A Phase and Amplitude Tunable Quadrature $LC$ Oscillator: Analysis and Design

This paper presents a new analytical approach to extract closed form equations for phase and amplitude imbalances raised from mismatches between two LC-tanks in quadrature oscillators. For more generality, we considered different coupling factors for the two coupled oscillators. This makes our analysis so general that we could design a phase and amplitude tunable quadrature oscillator accordingly. We show that choosing appropriate inversely proportional coupling factors makes it possible to have exactly zero phase and amplitude errors. Choosing so does not have any impacts on phase noise; indeed, the trade-off between phase noise and phase error in coupled quadrature oscillators has been broken here. We show that using differential stages for tuning tail currents of oscillating stages can somehow implement the inversely proportional coupling factors. Tuning the phase and amplitude errors, the frequency does not change and power consumption remains constant too; these are the advantages of the proposed circuit. The theoretical results and proposed quadrature oscillator are evaluated and confirmed through simulations using TSMC 0.18 model technology on a 5-GHz quadrature oscillator with current consumption of 4.2 mA at 1.8 V supply voltage.

[1]  Pietro Andreani,et al.  Analysis and Design of a 1.8-GHz CMOS LC , 2002 .

[2]  Ching-Yi Chen,et al.  Analysis and Design of a Wide-Tuning-Range VCO With Quadrature Outputs , 2008, IEEE Transactions on Circuits and Systems II: Express Briefs.

[3]  S. Raman,et al.  A 5 GHz I/Q Phase-tunable CMOS LC Quadrature VCO (PT-QVCO) for Analog Phase Calibrated Receiver Architectures , 2007, 2007 Topical Meeting on Silicon Monolithic Integrated Circuits in RF Systems.

[4]  S. Raman,et al.  Analysis and Design of a CMOS Phase-Tunable Injection-Coupled LC Quadrature VCO (PTIC-QVCO) , 2009, IEEE Journal of Solid-State Circuits.

[5]  V. Gopinathan,et al.  An injection locking scheme for precision quadrature generation , 2002, Proceedings of the 27th European Solid-State Circuits Conference.

[6]  A. Rofougaran,et al.  A 900 MHz CMOS LC-oscillator with quadrature outputs , 1996, 1996 IEEE International Solid-State Circuits Conference. Digest of TEchnical Papers, ISSCC.

[7]  A.A. Abidi,et al.  The Quadrature LC Oscillator: A Complete Portrait Based on Injection Locking , 2007, IEEE Journal of Solid-State Circuits.

[8]  Manoj Sachdev,et al.  A method to derive an equation for the oscillation frequency of a ring oscillator , 2003 .

[9]  Ali Hajimiri,et al.  A general theory of phase noise in electrical oscillators , 1998 .

[10]  A. Abidi,et al.  Physical processes of phase noise in differential LC oscillators , 2000, Proceedings of the IEEE 2000 Custom Integrated Circuits Conference (Cat. No.00CH37044).

[11]  Sang-Gug Lee,et al.  360-µW/1 mW Complementary Cross-Coupled Differential Colpitts LC-VCO/QVCO in 0.25-µm CMOS , 2007, IEICE Trans. Electron..

[12]  Salvatore Levantino,et al.  Multiphase LC oscillators , 2006, IEEE Transactions on Circuits and Systems I: Regular Papers.

[13]  A. Bonfanti,et al.  Analysis and design of a 1.8-GHz CMOS LC quadrature VCO , 2002, IEEE J. Solid State Circuits.

[14]  Pietro Andreani,et al.  A Time-Variant Analysis of Fundamental Phase Noise in CMOS Parallel , 2009 .

[15]  Andrea Mazzanti,et al.  A 1.8-GHz injection-locked quadrature CMOS VCO with low phase noise and high phase accuracy , 2006, IEEE Transactions on Circuits and Systems I: Regular Papers.

[16]  David J. Allstot,et al.  A gate-modulated CMOS LC quadrature VCO , 2009, 2009 IEEE Radio Frequency Integrated Circuits Symposium.

[17]  D.K. Ma,et al.  A subharmonically injected LC delay line oscillator for 17-GHz quadrature LO generation , 2004, IEEE Journal of Solid-State Circuits.

[18]  F. Svelto,et al.  On the amplitude and phase errors of quadrature LC-tank CMOS oscillators , 2006, IEEE Journal of Solid-State Circuits.

[19]  Pietro Andreani,et al.  A Time-Variant Analysis of Fundamental $1/f^{3}$ Phase Noise in CMOS Parallel $LC$ -Tank Quadrature Oscillators , 2009, IEEE Transactions on Circuits and Systems I: Regular Papers.

[20]  Ook Kim,et al.  A 1.8-GHz self-calibrated phase-locked loop with precise I/Q matching , 2001, IEEE J. Solid State Circuits.

[21]  Liang-Hung Lu,et al.  A Low-Power Quadrature VCO and Its Application to a 0.6-V 2.4-GHz PLL , 2010, IEEE Transactions on Circuits and Systems I: Regular Papers.

[22]  D. Kasperkovitz,et al.  Analysis and design of an optimally coupled 5-GHz quadrature LC oscillator , 2002, IEEE J. Solid State Circuits.

[23]  Sao-Jie Chen,et al.  An auto-I/Q calibrated CMOS transceiver for 802.11 g , 2005, ISSCC. 2005 IEEE International Digest of Technical Papers. Solid-State Circuits Conference, 2005..

[24]  Sheng-Lyang Jang,et al.  A 0.22 V Quadrature VCO in 90 nm CMOS Process , 2009, IEEE Microwave and Wireless Components Letters.

[25]  J.R. Long,et al.  A low-voltage 5.1-5.8-GHz image-reject receiver with wide dynamic range , 2000, IEEE Journal of Solid-State Circuits.

[26]  M. Horowitz,et al.  Precise delay generation using coupled oscillators , 1993, 1993 IEEE International Solid-State Circuits Conference Digest of Technical Papers.

[27]  Bernabé Linares-Barranco,et al.  A precise 90/spl deg/ quadrature OTA-C oscillator tunable in the 50-130-MHz range , 2004, IEEE Transactions on Circuits and Systems I: Regular Papers.

[28]  Behzad Razavi,et al.  A study of phase noise in CMOS oscillators , 1996, IEEE J. Solid State Circuits.

[29]  Behzad Razavi,et al.  RF Microelectronics , 1997 .

[30]  F. Ali,et al.  Direct conversion radio for digital mobile phones-design issues, status, and trends , 2002 .

[31]  Salvatore Levantino,et al.  Phase noise and accuracy in quadrature oscillators , 2004, 2004 IEEE International Symposium on Circuits and Systems (IEEE Cat. No.04CH37512).

[32]  B. Razavi.  A study of injection locking and pulling in oscillators , 2004, IEEE Journal of Solid-State Circuits.

[33]  Michiel Steyaert,et al.  Low-IF topologies for high-performance analog front ends of fully integrated receivers , 1998 .

[34]  Asad A. Abidi,et al.  CMOS mixers and polyphase filters for large image rejection , 2001, IEEE J. Solid State Circuits.

[35]  Tzuen-Hsi Huang,et al.  A 1 V 2.2 mW 7 GHz CMOS Quadrature VCO Using Current-Reuse and Cross-Coupled Transformer-Feedback Technology , 2008, IEEE Microwave and Wireless Components Letters.

[36]  A. Hajimiri,et al.  Corrections to "A General Theory of Phase Noise in Electrical Oscillators" , 1998 .

[37]  S.-L. Jang,et al.  CMOS Colpitts Quadrature VCO Using the Body Injection-Locked Coupling Technique , 2009, IEEE Microwave and Wireless Components Letters.

[38]  Sanjay Raman,et al.  A Comprehensive Analysis of Quadrature Signal Synthesis in Cross-Coupled RF VCOs , 2007, IEEE Transactions on Circuits and Systems I: Regular Papers.

[39]  J. M. Mora,et al.  A Precise 90 Quadrature OTA-C Oscillator Tunable in the 50 – 130-MHz Range , 2004 .