Phase-shift Oscillator Research Articles

Fractional-order sinusoidal oscillators: Design procedure and practical examples

Sinusoidal oscillators are known to be realized using dynamical systems of second-order or higher. Here we derive the Barhkausen condition for a linear noninteger-order (fractional-order) dynamical system to oscillate. We show that the oscillation condition and oscillation frequency of some famous integer-order sinusoidal oscillators can be obtained as special cases from general equations governing their fractional-order counterparts. Examples including fractional-order Wien oscillators, Colpitts oscillator, phase-shift oscillator and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LC</i> tank resonator are given supported by numerical and PSpice simulations.

Amplitude and Frequency Control: Stability of Limit Cycles in Phase-Shift and Twin-T Oscillators

We show a technique for external direct current (DC) control of the amplitudes of limit cycles both in the Phase-shift and Twin-T oscillators. We have found that amplitudes of the oscillator output voltage depend on the DC control voltage. By varying the total impedance of each oscillator oscillatory network, frequencies of oscillations are controlled using potentiometers. The main advantage of the proposed circuits is that both the amplitude and frequency of the waveforms generated can be independently controlled. Analytical, numerical, and experimental methods are used to determine the boundaries of the states of the oscillators. Equilibrium points, stable limit cycles, and divergent states are found. Analytical results are compared with the numerical and experimental solutions, and a good agreement is obtained.

An AGC Circuit Design for a Variable-Frequency Sinusoidal Oscillator with Wide Frequency Range and Low Distortion Level

An up-down counter, multiplier, digital-to-analog (D/A) converter, and high-speed comparators are employed to achieve an automatic gain control (AGC) circuit, which corrects the pair of characteristic roots of the overall system automatically to the imaginary axis of the complex frequency plane. A negative feedback technique with digital hardware is applied on the loop gain control. No lowpass filter is needed to detect the oscillation amplitude. Thus, this technique is suitable for sinusoidal oscillators with a wide oscillation frequency range. Wien-bridge and phase-shift oscillators with an oscillation frequency range from 17 Hz to 1 MHz are tested with the proposed AGC circuit. The total harmonic distortions of the Wien-bridge sinusoidal oscillator with the proposed AGC circuit are verified to be very small. An application to a variable-frequency sinusoidal oscillator is also described. The experimental results demonstrate the static characteristics and dynamic responses of the overall system.

A voltage‐controlled cmos phase‐shift oscillator for short‐range wireless communications

AbstractThis paper presents a voltage‐controlled CMOS phase‐shift oscillator which can output a sinusoidal signal with a simple circuit configuration requiring no on‐chip inductor, which is intended for use in short‐range wireless communications such as a chip‐to‐chip wireless communications interface. A CMOS phase‐shift oscillator is experimentally fabricated by a 0.6‐µm CMOS process, with an oscillation frequency of approximately 600 MHz. Characteristics such as harmonics, the tuning range of the oscillation frequency, and phase noise are examined, and it is found that the proposed voltage‐controlled CMOS phase‐shift oscillator can be used in short‐range wireless communications, thus drastically reducing the circuit size. © 2003 Wiley Periodicals, Inc. Electron Comm Jpn Pt 2, 86(9): 24–30, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjb.10080

A bifurcation of a synchronous oscillations into a torus in a system of two mutually inhibitory aVLSI neurons: experimental observation

We studied a system of two ‘identical’ oscillatory aVLSI neurons with mutually inhibitory connections. The system demonstrates different oscillatory behaviors depending on the strength of the inhibitory connections: anti-phasic, synchronous, phase-shifted, and quasiperiodic oscillations. We experimentally observed a bifurcation of synchronous oscillations into quasiperiodic oscillations with two independent frequencies. This bifurcation was confirmed by the analysis of the phase between neuronal outputs, the cross-correlation function, the amplitude spectrum, and the correlation dimension. The observation of this bifurcation in a physical system suggests that this scenario might also occur in living half-center oscillators, such as those found in central pattern generators.

Oscillatory clusters in a model of the photosensitive belousov-zhabotinsky reaction system with global feedback

Oscillatory cluster patterns are studied numerically in a reaction-diffusion model of the photosensitive Belousov-Zhabotinsky reaction supplemented with a global negative feedback. In one- and two-dimensional systems, families of cluster patterns arise for intermediate values of the feedback strength. These patterns consist of spatial domains of phase-shifted oscillations. The phase of the oscillations is nearly constant for all points within a domain. Two-phase clusters display antiphase oscillations; three-phase clusters contain three sets of domains with a phase shift equal to one-third of the period of the local oscillation. Border (nodal) lines between domains for two-phase clusters become stationary after a transient period, while borders drift in the case of three-phase clusters. We study the evolving border movement of the clusters, which, in most cases, leads to phase balance, i.e., equal areas of the different phase domains. Border curling of three-phase clusters results in formation of spiral clusters-a combination of a fast oscillating cluster with a slow spiraling movement of the domain border. At higher feedback coefficient, irregular cluster patterns arise, consisting of domains that change their shape and position in an irregular manner. Localized irregular and regular clusters arise for parameters close to the boundary between the oscillatory region and the reduced steady state region of the phase space.

Frequency counting interrogation techniques applied to gas sensor arrays

This paper presents a simple, elegant interrogation technique for conducting polymer gas sensor arrays which takes advantage of their resistive and capacitive properties. To accomplish this, a four-channel Wien bridge oscillator system has been designed and constructed in which the conducting polymer sensor forms one of the arms of the bridge circuit. As gas or odour molecules adsorb and desorb from the sensor surface, the resistance and capacitance changes cause a consequent change in the Wien bridge oscillator frequency which is readily measured. Results of experiments using several volatile species are reported herein. Methods of improving the sensitivity of the oscillator-based approach have also been investigated and preliminary results of these investigations are also reported. The approach that has been adopted is applicable to any other form of sensor where the electrical properties change in response to a stimulus. Many other forms of phase shift oscillator can also be employed.

Frequency-modulation type magnetic field sensor using transmission-line magnetic device

A novel frequency-modulation type magnetic field sensor composed of transmission-line magnetic device and phase-shift type oscillator has been developed. The transmission line magnetic device consists of soft magnetic layers, dielectric layers and conductor lines, which operate as a distributed constant circuit. The transmission characteristics such as voltage-gain and phase are influenced by permeability change due to the external magnetic field applied to the magnetic layer. A transmission-line device developed by using Co based amorphous ribbon was used in the feedback circuit of a phase-shift type oscillator. The oscillation frequency of the oscillator increased with increasing magnetic field.

Current-mode oscillators using single output current conveyors

It is shown that the voltage-mode oscillators employing noninverting or inverting voltage controlled voltage sources can be transformed directly to current-mode oscillators by element replacement technique and using composite current conveyors. Examples of the Wien oscillator and the phase shift oscillator together with PSpice simulation results are included.

A gene that resuscitates a theory—somitogenesis and a molecular oscillator

A gene that resuscitates a theory—somitogenesis and a molecular oscillator

A method to reduce the frequency fluctuation in a phase-shift transistor oscillator

The frequency and current fluctuations, and their correlation were measured in a phase shift transistor oscillator. The spectra are of 1/f type and both are correlated. A demonstration was carried out to reduce the frequency fluctuation, and a useful method to reduce the fluctuation is proposed in an oscillator.

Vertical signal flow and oscillations in a three-layer model of the cortex.

A model of vertical signal flow across a layered cortical structure is presented and analyzed. Neurons communicate through spikes, which evoke an excitatory or inhibitory postsynaptic potential (spike response model). The layers incorporate two anatomical features-dendritic and axonal arborization patterns and distance-dependent time delays. The vertical signal flow through the network is discussed for various stimulus conditions using two different, but typical, axonal arborization patterns. We find stationary as well as oscillatory response, but the oscillatory response may be restricted to a single layer. Confronted with conflicting stimuli the network separates the patterns through phase-shifted oscillations. We also discuss two hypothetical animals, to be called "cat" and "mouse." These have different axonal arborizations, which give rise to a different oscillatory response (if any) of the various layers.

Digital ultrafast carrier recovery for interactive transmission systems

An ultrafast, all-digital method for phase synchronization and coherent carrier recovery is presented for time division multiple access (TDMA) and code division multiple access (CDMA) burst data communication systems. A new adaptive phase tracking (APT) method, presented and analyzed in this paper, uses a hard-limited IF signal in a feed forward configuration for carrier phase detection and recovery. A novel new technique of phase window filtering is presented as a means to combat noise induced phase errors, and improved the performance of a digital controlled phase shift oscillator by 7 dB. Experimental measurements show APT provides robust bit error rate (BER) performance within 1 dB of the theoretical binary phase shift keyed (BPSK) and tenths of dBs of an ideal hard wired clock. APT achieves acquisition within one- to four-bits-5 to 10 times faster than present requirements. A low power, low cost single chip fast carrier synchronization and demodulation solution for QPSK, GMSK and GSM compatible OQPSK and Feher's quadrature phase shift keyed (FQPSK) and binary phase shift keyed (FBPSK) systems are also presented.

Partial conservativity and its applications to multiphase oscillators and other oscillators

The well-known Barkhausen Criterion deals with designing oscillators which can be regarded either as “partially conservative” or as (“fully”) conservative. The present paper develops the concept of partial conservativity and shows how to distinguish between the two types of systems. It demonstrates that the concept is on the one hand related to practical aspects of well-established oscillators (phase-shift oscillator, and Colpitts and Hartley oscillators). On the other hand, the concept is helpful in developing new types of multiphase oscillators with potential practical advantages for power electronics and for feeding phased array antennae.

For the record: Kilby and the IC

The records that Jack Kilby, developer of the monolithic integrated circuit, kept of his progress 30 years ago are examined. His was a demonstration of the first working semiconductor integrated circuit, a phase-shift oscillator. This showed that the IC concept was applicable to linear circuits. >

The loop-gain modulator: A new class of linear amplitude modulators

A new type of class A modulator is introduced. This circuit, called the loop-gain modulator, exhibits a high degree of modulation linearity even for an index of modulation approaching unity. The concept is based on modifying the loop-gain of an oscillator with the modulating voltage. An analysis is done for the RC phase shift oscillator, although the method can be used with any oscillator. Experimental results that verify this analysis are reported.

Steady state analysis of oscillatory circuits with harmonic components by volterra series

AbstractChua and Tang reported a method based on the Volterra series to find the amplitude and frequency of the unknown fundamental wave component of a steady‐state oscillation resembling a sinusoidal wave generated in a self‐starting oscillation circuit. In the present paper, the method is used to find the higher‐order terms so that the harmonic components generated from the term related to the determination of the fundamental component can be found relatively easily. Formulas for the determination of such quantities are derived. Next, this method is used for the analysis of the van der Pol oscillator for which the detailed nature of the solution is available. The validity and the limitation of the application are studied. From the results, it is shown that reasonably accurate solutions can be derived for an oscillation waveform close to a sinusoid as well as a distorted one containing harmonic components. In this method there is no need to derive the differential equation for the oscillator. Insteady, only the algebraic equation found from the circuit diagram must be solved. Finally, this characteristic is used for analysis of an RC phase shift oscillator.

The distributed RC variable-frequency phase-shift oscillator

Methods of realising the voltage-controlled variable-frequency distributed RC phase-shift oscillator in integrated form are considered. A metal-oxide-semiconductor capacitor structure in which the metal is a nichrome resistor is specified. Two methods of varying the oscillation frequency are considered. The first uses the voltage-variable capacitance of the MOS structure. A simplified theory predicts the transfer characteristics well. The available frequency range as an oscillator is small because of the limited capacitance range of the devices used. However a frequency-voltage characteristic linear to better than 0.05% from 4.85 MHz to 5.1 MHz is observed. A very much wider frequency range is expected with improved devices. A second method of varying oscillation frequency uses a shunt varactor diode. The theory presented gives good agreement with measurements of transfer characteristics and predicts an attenuation near to 21 dB at 180° phase shift over a useful frequency range. This is also confirmed experimentally. The performance as an oscillator is limited in frequency by the non-ideal amplifiers used.

The distributed RC variable-frequency phase-shift oscillator : C. A. Miller and D. L. Waller. Microelectron. Reliab.17, 457 (1978)

The distributed RC variable-frequency phase-shift oscillator : C. A. Miller and D. L. Waller. Microelectron. Reliab.17, 457 (1978)

Analysis of biochemical phase shift oscillators by a harmonic balancing technique.

The use of harmonic balancing techniques for theoretically investigating a large class of biochemical phase shift oscillators is outlined and the accuracy of this approximate technique for large dimension nonlinear chemical systems is considered. It is concluded that for the equations under study these techniques can be successfully employed to both find periodic solutions and to indicate those cases which can not oscillate. The technique is a general one and it is possible to state a step by step procedure for its application. It has a substantial advantage in producing results which are immediately valid for arbitrary dimension. As the accuracy of the method increases with dimension, it complements classical small dimension methods. The results obtained by harmonic balancing analysis are compared with those obtained by studying the local stability properties of the singular points of the differential equation. A general theorem is derived which identifies those special cases where the results of first order harmonic balancing are identical to those of local stability analysis, and a necessary condition for this equivalence is derived. As a concrete example, the n-dimensional Goodwin oscillator is considered where p, the Hill coefficient of the feedback metabolite, is equal to three and four. It is shown that for p = 3 or 4 and n less than or equal to 4 the approximation indicates that it is impossible to construct a set of physically permissible reaction constants such that the system possesses a periodic solution. However for n greater than or equal to 5 it is always possible to find a large domain in the reaction constant space giving stable oscillations. A means of constructing such a parameter set is given. The results obtained here are compared with previously derived results for p = 1 and p = 2.