A method for the nonlinear analysis of voltage-controlled oscillators (VCOs) is presented, accounting for the nonlinear effect of both the varactors and the active devices. A nonlinear perturbation model of VCOs is presented, as well as a method for finding their steady-state oscillation, overcoming the limitation of previous analyses which rely on the solution of the tank balance equation only. Simple formulas for predicting the oscillation and its frequency correction due to the effect of nonlinearities are presented, allowing us to accurately predict the tuning curve of VCOs as well as the amplitude to phase-noise conversion due to the varactors. Their accuracy was validated by circuit simulations.

Nonlinear Analysis of Voltage-Controlled Oscillators: A Systematic Approach

Especially in the automotive domain wheel speed sensors face increasing quality and reliability requirements due to novel vehicle concepts as well as new legal regulations. From this follows, that next generation sensors have to possess a higher robustness against harsh environmental conditions. A large operating temperature range as well as a high stray field immunity are key-requirements. In this paper a novel magnetoresistive wheel speed sensor is presented, whereby its transfer function is linearized in the frequency domain. From this follows directly an improvement of the sensor reliability, since temperature and lifetime drift are significantly reduced. Moreover, the concept enables measurement of disturbing fields perpendicular to sensing direction, which cannot be detected by existing speed sensors. Furthermore, promising measurement results validate the feasibility and performance of the presented sensory system.

A novel magnetoresistive wheel speed sensor with low temperature drift and high stray field immunity

The effect of deliberate circuit mismatches in an LC VCO is investigated and it is shown that such mismatches can significantly reduce the oscillation start-up time. An analysis is presented that shows that the presence of mismatches results in a common-mode disturbance simultaneous with the turn-on of the tail current. The use of this technique is applied to a low-power transmitter for an ultra-wideband wireless communication system using the on-off keying modulation scheme. Simulations using a 0.18-µm CMOS technology with a 4 GHz carrier frequency give 34.5 pJ/bit assuming a repetition rate of 1 Mb/s.

Fast startup of LC VCOs using circuit asymmetries

In his paper the design of LC-VCOs is addressed. Due to the high-density integration needs as well as to low cost fabrication, RF applications are usually implemented in CMOS technology. However, this technology development brought up several issues such as the degradation of on-chip LC tank quality factor, yielding VCO's phase noise limitation. To overcome phase-noise limitations, optimization design methodologies are usually used. Since electromagnetic simulations are timely expensive, model based approaches are needed. In this work the characterization of the oscillator behaviour is guaranteed by a set of analytical models describing each circuit element performance. A set of working examples for UMC130 technology, aiming the VCO phase noise and power consumption optimization, is addressed. The results presented, spotlight the potential of the proposed design methodology, combined with a GA optimization procedure, for an accurate and timely efficient oscillator design. The accuracy of the results is checked against HSPICE/RF simulator.

LC-VCO design methodology based on evolutionary algorithms

The need for implementing low cost, fully integrated RF wireless transceivers has motivated the widespread use CMOS technology. However, in the particular case for voltage-controlled oscillators (VCO) where ever more stringent specifications in terms of phase-noise must be attained, the design of the on-chip LC tank is a challenging task, where fully advantage of the actual technologies characteristics must be pushed to nearly its limits. To overcome phase-noise limitations arising from the low quality factor of integrated inductors, optimization design methodologies are usually used. In this paper a model-based optimization approach is proposed. In this work the characterization of the oscillator behaviour is guaranteed by a set of analytical models describing each circuit element performance. A set of working examples for UMC130 technology, aiming the minimization of both VCO phase noise and power consumption, is addressed. The results presented, illustrate the potential of a GA optimization procedure design methodology yielding accurate and timely efficient oscillator designs. The validity of the results is checked against HSPICE/RF simulations.

Optimal LC-VCO design through evolutionary algorithms

Since the beginning of the last century, the problem of oscillator circuit design is a main subject for analog circuit designers. In recent years, the study of differential VCOs has received attention because of their importance in a number of applications. We present an analysis of the steady state oscillation of integrated differential VCOs which is based on a nonlinear model of the oscillator. Starting from the Andronov Hopf theorem, we analyze the stability and we also apply methods to predict the amplitude.

Bifurcation analysis of on-chip LC VCOs

. Electrical oscillators play a decisive role in integrated transceivers for wired and wireless communication systems. In this context the study of fully integrated differential VCOs has received attention. In this paper formulas for investigations of the stability as well as the amplitude of CMOS LC tank oscillators are derived, where an overall model of nonlinear gain elements is used. By means of these results we are able to present an improved design approach which gives a deeper insight into the functionality of LC tank VCOs.

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A design approach for integrated CMOS LC-tank oscillators using bifurcation analysis

In this paper we present an analytic methodology for the analysis of a class of electrical harmonic oscillators. We combine geometric methods with the theory of singularly perturbed systems, which we use as tool for reduced order modeling. So we are able to define an easy to use formula in order to reduce an oscillatory system to center manifold. Thus we get a model for the start-up behavior as well as for the steady-state oscillation of sinusoidal oscillators. Furthermore, we demonstrate our technique by means of the Clapp oscillator which is an important member of the Colpitts, Clapp and Pierce oscillator family.

On the Start-Up Behavior and Steady-State Oscillation of Singularly Perturbed Harmonic Oscillators

Emitter-coupled multivibrators play a decisive role in electrical engineering, especially for phase locked loops which are key-building blocks of analogue RF front-ends. Since multivibrators correspond to relaxation oscillators, in the following the modelling and analysis by the theory of singularly perturbed systems is presented. Models for fast and slow phenomena are derived, and the fast transients of emitter-coupled multivibrators are analysed for the first time. The results of our analysis lead to significant advantages for the design of electrical multivibrators.

https://www.tandfonline.com/doi/pdf/10.1080/13873950701379888

Analysis of emitter-coupled multivibrators by singularly perturbed systems

Fully integrated LC tank oscillators are widely used because they are able to fulfil the increasing requirements in the field of RF applications. In this paper formulas for investigations of the stability as well as the amplitude of CMOS LC tank oscillators are derived, where an overall model of nonlinear gain elements is used. By means of these results we are able to present an improved design approach which gives a deeper insight into the functionality of LC tank VCOs.

M. Prochaska

Papers

Bifurcation analysis of on-chip LC VCOs

A design approach for integrated CMOS LC-tank oscillators using bifurcation analysis

On the Start-Up Behavior and Steady-State Oscillation of Singularly Perturbed Harmonic Oscillators

Analysis of emitter-coupled multivibrators by singularly perturbed systems

An improved design approach for LC tank VCOs