJjfICBDYh4CDjM7AD758M8/xJ4jGeAtPwjSguPcTJvWwKPgUSOcQJjGzFaDvMUG8/sS+CROPMs2SCxL5mHsJbj7ZulC74l2PO3Jx+W+PDNTk6+h4AW1MhIAMYpIQ2jYBSMglEwCogAACCRNGaUhmnDAAAAAElFTkSuQmCC","orcid":"https://orcid.org/0000-0002-4251-1138","institution":"University of Kurdistan","correspondingAuthor":true,"prefix":"","firstName":"Meysam","middleName":"","lastName":"Akbari","suffix":""}],"badges":[],"createdAt":"2024-08-25 03:37:21","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-4971100/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4971100/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":63331129,"identity":"3bc8f9d2-0715-4f27-bb3d-7919de052010","added_by":"auto","created_at":"2024-08-27 04:26:22","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":11522,"visible":true,"origin":"","legend":"\u003cp\u003e(a) Conventional current generator circuit, and (b) proposed self-biasing transconductance cell.\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-4971100/v1/87f42b509f497b5a120f4c81.png"},{"id":63331132,"identity":"132f317f-f2a5-4ecc-86b7-b9e76af37115","added_by":"auto","created_at":"2024-08-27 04:26:23","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":13080,"visible":true,"origin":"","legend":"\u003cp\u003eFrequency response.\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-4971100/v1/16298c5fdec4475a827a6b63.png"},{"id":63331131,"identity":"7a6a19fe-9c7f-4b49-93fa-7895390604cd","added_by":"auto","created_at":"2024-08-27 04:26:22","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":10283,"visible":true,"origin":"","legend":"\u003cp\u003eStep response.\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-4971100/v1/c81f9d1853eb30c32176f927.png"},{"id":63331565,"identity":"a2d0a3f9-8e9b-4cf6-8fe6-a2112fd66aab","added_by":"auto","created_at":"2024-08-27 04:34:22","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":375400,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4971100/v1/cdb7dd56-9385-434c-9348-fc32fa50d6e5.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eThe Self-Biasing Current Generator: A Useful Transconductance Cell\u003c/p\u003e","fulltext":[{"header":"I.\tINTRODUCTION","content":"\u003cp\u003eTRANSCONDUCTANCE cells are widely used in analog and mixed-signal circuits such as operational transconductance amplifiers (OTA) [1], rail-to-rail circuits [2], tunable filters [3, 4], etc. Among all these circuits, the ultra-low-power (ULP) OTAs are widely used because of their capability of playing the role of many different functions. Recently, several OTAs have been enhanced based on the positive feedback topologies in [5, 6], which are suitable for ultra-low-voltage (ULV) applications. In this way, bulk terminals of the differential pair topology were used as the input nodes to provide a high input dynamic range. Nonetheless, due to a lower bulk transconductance than that of the gate terminal, designers face some disadvantages such as lower gain bandwidth (GBW), lower DC gain, lower slew rate (SR), larger input noise, and larger offset, which were carefully analyzed and reduced in [5–7].\u003c/p\u003e"},{"header":"II.\tPROPOSED TRANSCONDUCTANCE CELL","content":"\u003cp\u003eFigure\u0026nbsp;1 (a) shows the basic idea of a conventional current generator circuit, which its performance can be improved by adding a resistance at the source terminal of transistor M4 [\u003cspan class=\"CitationRef\"\u003e8\u003c/span\u003e]. This circuit forms a positive feedback loop and will be stable for a loop gain less than unity. This structure is very useful to design a transconductance cell with a self-biasing topology.\u003c/p\u003e\n\u003cp\u003eFigure\u0026nbsp;1 (b) shows the proposed self-biasing transconductance cell [\u003cspan class=\"CitationRef\"\u003e9\u003c/span\u003e]. As is seen, transistor M0 is added as the tail current to create a virtual ground at the source of M1-M2, which results in a special differential pair. Based on the analysis done in [\u003cspan class=\"CitationRef\"\u003e9\u003c/span\u003e], having a tail current will increase the common-mode-rejection ratio (CMRR) of the structure. This circuit can only be converted to a bulk-driven transconductance cell because there is no more idle terminal to be used as the input node except bulks. Therefore, the bulk terminals of P-type transistors M1-M2 are used as the input nodes that offer a high input dynamic range.\u003c/p\u003e\n\u003cp\u003eTo stabilize the proposed structure, an adjustable current source, M5, should be paralleled with one of the non-diode-connected transistors M2-M3. Actually, without employing M5, the proposed structure provides an infinite output impedance casing an unstable behavior in the transient response. Eq.\u0026nbsp;(\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e) expresses the impedance seen from both outputs where its amount is adjusted by the transconductance of M5, \u003cem\u003egm\u003c/em\u003e\u003csub\u003e5\u003c/sub\u003e, and the pole associated with output nodes can be moved by tuning \u003cem\u003eV\u003c/em\u003e\u003csub\u003eb2\u003c/sub\u003e.\u003c/p\u003e\n\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\n \u003cdiv class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e$${R_{out \\pm }} \\approx \\frac{1}{{g{m_1}\\left( {1 - \\frac{{g{m_2}\\left( {g{m_1} - g{m_5}} \\right)}}{{g{m_1}g{m_4}}}} \\right)}}$$\u003c/div\u003e\n \u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003ewhere \u003cem\u003egm\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e represents the transconductance of the corresponding transistors, and (\u003cem\u003egm\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e-\u003cem\u003egm\u003c/em\u003e\u003csub\u003e5\u003c/sub\u003e)\u0026thinsp;=\u0026thinsp;\u003cem\u003egm\u003c/em\u003e\u003csub\u003e3\u003c/sub\u003e. Therefore, to achieve a finite positive impedance at the output, \u003cem\u003egm\u003c/em\u003e\u003csub\u003e5\u003c/sub\u003e should have a non-zero value. It is obvious that the proposed structure benefits from a high output impedance, which results in a higher transconductance and a larger DC gain in comparison with a conventional bulk-driven structure. In addition, the proposed cell provides a double-ended structure, while the output common mode voltages are controlled by its self-biasing topology without employing any common-mode feedback (CMFB) circuit. By employing two of the proposed cells, a self-biasing high-performance transconductance amplifier can easily be designed as a tunable high dynamic range circuit.\u003c/p\u003e"},{"header":"III. SIMULATION RESULTS","content":"\u003cp\u003eThe proposed circuit was simulated in TSMC 0.18 µm CMOS technology @ 0.4 V driving a 2×2 pF capacitive load. The frequency response of the amplifier is shown in Fig. 2, while a DC gain and a gain bandwidth of 25 dB and 3 kHz were respectively achieved. To simulate the step response, a unity-gain capacitive buffer employed in [10] was used. In this way, a large differential step of 0.2V at 50 kHz was applied to the inputs. Fig. 3 shows the step response of the amplifier representing an average slew rate of 32 V/ms. Thanks to the use of the bulk-driven method, Fig. 3 also shows that a differential input/output voltage swing of 0.4V was achieved. Table 1 reports the main specifications of the proposed transconductance cell, while it consumes just 4 nW power. As a result, the proposed circuit can be very useful in configuring a high-performance bulk-driven transconductance amplifier, specially those that operate under sub-threshold supplies with a self-biasing topology.\u003c/p\u003e"},{"header":"IV. CONCLUSION","content":"\u003cp\u003eThis brief re-configured a basic self-biasing current generator circuit as a high-performance transconductance cell. The proposed structure used the bulk terminals of P-type transistors as the input nodes to provide a high input dynamic range. To stabilize the circuit, an additional transistor was used as a shunt-current method to finite the output impedance. The circuit was designed and simulated in TSMC 0.18 µm CMOS technology under a supply voltage of 0.4 V. Simulation results showed a DC gain of 25 dB and an average slew rate of 32 V/ms for a capacitive load of 2×2 pF.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n \u003cli\u003eM. Akbari, S. M. Hussein, Y. Hashim and K. -T. Tang, \u0026quot;An Enhanced Input Differential Pair for Low-Voltage Bulk-Driven Amplifiers,\u0026quot; in IEEE Transactions on Very Large Scale Integration (VLSI) Systems, vol. 29, no. 9, pp. 1601-1611, Sept. 2021.\u003c/li\u003e\n \u003cli\u003eM. Akbari, S. M. Hussein, Y. Hashim, F. Khateb and K. -T. Tang, \u0026quot;A Rail-to-Rail Transconductance Amplifier Based on Current Generator Circuits,\u0026quot; in IEEE Transactions on Very Large Scale Integration (VLSI) Systems, vol. 31, no. 10, pp. 1624-1628, Oct. 2023.\u003c/li\u003e\n \u003cli\u003eE. Derogar, M. Akbari, and O. Hashemipour, \u0026ldquo;A self-biased transconductor with widely input linear range for Gm-C filters,\u0026rdquo; International Journal of Electronics Letters., 2020 Jan 2;8(1):70-82.\u003c/li\u003e\n \u003cli\u003eM. Akbari, S. M. Hussein, Y. Hashim and K. -T. Tang, \u0026quot;An Adjustable Dual-Output Current Mode MOSFET-Only Filter,\u0026quot; in \u003cem\u003eIEEE Transactions on Circuits and Systems II: Express Briefs\u003c/em\u003e, vol. 68, no. 6, pp. 1817-1821, June 2021.\u003c/li\u003e\n \u003cli\u003eM. Akbari, and O. Hashemipour, \u0026ldquo;A 63‐dB gain OTA operating in subthreshold with 20‐nW power consumption,\u0026rdquo; \u003cem\u003eInternational Journal of Circuit Theory and Applications\u003c/em\u003e., 2017 Jun;45(6):843-50.\u003c/li\u003e\n \u003cli\u003eM. Akbari, S. M. Hussein, Y. Hashim, F. Khateb, T. Kulej and K. -T. Tang, \u0026quot;Implementation of a Multipath Fully Differential OTA in 0.18-\u0026mu;m CMOS Process,\u0026quot; in IEEE Transactions on Very Large Scale Integration (VLSI) Systems, vol. 31, no. 1, pp. 147-151, Jan. 2023.\u003c/li\u003e\n \u003cli\u003eM. Akbari, O. Hashemipour and F. Moradi, \u0026quot;Input Offset Estimation of CMOS Integrated Circuits in Weak Inversion,\u0026quot; in \u003cem\u003eIEEE Transactions on Very Large Scale Integration (VLSI) Systems\u003c/em\u003e, vol. 26, no. 9, pp. 1812-1816, Sept. 2018.\u003c/li\u003e\n \u003cli\u003eS. Lee and E. S\u0026aacute;nchez-Sinencio, \u0026quot;Current Reference Circuits: A Tutorial,\u0026quot; in \u003cem\u003eIEEE Transactions on Circuits and Systems II: Express Briefs\u003c/em\u003e, vol. 68, no. 3, pp. 830-836, March 2021.\u003c/li\u003e\n \u003cli\u003eM. Akbari, S. M. Hussein, Y. Hashim and K. -T. Tang, \u0026quot;0.4-V Tail-Less Quasi-Two-Stage OTA Using a Novel Self-Biasing Transconductance Cell,\u0026quot; in IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 69, no. 7, pp. 2805-2818, July 2022.\u003c/li\u003e\n \u003cli\u003eM. Akbari, \u0026ldquo;Single-stage fully recycling folded cascode OTA for switched-capacitor circuits,\u0026rdquo; \u003cem\u003eElectronics Letters\u003c/em\u003e., 2015 Jun 4;51(13):977-9.\u003c/li\u003e\n\u003c/ol\u003e"},{"header":"Table","content":"\u003cp\u003e\u003cstrong\u003eTable 1:\u003c/strong\u003e Specifications of the proposed transconductance cell.\u003c/p\u003e\n\u003cp\u003e\u003cimg 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