Skip to main content
  • 1222 Accesses

Abstract

Multiplier circuits represent important building blocks in VLSI designs, finding multiple applications in telecommunication circuits, medical equipments, hearing devices or disk drives. In bipolar technology, the multiplying function could be easily obtained from the logarithmical characteristic of the bipolar transistor, the circuits presenting important errors caused by the nonzero values of the base currents, and also by the temperature dependence of the bipolar transistor parameters. For obtaining a good circuit frequency response, the multiplying function can be achieved in CMOS technology by employing the square-law model of MOS transistor biased in saturation region. In order to respond to the low-power requirements of the newest CMOS designs, the subthreshold operation of the MOS transistor represents an interesting choice. Based on the logarithmical law of a MOS transistor in weak inversion, the complexity of CMOS multiplier circuits can be strongly reduced. Because it exists a relative limited number of mathematical principles that are used for implementing the multiplier circuits, the first part of the chapter is dedicated to the analysis of the mathematical relations that represent the functional core of the designed circuits. In the second part of the chapter, starting from these elementary principles, there are analyzed and designed concrete multiplier circuits, grouped following the mathematical principle they are based on.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Kim YH, Park SB (1992) Four-quadrant CMOS analogue multiplier. Electron Lett 28:649–650

    Article  Google Scholar 

  2. Wallinga H, Bult K (1989) Design and analysis of CMOS analog signal processing circuits by means of a graphical MOST model. IEEE J Solid-State Circuits 24:672–680

    Article  Google Scholar 

  3. Shen-Iuan L, Chen-Chieh C (1997) Low-voltage CMOS four-quadrant multiplier. Electron Lett 33:207–208

    Article  Google Scholar 

  4. Gunhee H, Sanchez-Sinencio E (1998) CMOS transconductance multipliers: a tutorial. IEEE Trans Circuits Syst II: Analog Digit Signal Process 12:1550–1563

    Article  Google Scholar 

  5. Chen JJ, Liu SI, Hwang YS (1998) Low-voltage single power supply four-quadrant multiplier using floating-gate MOSFETs. IEE proceedings on circuits, devices and systems, pp 40–43

    Google Scholar 

  6. Sawigun C, Mahattanakul J (2008) A 1.5 V, wide-input range, high-bandwidth, CMOS four-quadrant analog multiplier. IEEE international symposium on circuits and systems, pp 2318–2321, Washington, USA

    Google Scholar 

  7. Sawigun C, Demosthenous A, Pal D (2007) A low-voltage, low-power, high-linearity CMOS four-quadrant analog multiplier. European conference on circuit theory and design, pp 751–754, Seville, Spain

    Google Scholar 

  8. Liu SI, Hwang YS (1993) CMOS four-quadrant multiplier using bias offset crosscoupled pairs. Electron Lett 29:1737–1738

    Article  Google Scholar 

  9. Ramirez-Angulo J, Carvajal RG, Martinez-Heredia J (2000) 1.4 V supply, wide swing, high frequency CMOS analogue multiplier with high current efficiency. IEEE international symposium on circuits and systems, pp 533–536, Geneva, Switzerland

    Google Scholar 

  10. Popa C (2006) Improved linearity active resistor with controllable negative resistance. IEEE international conference on integrated circuit design and technology, pp 1–4, Padova, Italy

    Google Scholar 

  11. Langlois PJ (1990) Comments on “A CMOS four-quadrant multiplier”: effects of threshold voltage. IEEE J Solid-State Circuits 25:1595–1597

    Article  Google Scholar 

  12. Zarabadi SR, Ismail M, Chung-Chih H (1998) High performance analog VLSI computational circuits. IEEE J Solid-State Circuits 33:644–649

    Article  Google Scholar 

  13. Popa C (2009) High accuracy CMOS multifunctional structure for analog signal processing. International semiconductor conference, pp 427–430, Sinaia, Romania

    Google Scholar 

  14. De La Cruz Blas CA, Feely O (2008) Limit cycle behavior in a class-AB second-order square root domain filter. IEEE International conference on electronics, circuits and systems, pp 117–120, St. Julians, Malta

    Google Scholar 

  15. Popa C (2001) Low-power rail-to-rail CMOS linear transconductor. International semiconductor conference, pp 557–560, Sinaia, Romania

    Google Scholar 

  16. Sakurai S, Ismail M (1992) A CMOS square-law programmable floating resistor independent of the threshold voltage. IEEE Trans Circuits Syst II: Analog Digit Signal Process 39:565–574

    Article  Google Scholar 

  17. Jong-Kug S, Charlot J (2000) A CMOS inverse trigonometric function circuit. IEEE midwest symposium on circuits and systems, pp 474–477, Michigan, USA

    Google Scholar 

  18. Popa C (2010) CMOS multifunctional computational structure with improved performances. International semiconductors conference, pp 471–474, Sinaia, Romania

    Google Scholar 

  19. Popa C (2002) CMOS transconductor with extended linearity range. IEEE international conference on automation, quality and testing, robotics, pp 349–354, Cluj, Romania

    Google Scholar 

  20. Manolescu AM, Popa C (2009) Low-voltage low-power improved linearity CMOS active resistor circuits. Springer J Analog Integr Circuits Signal Process 62:373–387

    Article  Google Scholar 

  21. Babanezhad JN, Temes GC (1985) A 20-V four-quadrant CMOS analog multiplier. IEEE J Solid-State Circuits 20:1158–1168

    Article  Google Scholar 

  22. Popa C, Manolescu AM (2007) CMOS differential structure with improved linearity and increased frequency response. International semiconductor conference, pp 517–520, Sinaia, Romania

    Google Scholar 

  23. Popa C (2008) Programmable CMOS active resistor using computational circuits. International semiconductor conference, pp 389–392, Sinaia, Romania

    Google Scholar 

  24. Popa C (2009) Multiplier circuit with improved linearity using FGMOS transistors. International symposium ELMAR, pp 159–162, Zadar, Croatia

    Google Scholar 

  25. Seng YK, Rofail SS (1998) Design and analysis of a ±1 V CMOS four-quadrant analogue multiplier. IEE proceedings on circuits, devices and systems, pp 148–154, Florida, USA

    Google Scholar 

  26. Kathiresan G, Toumazou C (1999) A low voltage bulk driven downconversion mixer core. IEEE international symposium on circuits and systems, pp 598–601, Florido, USA

    Google Scholar 

  27. Szczepanski S, Koziel S (2004) 1.2 V low-power four-quadrant CMOS transconductance multiplier operating in saturation region. International symposium on circuits and systems, pp 1016–1019, Vancouver, Canada

    Google Scholar 

  28. Coban AL, Allen PE (1994) A 1.5 V four-quadrant analog multiplier. Midwest symposium on Sch of Electr and Comput Eng, pp 117–120, La Fayette, USA

    Google Scholar 

  29. Manolescu AM, Popa C (2011) A 2.5 GHz CMOS mixer with improved linearity. J Circuits Syst Comp 20:233–242

    Article  Google Scholar 

  30. Popa C, Coada D (2003) A new linearization technique for a CMOS differential amplifier using bulk-driven weak-inversion MOS transistors. International symposium on circuits and systems, pp 589–592, Iasi, Romania

    Google Scholar 

  31. Akshatha BC, Akshintala VK (2009) Low voltage, low power, high linearity, high speed CMOS voltage mode analog multiplier. International conference on emerging trends in engineering and technology, pp 149–154, Nagpur, India

    Google Scholar 

  32. Shen-Iuan L, Yuh-Shyan H (1995) CMOS squarer and four-quadrant multiplier. IEEE Trans Circuits Syst I: Fundam Theory Appl 42:119–122

    Article  Google Scholar 

  33. Xiang-Luan Jia WH, Shi-Cai Q (1995) A new CMOS analog multiplier with improved input linearity. IEEE region 10 international conference on microelectronics and VLSI, pp 135–136, Hong Kong

    Google Scholar 

  34. Szczepanski S, Koziel S (2002) A 3.3 V linear fully balanced CMOS operational transconductance amplifier for high-frequency applications. IEEE international conference on circuits and systems for communications, pp 38–41, St. Petersburg, Russia

    Google Scholar 

  35. Mahmoud SA (2009) Low voltage low power wide range fully differential CMOS four-quadrant analog multiplier. IEEE international midwest symposium on circuits and systems, pp 130–133, Cancun, Mexico

    Google Scholar 

  36. Popa C (2010) Improved linearity CMOS active resistor based on complementary computational circuits. IEEE international conference on electronics, circuits, and systems, pp 455–458, Athens, Greece

    Google Scholar 

  37. Psychalinos C, Vlassis S (2002) A systematic design procedure for square-root-domain circuits based on the signal flow graph approach. IEEE Trans Circuits Syst I: Fundam Theory Appl 49:1702–1712

    Article  Google Scholar 

  38. Naderi A et al (2009) Four-quadrant CMOS analog multiplier based on new current squarer circuit with high-speed. IEEE international conference on “Computer as a tool”, pp 282–287, St. Petersburg, Russia

    Google Scholar 

  39. Naderi A, Khoei A, Hadidi K (2007) High speed, low power four-quadrant CMOS current-mode multiplier. IEEE international conference on electronics, circuits and systems, pp 1308–1311, Marracech, Morocco

    Google Scholar 

  40. Arthansiri T, Kasemsuwan V (2006) Current-mode pseudo-exponential-control variable-gain amplifier using fourth-order Taylor’s series approximation. Electron Lett 42:379–380

    Article  Google Scholar 

  41. Bult K, Wallinga H (1987) A class of analog CMOS circuits based on the square-law characteristic of an MOS transistor in saturation. IEEE J Solid-State Circuits 22:357–365

    Article  Google Scholar 

  42. Popa C (2003) Low-power CMOS bulk-driven weak-inversion accurate current-mode multiplier/divider circuits. International conference on electrical and electronics engineering, pp 66–73, Bursa, Turkey

    Google Scholar 

  43. Popa C (2009) Computational circuits using bulk-driven MOS devices. IEEE international conference on “Computer as a tool”, pp 246–251, St. Petersburg, Russia

    Google Scholar 

  44. Wilamowski BM (1998) VLSI analog multiplier/divider circuit. IEEE international symposium on industrial electronics, pp 493–496, Pretoria, South Africa

    Google Scholar 

  45. De La Cruz-Blas CA, Lopez-Martin A, Carlosena A (2003) 1.5-V MOS translinear loops with improved dynamic range and their applications to current-mode signal processing. IEEE Trans Circuits Syst II: Analog Digit Signal Process 50:918–927

    Article  Google Scholar 

  46. Popa C (2003) A new curvature-corrected voltage reference based on the weight difference of gate-source voltages for subthreshold-operated MOS transistors. International symposium on circuits and systems, pp 585–588, Iasi, Romania

    Google Scholar 

  47. Cheng-Chieh C, Li S-I (1998) Weak inversion four-quadrant multiplier and two-quadrant divider. Electron Lett 34:2079–2080

    Article  Google Scholar 

  48. Khateb F, Biolek D, Khatib N, Vavra J (2010) Utilizing the bulk-driven technique in analog circuit design. IEEE international symposium on design and diagnostics of electronic circuits and systems, pp 16–19, Vienna, Austria

    Google Scholar 

  49. Shu-Xiang S, Guo-Ping Y, Hua C (2007) A new CMOS electronically tunable current conveyor based on translinear circuits. International conference on ASIC, pp 569–572, Guilin, China

    Google Scholar 

  50. Gravati M, Valle M, Ferri G, Guerrini N, Reyes N (2005) A novel current-mode very low power analog CMOS four quadrant multiplier. Solid-state circuits conference, pp 495–498, Grenoble, France

    Google Scholar 

  51. Oliveira VJS, Oki N (2005) Low voltage analog synthesizer of orthogonal signals: a current-mode approach. IEEE international symposium on circuits and systems, pp 3708–3712, Kobe, Japan

    Google Scholar 

  52. Gravati M, Valle M, et al (2005) A novel current-mode very low power analog CMOS four quadrant multiplier. Solid-state circuits conference, pp 495–498, Grenoble, France

    Google Scholar 

  53. Cheng-Chieh C, Shen-Iuan L (1998) Weak inversion four-quadrant multiplier and two-quadrant divider. Electron Lett 34:2079–2080

    Article  Google Scholar 

  54. Sawigun C, Serdijn WA (2009) Ultra-low-power, class-AB, CMOS four-quadrant current multiplier. Electron Lett 45:483–484

    Article  Google Scholar 

  55. Hidayat R, Dejhan K, Moungnoul P, Miyanaga Y (2008) OTA-based high frequency CMOS multiplier and squaring circuit. International symposium on intelligent signal processing and communications systems, pp 1–4, Bangkok, Thailand

    Google Scholar 

  56. Machowski W, Kuta S, Jasielski J, Kolodziejski W (2010) Quarter-square analog four-quadrant multiplier based on CMOS inverters and using low voltage high speed control circuits. International conference on mixed design of integrated circuits and systems, pp 333–336, Wroclaw, Poland

    Google Scholar 

  57. Ehsanpour M, Moallem P, Vafaei A (2010) Design of a novel reversible multiplier circuit using modified full adder. International conference on computer design and applications, pp V3-230–V3-234, Hebei, China

    Google Scholar 

  58. Parveen T, Ahmed MT (2009) OFC based versatile circuit for realization of impedance converter, grounded inductance, FDNR and component multipliers. International multimedia, signal processing and communication technologies, pp 81–84, Aligarh, India

    Google Scholar 

  59. Feldengut T, Kokozinski R, Kolnsberg S (2009) A UHF voltage multiplier circuit using a threshold-voltage cancellation technique. Research in microelectronics and electronics, pp 288–291, Cork, Ireland

    Google Scholar 

  60. Naderi A, Mojarrad H, Ghasemzadeh H, Khoei A, Hadidi K (2009) Four-quadrant CMOS analog multiplier based on new current squarer circuit with high-speed. IEEE international conference on “Computer as a tool”, pp 282–287, St. Petersburg, Russia

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Cosmin Radu Popa .

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer Science+Business Media, LLC

About this chapter

Cite this chapter

Popa, C.R. (2012). Voltage and Current Multiplier Circuits. In: Synthesis of Computational Structures for Analog Signal Processing. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-0403-3_2

Download citation

  • DOI: https://doi.org/10.1007/978-1-4614-0403-3_2

  • Published:

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4614-0402-6

  • Online ISBN: 978-1-4614-0403-3

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics