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This paper aims to find a closed-form expression for the frequency and amplitude of single-ended ring oscillators when transistors experience all regions.

In this paper, the analytical relationships presented for ring oscillator amplitude and frequency are approximately derived due to the nonlinear nature of this oscillator, taking into account the differential equation that governs the ring oscillator and its output waveform.

In the case where the transistors experience the cut-off region, the relationships presented so far have no connection between the frequency and the dimensions of the transistor, which is not valid in practice. The relationship is presented for the frequency, including the dimensions of the transistor. Also, a simple and approximately accurate relationship for the oscillator amplitude is provided in this case.

The validity of these relationships has been investigated by analyzing and simulating a single-ended oscillator in 0.18 µm technology.

The purpose of this paper is to find a closed relation for the phase noise of LC oscillators.

The governing equation of oscillators is generally a stochastic nonlinear differential equation. In this paper, a closed relation for the phase noise of LC oscillators was obtained by approximating the I–V characteristic of the oscillator with third-degree polynomials and analyzing its differential equation.

This relation expresses phase noise directly in terms of circuit parameters, including the sizes of the transistors and the bias. Next, for evaluation, the phase noise of the cross-coupled oscillator without tail current was calculated with the proposed model. In this approach, the obtained equations are expressed independently of technology by combining the obtained phase noise relation and g_m/I_D method.

A technology-independent method using the g_m/I_D method and the closed relationship is provided to calculate phase noise.

Biomedical radio frequency (RF) transceivers require miniaturized forms with long battery life and low power consumption. The medical implant communication service (MICS) band in the frequency range of 402–405 MHz is widely used for medical RF transceivers because the MICS band signals have reasonable propagation characteristics and are suited to achieve good results. The implementation of the RF front-end for medical devices has many challenges as these dictate low power consumption. In particular, phase-locked loop is one of the most critical blocks of the RF front-end. The purpose of this paper is to the design of controller-based all-digital phase-locked loop (ADPLL) in a 45 nm CMOS process.

Initially, an open-loop architecture phase frequency detector (PFD) is designed. Then based on the concept of differential buffer, a differential ring oscillator (RO) is built using capacitive boosting technique. After that, the frequency controller block is built by proper mathematical modeling that does the job of loop filter, which behaves like a phase interpolator. Frequency controller block has tuning register block, tuning word register. The tuning block is built using the Metal Oxide Semiconductor (MOS) caps. Finally, the integration of all the blocks is done and the ADPLL architecture that locks at 402 MHz is achieved.

The designed PFD is dead zone free that operates at 1 GHz. The differential RO oscillates at 495 MHz. The proposed ADPLL operates at 402 MHz with measured phase noise of −98.36 at 1-MHz offset. This ADPLL exhibits rms jitter of 4.626 ps with a total power consumption of 216.5 µW.

A time to digital converter (TDC)-less controller-based low power ADPLL covering the MICS frequency band for biomedical applications has been designed in 45 nm/0.68 V CMOS technology. The ADPLL proposed in this draft uses differential oscillator with capacitively boosted technique which reduced the operating voltage to as low as 0.68 V. This ADPLL has a bandwidth of 20 kHz and works at reference frequency of 20 MHz consumed power of 216.5 µW, while generating an output frequency of 402 MHz. The tuning range is from 375 to 428 MHz. With the phase noise of −98.36 dbc/Hz at 1 MHz, a frequency controller block replaces the usage of TDC.

The designed ADPLL will definitely pave way to greater research arena in the field of biomedical field. This ADPLL is a unique combination that combines electronics and biomedical field. The designed ADPLL is itself a broader application to biomedical field that will have a positive impact on the society.

The implementation of open-loop PFD and RO using the capacitive boosting technique is a unique combination. This is comprehended well with frequency controller block that eliminates the usage of TDC and behaves as phase interpolator. The entire design of ADPLL which suits the application of MICS band of frequency has been designed carefully to work at low power.

The primary aim of this paper is to present a novel design approach for a ring voltage-controlled oscillator (VCO) suitable for L-band applications, whose oscillation frequency is less sensitive to power supply variations. In a few decades, with the advancement of modern wireless communication equipment, there has been an increasing demand for low-power and robust communication systems for longer battery life. A sudden drop in power significantly affects the performance of the VCO. Supply insensitive circuit design is the backbone of uninterrupted VCO performance. Because of their important roles in a variety of applications, VCOs and phase locked loops (PLLs) have been the subject of significant research for decades. For a few decades, the VCO has been one of the major components used to provide a local frequency signal to the PLL.

First, this paper chose to present recent developments on implemented techniques of ring VCO design for various applications. A complementary metal oxide semiconductor (CMOS)-based supply compensation technique is presented, which aims to reduce the change in oscillation frequency with the supply. The proposed circuit is designed and simulated on Cadence Virtuoso in 0.18 µm CMOS process under 1.8 V power supply. Active differential configuration with a cross-coupled NMOS structure is designed, which eliminates losses and negates supply noise. The proposed VCO is designed for excellent performance in many areas, including the L-band microwave frequency range, supply sensitivity, occupied area, power consumption and phase noise.

This work provides the complete design aspect of a novel ring VCO design for the L-band frequency range, low phase noise, low occupied area and low power applications. The maximum value of the supply sensitivity for the proposed ring VCO is 1.31, which is achieved by changing the VDD by ±0.5%. A tuning frequency range of 1.47–1.81 GHz is achieved, which falls within the L-band frequency range. This frequency range is achieved by varying the control voltage from 0.0 to 0.8 V, which shows that the proposed ring VCO is also suitable for low voltage regions. The total power consumed by the proposed ring VCO is 14.70 mW, a remarkably low value using this large transistor count. The achievable value of phase noise is −88.76 dBc/Hz @ 1 MHz offset frequency, which is a relatively small value. The performance of the proposed ring VCO is also evaluated by the figure of merit, achieving −163.13 dBc/Hz, which assures the specificity of the proposed design. The process and temperature variation simulations also validate the proposed design. The proposed oscillator occupied an extremely small area of only 0.00019 mm² compared to contemporary designs.

The proposed CMOS-based supply compensation method is a unique design with the size and other parameters of the components used. All the data and results obtained show its originality in comparison with other designs. The obtained results are preserved to the fullest extent.

The purpose of this paper is to investigate a more robust ring oscillator. Less sensitivity to power supply variations is a target. This is important since low-quality ring oscillators could be exploited in numerous systems to reduce die costs.

The method in this work is large signal analysis. Delay time as the large signal parameter is calculated symbolically to explore dependency on a power supply voltage. Then simulations are performed to make a comparison. In this work, mathematical justifications are verified via HSPICE circuit simulator outputs, while 0.18 µm TSMC CMOS technology is exploited.

At least two combined configurations are presented with higher robustness. These circuits are more appropriate in noisy conditions. Both theoretical calculations and simulation results verify less sensitive oscillation against supply voltage ripples and temperature variations.

Introducing a band-switched inverter in combined configurations is contribution. In this way, three structures are presented which both show higher stability in oscillation frequency. The band switched delay time calculations are quite new and also the validity of the symbolical delay time approach is verified by circuit simulations.

The purpose of this work in designing a wideband ring voltage-controlled oscillator (VCO) based on programmable current topology. It occupies a very tiny area yet achieving a good phase noise performance, which is suitable to be implemented in cost-effective and wideband frequency synthesizers.

The tuning range and gain are improved by dividing the VCO tuning curve into multiple curves controlled by programmable current sources without introducing additional parasitic capacitance.

Fabricated in 130-nm standard complementary metal oxide semiconductor technology and occupying an area of 0.079 mm², the VCO is tunable from 2.05 to 4.19 GHz, with a tuning percentage of 68.5 per cent. The VCO measures a phase noise performance of −96.7 dBc/Hz at an offset of 1 MHz from a 4.19 GHz carrier while consuming an average current of 6.5 mA, achieving figure of merit (FoM) and FoM_T of −158.9 and −175.6 dBc/Hz, respectively.

The proposed design uses programmable current topology without introducing parasitic capacitance, hence achieving wideband operation. It also occupies a tiny area and achieves a good phase noise performance.

Several ultra-low power and gigahertz current-starved voltage-controlled oscillator (CSVCO) circuits have been proposed and compared here. The presented structures are based on the three-stage hybrid circuit of the carbon nanotube field-effect transistors (CNTFETs) and low-power MOSFETs. The topologies exploit modified and compensated Schmitt trigger comparator parts to demonstrate better consumption power and frequency characteristics. The basic idea in the presented topologies is to compensate the Schmitt trigger comparator part of the basic CSVCO for achieving faster carrier mobility of the holes, reducing transistor leakage current and eliminating dummy transistors.

This study aims to propose and compare three different comparator-based VCOs that have been implemented using the CNTFETs. The considered circuits are shown to be capable of delivering the maximum 35 tuning frequency in the order of 1 GHz to 5 GHz. A major power thirsty part of the high-frequency ring VCOs is the Schmitt trigger stage. Here, several fast and low-power Schmitt trigger topologies are exploited to mitigate the dissipation power and enhance the oscillation frequency.

As a result of proposed modifications, more than one order of magnitude mitigation in the VCO power consumption with respect to the previously presented three-stage CSVCO is reported here. Thus, a VCO dissipation power of 3.5 µW at the frequency of 1.1 GHz and the tuning range of 26 per cent is observed for the well-established 32 nm technology and the supply voltage of 1 V. Such a low dissipation power is obtained around the operating frequency of the battery-powered cellular phones. In addition, using the p-carrier mobility compensation and enhancing the rise time of the Schmitt trigger part of the CSVCO, a maximum of 2.38 times higher oscillation frequency and 72 per cent wider tuning range with respect to Rahane and Kureshi (2017) are observed. Simultaneously, this topology exhibits an average of 20 per cent reduction in the power consumption.

Several new VCO topologies are presented here, and it is shown that they can significantly enhance the power dissipation of the GHz CSVCOs.

Multiphase and quadrature voltage-controlled oscillators (QVCOs) play key roles in modern communication systems and their phase noise performance affects the performance of the overall system. Different studies are devoted to efficient quadrature signals generation. This paper aims to present a new low-phase noise superharmonic injection-locked QVCO.

The proposed QVCO is comprised of two identical inductor-capacitor circuit (LC)-voltage-controlled oscillators (VCOs) in which second harmonics, with 180° phase shift, are injected from one core VCO to the gate of tail current source of the other VCO via a coupling capacitor. Using second harmonics with high amplitude will switch the tail from the inversion to the accumulation, and therefore, flicker noise is reduced. Also, because of the use of lossless and noiseless coupling elements, that is, coupling capacitors, and also because of the existence of an inherent high-pass filter, the proposed LC-QVCO has a good phase noise performance.

The introduced technique is designed and simulated in a commercial 0.18 µm radio frequency complementary metal oxide semiconductor (RF-CMOS) technology and 10 dB improvement of close-in phase noise is achieved (compared to the conventional method). Simulation results show that the phase noise of the proposed QVCO is −130.3 dBc/Hz at 3 MHz offset from 5.76 GHz center frequency, while the total direct current (DC) current drawn from a 0.9-V power supply is 4.25 mA (figure of merit = −190.2 dBc). Monte Carlo simulation results show that the figure of merit of the circuit has a Gaussian distribution with mean value and standard deviation of −189.97 dBc and 0.183, respectively.

This technique provides a new simple but efficient superharmonic coupling and noise shaping method that reduces close-in phase noise of superharmonic multiphase VCOs by switching of tail transistors with 2 ω0 (second harmonic of oscillation frequency). No extra devices such as area-consuming transformer or additional power-hungry oscillator are used for coupling.

The paper aims to present the novel design approach for a low power LC-voltage-controlled oscillators (VCO) design with low phase noise that too targeted at the most sought band of Bluetooth applications. Owing to their crucial role in a wide variety of modern applications, VCO and phase-locked loop (PLL) frequency synthesizers have been the subject of extensive research in recent years. In fact, VCO is one of the key components being used in a modern PLL to provide local frequency signal since a few decades. The complicated synthesizer requirements imposed by cellular phone applications have been a key driver for PLL research.

This paper first opted to present the recent developments on implemented techniques of LC-VCO designs in popular RF bands. An LC-VCO with a differential (cross-coupled) MOS structure is then presented which has aimed to compensate the losses of an on-chip inductor implemented in UMC’s 130 nm RF-CMOS process. The LC-VCO is finally targeted to embed onto the synthesizer chip, to address the narrowband (S-Band) applications where Bluetooth has been the most sought one. The stacked inductor topology has been adopted to get the benefit of its on-chip compatibility and low noise. The active differential architecture, which basically is a cross-coupled NMOS structure, has been then envisaged for the gain which counters the losses completely. Three major areas of LC-VCO design are considered and worked upon for the optimum design parameters, which includes Bluetooth coverage range of 2.410 GHz to 2.490 GHz, better linearity and high sensitivity and finally the most sought phase noise performance for an LC-VCO.

The work provides the complete design aspect of a novel LC-VCO design for low phase noise narrowband applications such as Bluetooth. Using tuned MOS varactor, in 130 nm-RF CMOS process, a high gain sensitivity of 194 MHz/Volt was obtained. Thus, the entire frequency range of 2415-2500 MHz for Bluetooth applications, supporting multiple standards from 3G to 5G, was covered by voltage tuning of 0.7-1.0 V. To achieve the low power dissipation, low bias (1.2 V) cross-coupled differential structure was adopted, which completely paid for the losses occurred in the LC resonator. The power dissipation comes out to be 8.56 mW which is a remarkably small value for such a high gain and low noise VCO. For the VCO frequencies in the presented LO-plan, the tank inductor was allowed to have a moderate value of inductance (8 nH), while maintaining a very high Q factor. The LC-VCO of the proposed LO-generator achieved extremely low phase noise of −140 dBc/Hz @ 1 MHz, as compared to the contemporary designs.

Though a professional tool for inductor and circuit design (ADS-by Keysight Technologies) has been chosen, actual inductor and circuit implementation on silicon may still lead to various parasitic evolutions; therefore, one must have that margin pre-considered while finalizing the design and testing it.

The proposed LC-VCO architecture presented in this work shows low phase noise and wide tuning range with high gain sensitivity in S-Band, low power dissipation and narrowband nature of wireless applications.

The on-chip stacked inductor has uniquely been designed with the provided dimensions and other parameters. Though active design is in a conventional manner, its sizing and bias current selection are unique. The pool of results obtained completely preserves the originally to the full extent.

The purpose of this paper is to design and implement a fully integrated low‐phase noise and large tuning range dual‐band LC voltage‐controlled oscillator (VCO) in 0.13 μm complementary metal oxide semiconductor (CMOS) technology.

Two parallel‐connected single‐band VCOs are designed to implement the proposed VCO. Adopting a simple and straight‐forward architecture, the dual‐band VCO is configured to operate at two frequency bands, which are from 1.48 GHz to 1.78 GHz and from 2.08 GHz to 2.45 GHz. A band selection circuit is designed to perform band selection process based on the controlling input signal.

The proposed VCO features phase noise of −104.7 dBc/Hz and −108.8 dBc/Hz at 1 MHz offset frequency for both low corner and high corner end of the low‐band operation. For high‐band operation, phase‐noise performance of −101.1 dBc/Hz and −110.4 dBc/Hz at 1 MHz offset frequency are achieved. The measured output power of the dual‐band VCO ranges from −8.4 dBm to −5.8 dBm and from −9.6 dBm to −8.0 dBm for low‐band and high‐band operation, respectively. It was also observed that the power differences between the fundamental spectrum and the nearby spurious tone range from −67.5 dBc to −47.7 dBc.

The paper is useful to both the academic and industrial fields since it promotes the concept of multi‐band or multi‐standard system which is currently in demand in the telecommunication industry.