A generalized family of memristor‐based voltage controlled relaxation oscillator

Recently, memristive oscillators are a significant topic in the nonlinear circuit theory where there is a possibility to build relaxation oscillators without existence of reactive elements. In this paper, a family of voltage‐controlled memristor‐based relaxation oscillator including two memristors is presented. The operation of two memristors‐based voltage relaxation oscillator circuits is demonstrated theoretically with the mathematical analysis and with numerical simulations. The generalized expressions for the oscillation frequency and conditions are derived for different cases, where a closed form is introduced for each case. The effect of changing the circuit parameters on the oscillation frequency and conditions is investigated numerically. In addition, the derived equations are verified using several transient PSPICE simulations. The power consumption of each oscillator is obtained numerically and compared with its PSPICE counterpart. Furthermore, controlling the memristive oscillator with a voltage grants the design an extra degree of freedom which increases the design flexibility. The nonlinear exponential model of memristor is employed to prove the oscillation concept. As an application, two examples of voltage‐controlled memristor‐based relaxation oscillator are provided to elaborate the effect of the reference voltage on the output voltage. This voltage‐controlled memristor‐based relaxation oscillator has nano size with storage property that makes it more efficient compared with the conventional one. It would be helpful in many communication applications.     

A family of memristor‐based reactance‐less oscillators

In this paper, we present for the first time a family of memristor‐based reactance‐less oscillators (MRLOs). The proposed oscillators require no reactive components, that is, inductors or capacitors, rather, the ‘resistance storage’ property of memristor is exploited to generate the oscillation. Different types of MRLO family are presented, and for each type, closed form expressions are derived for the oscillation condition, oscillation frequency, and range of oscillation. Derived equations are further verified using transient circuit simulations. A comparison between different MRLO types is also discussed. In addition, detailed fabrication steps of a memristor device and experimental results for the first MRLO physical realization are presented. Copyright © 2013 John Wiley & Sons, Ltd.     

Time‐domain analysis of phase‐noise and jitter in oscillators due to white and colored noise sources

This paper presents an original time‐domain analysis of the phase‐diffusion process, which occurs in oscillators due to the presence of white and colored noise sources. It is shown that the method supplies realistic quantitative predictions of phase‐noise and jitter and provides useful design‐oriented closed‐form expressions of such phenomena. Analytical expressions and numerical simulations are verified through measurements performed on a relaxation oscillator whose behavior is perturbed by externally controlled noise sources. Copyright © 2011 John Wiley & Sons, Ltd.     

Evaluation and comparison of GHz‐range LC oscillators using time‐varying root‐locus

This paper presents a comprehensive comparison between complementary metal‐oxide‐semiconductor (CMOS) LC‐oscillator topologies often used in GHz‐range transceivers. The comparison utilizes the time‐varying root‐locus (TVRL) method to add new insights into the operation of different oscillators. The paper focuses on the treatment of the TVRL trajectories obtained for different oscillators and establishes links between the trajectories and physical phenomena in oscillators. The evaluation of the root trajectories shows the advantages of the TVRL method for comparing oscillator topologies, which is also extended towards the analysis of voltage‐controlled oscillators. The necessary circuit simplifications required in closed‐form root‐locus analysis are avoided by the TVRL, which allows precise oscillator comparison and reveals details on the topology specifics. The derived conclusions have been verified by the Cadence Spectre‐RF simulator on 130‐nm CMOS process. Copyright © 2011 John Wiley & Sons, Ltd.     

Resistive‐less memcapacitor‐based relaxation oscillator

Recently, the realization of the conventional relaxation oscillators was introduced based on memristors. This paper validates the concept using two series memcapacitors in general which is applicable for a capacitor and memcapacitor as well. Furthermore, the necessary conditions for oscillation are introduced, and a generalized closed‐form expression for the oscillation frequency is derived. Two special cases are introduced and verified using PSPICE simulations showing a perfect matching. Copyright © 2014 John Wiley & Sons, Ltd.     

Modelling and analysis of differential VCOs

We present a systematic non‐linear analysis of differential voltage controlled oscillators (VCOs), both bipolar and MOS. Using the standard device models, we derive the second‐order non‐linear equation describing the behaviour of these oscillators, which is formulated in a perturbation form. The solution of this equation is obtained as a particular case of the solution of the most general equation of second‐order oscillators, which is solved through a suitable perturbation method. Unlike a pure numerical analysis, simple analytical relationships are derived for predicting the steady‐state oscillation, its transient behaviour and for ascertaining the existence of a stable oscillation in differential VCOs. These relationships, leading to results which well agree with the SPICE simulations, are useful in both analysis and design. Copyright © 2004 John Wiley & Sons, Ltd.     

Phase noise characterization of subharmonic injection locked oscillators

In this work we present a detailed study of the phase noise of subharmonic injection locked oscillators (s‐ILOs). A new simple and efficient model has been presented for accurately predicting the phase noise of a microwave s‐ILO. The validity of the analytical technique is verified with measurement results obtained from a 5‐GHz fully differential Colpitts‐based s‐ILO. The results showed that a phase noise improvement of 12 dB at 1 kHz offset frequency compared to the free‐running case can be achieved, whereas the power consumption is 21 mW. Copyright © 2010 John Wiley & Sons, Ltd.     

Mode dynamics in fourth‐order LC oscillators

We present a complete analysis of single and concurrent modes in fourth‐order LC‐voltage‐controlled oscillators ( VCOs), which are increasingly applied in dual‐band communication systems. We give a procedure based on the averaging method that simplifies the derivation of the abridged equations, which are derived without resorting to a change of co‐ordinates. The amplitudes of the oscillatory modes in steady state and in transient are found in explicit form. Conditions for the stability of the single and concurrent modes are derived, which apply to any active one‐port dual‐band LC‐VCO and allow one to predict the nonlinearities ensuring the occurrence of a stable concurrent mode. Numerical and experimental results show a good accuracy of the presented formulas. Copyright © 2016 John Wiley & Sons, Ltd.     

New structures of four‐phase oscillators obtained by strongly interweaving mono‐phase limit‐cycle oscillators

The present work is a part of our effort of developing multiphase oscillators. The particular system dealt with here is that of strongly nonlinearly coupled four oscillators that form a multiphase source. Such sources possess potential applications in power electronics, in phased‐array antennas, and in modern methods of modulation and especially in demodulating multi‐phased modulated signals. The present system can be interpreted as embracing four two‐phase oscillators. Nevertheless, as a result of the strong coupling, the second state equation of each oscillator merges with the first equation of the following oscillator. The resulted four‐phase source is, therefore, represented by merely four state equations. The applications related to communications (especially those related to receivers) may be susceptible to the noise performance of the source. We believe that the presently suggested system, which relies on strong coupling of oscillators, is advantageous in its noise performance in comparison to more straightforward recently described multiphase sources, which incorporate loosely coupled oscillators. Copyright © 2007 John Wiley & Sons, Ltd.     

Experimental comparison of phase‐noise in cross‐coupled RC‐ and LC‐oscillators

Relaxation RC‐oscillators are notorious for their poor phase‐noise performance. However, there are reasons to expect a phase‐noise reduction in quadrature oscillators obtained by cross‐coupling two relaxation oscillators. We present measurements on 5 GHz oscillators, which show that in RC‐oscillators the coupling reduces both the phase‐noise and quadrature error, whereas in LC‐oscillators the coupling reduces the quadrature error, but increases the phase‐noise. A comparison using standard figures of merit indicates that quadrature RC‐oscillators may be a viable alternative to LC‐oscillators when area and cost are to be minimized. Copyright © 2009 John Wiley & Sons, Ltd.     

Design equations for fractional‐order sinusoidal oscillators: Four practical circuit examples

Four practical sinusoidal oscillators are studied in the general form where fractional‐order energy storage elements are considered. A fractional‐order element is one whose complex impedance is given by Z = a(jω)^±α, where a is a constant and α is not necessarily an integer. As a result, these oscillators are described by sets of fractional‐order differential equations. The integer‐order oscillation condition and oscillation frequency formulae are verified as special cases. Numerical and PSpice simulation results are given. Experimental results are also reported for a selected Wien‐bridge oscillator. Copyright © 2007 John Wiley & Sons, Ltd.     

Floquet theory and non‐linear perturbation analysis for oscillators with differential‐algebraic equations

Oscillators are key components of electronic systems. In RF communication systems, they are used for frequency translation of information signals and for channel selection, and in digital electronic systems, they are used as a time reference, i.e. a clock signal, in order to synchronize operations. Undesired perturbations in practical electronic systems adversely affect the spectral and timing properties of oscillators, which is a key performance limiting factor, being a major contributor to bit‐error‐rate (BER) of RF communication systems, and creating synchronization problems in clocked and sampled‐data systems. Characterizing how perturbations affect oscillators is therefore crucial for practical applications. The traditional approach to analysing perturbed nonlinear systems (i.e. linearization) is not valid for oscillators. In this paper, we present a theory and efficient numerical methods, for non‐linear perturbation and noise analysis of oscillators described by a system of differential‐algebraic equations (DAEs). Our techniques can be used in characterizing phase noise and timing jitter due to intrinsic noise in IC devices, and evaluating the effect of substrate and supply noise on the timing properties of practical oscillators. In this paper, we also establish novel results for periodically time‐varying systems of linear DAEs, which we rely on in developing the above theory and the numerical methods. Copyright © 2000 John Wiley & Sons, Ltd.     

An inductorless CMOS quadrature oscillator continuously tuneable from 3.1 to 10.6 GHz

Modern RF front‐ends require wide tuning‐range oscillators with quadrature outputs. In this paper we present a two‐integrator quadrature oscillator, which covers the whole bandwidth of UWB applications. A circuit prototype in a 130 nm CMOS technology is continuously tuneable from 3.1 to 10.6 GHz. The circuit die area is less than 0.013mm², leading to a figure‐of‐merit FOMA of ?176.7dBc/Hz at the upper frequency. The supply voltage is 1.2 V, and the power consumption is 7 mW at the lower frequency and 13 mW at the upper frequency. Copyright © 2010 John Wiley & Sons, Ltd.     

Analysis and design of LC oscillators associated with frequency multipliers: a phase noise perspective

When a local oscillator signal generation system is based on an LC oscillator and a frequency multiplier, the question of determining the optimal multiplication factor is a key issue. In this paper, the problem is addressed in order to minimize the 1/f ² phase noise within a tuning range constraint. The analysis, with a practical graphical representation, reveals the oscillator phase noise dependence on the oscillating frequency in the transition from two different regimes, named the inductor‐limited quality factor and the capacitor‐limited quality factor. The results obtained enable the evaluation of the phase noise performance of systems based on a sub‐harmonic and super‐harmonic oscillators and how they compare with an oscillator in the fundamental mode. Crucial questions like the phase noise improvement that these systems can achieve are analytically answered. A design methodology is thus proposed and verified through measurements on a frequency source at 31 GHz, composed by a sub‐harmonic voltage‐controlled oscillator followed by an injection‐locked frequency tripler, dedicated to backhauling applications, designed on a BiCMOS process technology. The tuning range is 10%, and the phase noise at a 1‐MHz offset is −112 dBc/Hz. Copyright © 2017 John Wiley & Sons, Ltd.     

Evaluating the spectrum of periodic pulling in subharmonic resonant LC circuits

We analyze the features of the oscillations arising in forced inductor–capacitor (LC) oscillators when they operate in the periodic pulling mode, under the action of a weak injection signal. In radio frequency integrated circuits, both voltage‐controlled oscillators subject to undesired couplings and injection‐locked frequency dividers behave like forced LC oscillators. These are modeled as second‐order driven oscillators working in the subharmonic (secondary) resonance regime. The analysis is based on the generalized Adler's equation, which we introduce to describe the phase dynamics of dividers of any division ratio and to derive closed‐form expressions for the spectrum components of the system's oscillatory response. We show that the spectrum is double‐sided and asymmetric, unlike the single‐sided spectrum of systems with primary resonance. Numerical and experimental results are given to validate the presented results, which significantly generalize those available in the literature. Copyright © 2014 John Wiley & Sons, Ltd.     

Memristor‐based voltage‐controlled relaxation oscillators

This paper introduces two voltage‐controlled memristor‐based reactance‐less oscillators with analytical and circuit simulations. Two different topologies which are R‐M and M‐R are discussed as a function of the reference voltage where the generalized formulas of the oscillation frequency and conditions for oscillation for each topology are derived. The effect of the reference voltage on the circuit performance is studied and validated through different examples using PSpice simulations. A memristor‐based voltage‐controlled oscillator (VCO) is introduced as an application for the proposed circuits which is nano‐size and more efficient compared to the conventional VCOs. Copyright © 2013 John Wiley & Sons, Ltd.     

All‐pass sections with rich cascadability and IC realization suitability

In this paper, two new circuit configurations for realizing voltage‐mode (VM) all‐pass sections (APSs) are presented. The proposed circuits employ only two differential voltage current conveyors (DVCCs) and are cascadable with other VM circuits due to their high‐input and low‐output impedances. The first configuration uses a grounded resistor and a grounded capacitor without requiring matching constraints, whereas the second employs two grounded resistors and a grounded capacitor with a single matching condition. While the first configuration can realize only one all‐pass response, the second can provide inverting and non‐inverting all‐pass responses with selection of appropriate input port. Adding two grounded resistors to the proposed filters, variable gain APSs can also be obtained. As applications, two quadrature oscillators, each of which using one of the proposed all‐pass circuits, one grounded resistor and one grounded capacitor are presented. SPICE simulation results are included to verify the theory. Copyright © 2010 John Wiley & Sons, Ltd.     

Low‐power quadrature generators for body area network applications

This paper presents different alternatives for the implementation of low‐power monolithic oscillators for wireless body area networks and describes the design of two quadrature generators operating in the 2.4‐GHz frequency range. Both implementations have been designed in a 90‐nm Complementary Metal‐Oxide Semiconductor (CMOS) technology and operate at 1 V of supply voltage. The first architecture uses a voltage‐controlled oscillator (VCO) running at twice the desired output frequency followed by a divider‐by‐2 circuit. It experimentally consumes 335 μW and achieves a phase noise of ?110.2 dBc/Hz at 1 MHz. The second architecture is a quadrature VCO that uses reinforced concrete phase shifters in the coupling path for phase noise improvement. Its power consumption is only 210 μW, and it obtains a phase noise of ?111.9 dBc/Hz at 1 MHz. Copyright © 2011 John Wiley & Sons, Ltd.     

Optimum design of high power and high efficiency mm‐wave fundamental oscillators

A systematic method to design high power and high efficiency mm‐wave fundamental oscillators is presented. By using a linear time variant method, we first obtain the optimum conditions and show that these conditions can be significantly different for high power and high efficiency fundamental oscillation. Next, we propose a modified multistage ring oscillator with interstage passive networks to exploit the full capacity of the transistors in terms of output power or efficiency. Analytical expressions are also derived to determine the value of passive elements used in the oscillator. To verify the validity of the method, a 77‐GHz two‐stage (differential) VCO is designed in a 65‐nm CMOS process. Careful electromagnetic and circuit simulations demonstrate that the designed VCO has 2‐GHz tuning range, maximum output power of 10.5 dBm and maximum DC to RF efficiency of 24.1%. The designed VCO shows 54.8% and 108.7% improvement in terms of maximum output power and efficiency compared with a conventional cross‐coupled VCO with the same tuning range.     

Analytical multi‐parametric stability boundaries of DC‐DC buck converters under V1 control concept

Two main methods for controlling switching converters exist in the literature. The direct one is the voltage mode control, which suffers from some disadvantages such as slow response to load variations and an input voltage‐dependent total loop gain. The current mode control can overcome these problems but at the expense of extra cost and more complex control design. V¹ concept is a new promising control technique for designing voltage mode control of buck‐type converters with an optimal response similar to current mode control. In this paper, the dynamics and the stability of buck converters under V¹ control are studied. In particular, subharmonic oscillation limits in the parameter space are addressed. First, a closed‐loop state‐space model is derived and then used to formulate an analytical matrix‐form expression for predicting the stability limit of the system. Using this expression, multi‐parametric stability boundaries are obtained. It is shown that the equivalent series inductance of the output capacitor can narrow the stability region. It is also demonstrated that the integral action in the feedback loop of a V¹‐controlled buck converter has a negligible effect on the subharmonic oscillation boundary. The theoretical analysis is validated through numerical simulation of the circuit‐level switched model of the system. Copyright © 2017 John Wiley & Sons, Ltd.