A 5 GHz quadrature relaxation oscillator with mixing for improved testability or compact front‐end implementation

SUMMARYWe propose a theoretical analysis of the class of quadrature VCOs (QVCOs) based on two LC-oscillators directly coupled by means of the second harmonic. The analysis provides the conditions for the existence and stability of steady-state quadrature oscillations and a simplified model for the phase noise (PN) transfer function with respect to a noise source in parallel to the tank. We show that the figure of merit defined as the product between PN and current equals that of the single VCO, confirming that quadrature generation is achieved by this class of QVCO without degrading that figure of merit. An analytical model for the phase quadrature error due to tank mismatches is also proposed. The validity of all analytical models is discussed against numerical simulations. A practical implementation at 3.26 GHz with ±20% tuning range in a 0.13 m CMOS technology is also presented, confirming the main theoretical findings.

Section: Discussionmentioning

confidence: 98%

Quadrature VCOs based on direct second harmonic locking: Theoretical analysis and experimental validation

Tortori

Guermandi

et al. 2010

“…Phase locked loops are widely used in many applications, such as frequency synthesis, synchronization, clock and data recovery, and clock generation [1][2][3][4][5]. Charge-pump phase-locked loops (CP-PLLs) have been one of the most popular phase-locked loop (PLL) structures since Gardner's work in 1980 [6].…”

Section: Introductionmentioning

confidence: 99%

Dynamics of charge‐pump phase‐locked loops

Curran

Feely

2012

Certain problems in the existing treatment of the stability of charge‐pump phase‐locked loops are identified and addressed in this work. New results concerning the instability, stability, and asymptotic stability of charge‐pump phase‐locked loops are obtained by means of Lyapunov's direct and indirect methods. Closer consideration of the local dynamics provides further insight into the system's patterns of behavior. In particular, the influence of circuit parameters on the nature of the steady‐state orbits is investigated. Copyright © 2012 John Wiley & Sons, Ltd.

“…Figure 5 shows the calculated values of the period for C varying from 10 pF up to 10 f F and, consequently, for ε from 2 up to 30. Negligible discrepancies are obtained using Equation (21), which demonstrates the high accuracy of the cubic approximation with r = 0, as well as the validity of the asymptotic approximation (20) in a wide interval of ε, i.e. of capacitance C. Further, the oscillation period tends, as expected, to the limit value (17), for C tending to zero.…”

Section: Numerical and Experimental Resultsmentioning

confidence: 93%

A new CMOS astable multivibrator and its nonlinear analysis

Buonomo¹

2011

SUMMARYWe present a nonlinear analysis of a new inductively tuned astable multivibrator obtained by connecting a timing inductor across a composite nonlinear resistor with a characteristic of N -type, which is made up of the parallel connection of two complementary pairs of cross-coupled MOS devices. Some possible practical applications of the circuit are also envisaged. Closed-form expressions for the amplitude and the period of the periodic oscillation are derived in both cases when the circuit exhibits a relaxation oscillation and in the more difficult case when, due to the effect of parasitic capacitances of the devices, the circuit has an almost-discontinuous relaxation oscillation with a nonzero switching time. The accuracy of the presented formulas, which are useful for both the analysis and design, is validated through circuit simulations and experimental results.