Injection locking characteristics of oscillators are derived and a graphical analysis is presented that describes injection pulling in time and frequency domains. An identity obtained from phase and envelope equations is used to express the requisite oscillator nonlinearity and interpret phase noise reduction. The behavior of phase-locked oscillators under injection pulling is also formulated.

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A study of injection locking and pulling in oscillators

A new concept for quadrature coupling of LC oscillators is introduced and demonstrated on a 5-GHz CMOS voltage-controlled oscillator (VCO). It uses the second harmonic of the outputs to couple the oscillators. The technique provides quadrature over a wide tuning range without introducing any increase in phase noise or power consumption. The VCO is tunable between 4.57 and 5.21 GHz and has a phase noise lower than -124 dBc/Hz at 1-MHz offset over the entire tuning range. The worst-case measured image rejection is 33 dB. The circuit draws 8.75 mA from a 2.5-V supply.

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A low-phase-noise 5-GHz CMOS quadrature VCO using superharmonic coupling

We show that the quadrature LC oscillator is best treated as two strongly coupled, nominally identical oscillators that are locked to the same frequency. Differential equations that extend Adler's description of locking to strong injection reveal the full dynamics of this circuit. With a simplifying insight, the analysis reveals all the modes of the oscillator, their stability, the effects of mismatch on quadrature phase accuracy, and through a novel use of the analysis, phase noise.

The Quadrature LC Oscillator: A Complete Portrait Based on Injection Locking

Radio frequency integrated circuits (RFICs) are the building blocks that enable every device from cable television sets to mobile telephones to transmit and receive signals and data. This newly revised and expanded edition of the 2003 Artech House classic, "Radio Frequency Integrated Circuit Design", serves as an up-to-date, practical reference for complete RFIC know-how. The second edition includes numerous updates, including greater coverage of CMOS PA design, RFIC design with on-chip components, and more worked examples with simulation results. By emphasizing working designs, this book practically transports readers into the authors' own RFIC lab so they can fully understand how these designs function. This title is suitable for radio frequency integrated circuit (RFIC) design engineers; radio systems architects; researchers and developers of RFIC technology; and, graduate level electrical engineering students.

Radio Frequency Integrated Circuit Design

This paper presents an analysis of phase noise in multiphase LC oscillators, and measurement results for several CMOS quadrature-voltage-controlled-oscillators (QVCOs) working in the 2-GHz frequency range. The phase noise data for a so-called BS-QVCO (-140 dBc/Hz or less at 3 MHz frequency offset from the carrier, for a power consumption of 20.8 mW and a figure-of-merit of 184 dBc/Hz) show that phase noise performances are close to the previously derived limits. A systematic cause of departure from ideal quadrature between QVCO signals is also analyzed and measured experimentally, and a compact LC-tank layout that removes this source of phase error is proposed. A TS-QVCO designed with this technique shows a phase-noise figure-of-merit improvement of 4 dB, compared to a previous implementation. The measured equivalent phase error for all QVCOs is between 0.6/spl deg/ and 1/spl deg/.

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On the phase-noise and phase-error performances of multiphase LC CMOS VCOs

This paper presents a quadrature voltage-controlled oscillator (QVCO) based on the coupling of two LC-tank VCOs A simplified theoretical analysis for the oscillation frequency and phase noise displayed by the QVCO in the 1/f/sup 3/ region is developed, and good agreement is found between theory and simulation results A prototype for the QVCO was implemented in a 035-/spl mu/m CMOS process with three standard metal layers The QVCO could be tuned between 164 and 197 GHz, and showed a phase noise of -140 dBc/Hz or less across the tuning range at a 3-MHz offset frequency from the carrier, for a current consumption of 25 mA from a 2-V power supply The equivalent phase error between I and Q signals was at most 025/spl deg/

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L. Romano

Papers

Analysis and design of a 1.8-GHz CMOS LC quadrature VCO