Rotary Traveling Wave Oscillator Research Articles

Automatic phase error compensation of rotary traveling wave oscillator: Analysis and design

Automatic phase error compensation of rotary traveling wave oscillator: Analysis and design

A 19.1–25.5-GHz Compact Dual-Mode Rotary Traveling-Wave Oscillator With 195.4-dBc/Hz FoM

In this letter, a dual-mode rotary traveling-wave oscillator (RTWO) is proposed to achieve wide operation bandwidth and multiple phases. Two twisted differential transmission lines are coupled together to form the dual-mode traveling-wave resonator. Sixteen pairs of back-to-back inverters and capacitors are connected to the resonators to introduce the multicore multi-phase operation. The mode switches are used to control the coupling direction and select the desired mode without degrading the quality factor. Verified in a 40-nm CMOS process, the proposed dual-mode RTWO exhibits a dual-mode frequency range from 19.1 to 25.5 GHz with the core size of 0.08 mm <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$^{\textbf {2}}$ </tex-math></inline-formula> . The measured 10-MHz phase noise at 25.30 and 22.12 GHz is −129.6 and −131.5 dBc/Hz, respectively. The best FoM and FoMT are 186.2 and 195.4 dBc/Hz, respectively.

Degradation performance analysis and operation optimization of rotary-traveling wave oscillators for RF-CMOS applications

In this work, the impact of the parasitic effects caused by discontinuities on Resonant Rotary Traveling Wave Oscillators (RTWO) for RF-CMOS applications, is analyzed and modeled. By using experimental data in addition to the full wave representation, semi-empirical models are obtained for different discontinuities contained in an RTWO. Then, using the proposed models and 180 nm CMOS process parameters, an RTWO was designed with an operating frequency of 20 GHz, whilst the impact of the discontinuities was quantified in its output signal. The results show that the impact of the parasitic elements due to these discontinuities present a filtering effect leading to a distortion of the magnitude and number of harmonics in the output signal, with a reduction of 13.8% when the effects of the geometrical discontinuities were included. In order to mitigate the parasitic effects due to discontinuities, the use of topological (layout) methods in stack paths and the Möbius connection are proposed. Additionally, a process variation analysis was conducted and the results show that the operation frequency could vary in a range from 17.21 GHz to 18.91 GHz; while the output voltage could fluctuate between 1.17 V and 1.91 V depending on the process, bias voltage and temperature (PVT) conditions. These effects must be taken into account in the design of RTWOs to avoid inefficient tuning stages, especially for high frequency applications, and for advanced technologies where the impact of the analyzed discontinuities is increased.

A 190.3‐dBc/Hz FoM 16‐GHz rotary travelling‐wave oscillator with reliable direction control

This letter presents a rotary travelling-wave oscillator (RTWO) with reliable direction control in a standard 130 nm complementary metal–oxide–semiconductor (CMOS) technology. To achieve low phase noise (PN), and low power consumption, 16-stages customised transmission line segments are designed and simulated on electromagnetic tools. The PN is investigated through modelling the RTWO as multiple standing-wave oscillators. The proposed oscillator achieves 11.2% tuning range, 190.3 dBc/Hz figure-of-merit (FoM) at 1 MHz offset and 192.3 dBc/Hz FoM at 10 MHz offset with 5.8-mW power consumption from 16-GHz carrier.

A Distributed Stubs Technique to Mitigate Flicker Noise Upconversion in a mm-Wave Rotary Traveling-Wave Oscillator

A rotary traveling-wave oscillator (RTWO) has an ability to generate multiple phases at millimeter-wave (mmW) frequencies while achieving low phase noise (PN). Unfortunately, due to the practically unavoidable transmission line (TL) dispersion, which causes the higher-order harmonics to travel faster than the fundamental, RTWOs suffer from flicker noise upconversion. In this article, we propose a “distributed stubs” technique to mitigate this mechanism in which tuning capacitors placed on the TL stubs away from the maintaining amplifiers will slow down the travel speed of higher-order harmonics relative to the fundamental, thus lowering the phase shifts due to the TL dispersion. We further provide a comprehensive analysis of the flicker noise upconversion mechanism due to the TL dispersion. The proposed 26.2-30-GHz RTWO is implemented in 22-nm fully depleted silicon-on-insulator (FD-SOI) CMOS with eight differential phases. At 30 GHz, it achieves PN of -107.6 and -128.9 dBc/Hz at 1- and 10-MHz offsets, respectively. This translates into figures-of-merit (FoMs) of 184.2 and 185.4 dB, respectively, for a single phase. The proposed architecture consumes 20 mW from 0.8-V supply. It achieves a flicker PN corner of 180 kHz, which is an order-of-magnitude better than currently achievable by state-of-the-art mmW RTWOs.

A 32–42-GHz RTWO-Based Frequency Quadrupler Achieving &gt;37 dBc Harmonic Rejection in 22-nm FD-SOI

In this letter, we propose a 32-42-GHz frequency quadrupler that performs digital logic operations between four phase-shifted differential signals at one-fourth of the output frequency. The four phase-shifted signals are generated via a 10-GHz rotary traveling-wave oscillator (RTWO) and are symmetrically routed to the quadrupler using a CMOS buffered clock tree. The harmonic rejection ratio (HRR) is enhanced by employing a differential LC filter tuned at its output center frequency. The proposed frequency quadrupler is implemented in 22-nm FD-SOI CMOS. At 37 GHz, it produces an output power of -4 dBm with a 10% drain efficiency. It consumes 4 mW from 0.8-V supply and occupies a core area of 0.021 mm2. The worst-case HRR for fundamental, second, third, and fifth harmonics are 41.3, 48.6, 41.3, and 37.3 dBc, respectively.

Thermal and flicker phase noise analysis in rotary traveling‐wave oscillator

SummaryThis paper analyzes the thermally induced phase noise and the up‐conversion of flicker noise into phase noise of rotary traveling‐wave oscillator (RTWO). Based on the analyses, this paper extracts the closed‐form formulas for the thermal and flicker phase noise of the RTWO. This paper compares the theoretical results with appropriate simulations to evaluate the accuracy of the derived closed‐form formulas. Comparisons confirm the accuracy of the extracted phase noise formulas. By using the presented straightforward approach along with accurate phase noise formulas, the designers can understand the RTWO's design tradeoffs. Also, they can design the RTWO for a specific phase noise without needing lengthy simulations.

A 42/84-GHz multi-ring rotary traveling-wave oscillator design in 0.13-µm BiCMOS

A multi-ring rotary traveling-wave oscillator (RTWO) is presented. The oscillation frequency of the main RTWO ring is designed for 42-GHz with 2-GHz tunability. Multi-phase signals generated in the main RTWO ring drive doubler circuits to generate second harmonic signals. The transformer used in each doubler circuit produces differential signals that are injected into the outer ring. Differential signals in the secondary terminals of the transformers are combined by coupled co-planar strip-line to support traveling-wave in the second ring. Bi-CMOS 0.13-µm technology is used to design and implement the multi-ring RTWO circuit. The chip area is 0.585-mm2. Total power consumption is 68-mW. SiGe HBT has been preferred over nMOS transistors to implement the gain stages, frequency doublers and the buffer circuits due to high fT and fmax of the SiGe HBTs. The measured frequency of oscillation is 42.24-GHz and 84.48-GHz with 5.6% tuning range and output power is − 20 dBm and − 45 dBm respectively. Phase noise at the main RTWO ring is − 97.5 dBc/Hz at 10 MHz.

RotaSYN: Rotary Traveling Wave Oscillator SYNthesizer

A physical design methodology is presented to synchronize digital application specific integrated circuit (ASIC) designs by a resonant rotary clock network. One novelty of the proposed RotaSYN flow is that the ASIC products of RotaSYN can operate at previously unattainable (relatively) low-frequency ranges of hundreds of megahertz. The dynamic resonant frequency divider is used to implement the low-frequency operation; and low in comparison to the norm of gigahertz-range of operation for resonant clocking reported in this paper. In SPICE -based simulations, the efficacy of the proposed flow and novel algorithms in RotaSYN is demonstrated using performance metrics of the wirelength, skew, and power on international symposium on physical design-10 clock benchmark circuits. In addition, RotaSYN is compared to three publicly available industrial designs that include the ARM Cortex M0 against equivalent clocks generated with a traditional phase locked loop (PLL) and distributed with an industrial clock tree synthesis tool flow. The RotaSYN methodology is implemented at three different target frequencies of 880 MHz, 500 MHz, and 220 MHz for the industrial designs. SPICE simulations show an average of 29% power savings for the industrial designs overall, solely thanks to 66% power savings on the clock generation and distribution networks, operating at a frequency of 880 MHz on comparison to the PLL-based design with a clock tree synthesized with an industrial EDA tool.

A Phase Tunable Rotary Traveling Wave Oscillator: Analysis and Calibration

In this paper, a new phase error analysis is introduced for rotary traveling wave oscillators (RTWOs). Two new analytical approaches are used to extract closed-form equations for the RTWOs phase error arising from asymmetric resonator and inequality of negative transconductors. Derived equations show that the phase error can be cancelled and even controlled by adjusting the bias current of negative transconductors without any undesirable changing in oscillation frequency. This characteristic is then used for introducing a new phase error calibration method for RTWOs. This calibration method is not limited by the problems that limit the usage of the prior calibration technique. Our theoretical results are compared with accurate simulations to evaluate the validity of the proposed analysis and accuracy of the closed-form equations. Simulations have been done in 0. 18- $\mu$ m CMOS technology with a 1.8-V supply voltage. The evaluations show good agreement between analytical phase-error equations and simulation results. Also, appropriate simulations confirm the validity of the calibration method that is introduced in this paper.

Topology, Discontinuities and Dimension Effects on CMOS Rotary Traveling Wave Oscillators

Topology, Discontinuities and Dimension Effects on CMOS Rotary Traveling Wave Oscillators

Amplifier Innovations for Improvement of Rotary Traveling Wave Oscillators

Rotary traveling wave oscillators use a transmission line connected as a closed loop as their resonant element. This allows the use of spatial degrees of freedom, not available in typical L–C oscillator topologies, in the design of the amplifier needed to sustain the oscillating mode. Here, we present a novel amplifier design that takes advantage of this extra degree of freedom to improve performance of RTWOs in two ways. If no precautions are taken then the oscillation can start in either a clockwise or anti-clockwise direction. The Phased amplifier, introduced here, forces one direction of oscillation with a measured probability of reverse oscillation of less than 0.43 ppm with a confidence level of 99%. No reverse oscillations were observed in 107 trials. This is accomplished by adding additional phase-dependent degeneration transistors and phase shifting the various amplifier inputs by taking them from different locations on the transmission line. Additionally, this amplifier design reduces the phase noise by reducing the amplifier noise during the time that the oscillator is most sensitive to phase perturbation, resulting in a 1.2-dB reduction in phase noise measured 1 MHz from the peak and a 2.9-dB improvement in the figure of merit.

Analytical formulation of transient oscillation amplitude in rotary traveling wave oscillators

This paper presents an accurate analysis for deriving transient oscillation amplitude of Rotary Traveling Wave Oscillators (RTWOs) as a transmission-line based and high frequency circuit. The procedure of the paper is based on considering the nonlinear behavior of negative transconductors that are used for loss compensation of the transmission line. Finally, a closed-form expression for the time-domain amplitude of the RTWOs is obtained. The proposed useful and accurate expression could be used for designing the RTWOs for high performance-high speed systems. Also, it enables us to analyze and synthesize the oscillators with the desired transient behavior. This aspect of the RTWOs is not studied in previous works. The proposed theoretical results are then compared with accurate simulations. Simulations have been done in 0.18 μm CMOS technology with 1.8 V supply voltage. Results show less than 10% difference in steady state oscillation amplitude of theoretical expression and simulations. Considering the nonlinear equation of the RTWOs amplitude, complicated type of solving, simplifications and its numerical solution, the proposed derived expression has a good agreement with simulations.

Tuning of the Relative Phases of a Rotary Travelling Wave Oscillator

This letter describes the implementation and performance of a phase detector and algorithm combination used to tune the relative phases of an 18-GHz RTWO. Symmetrical XOR phase detectors are designed (20 GHz simulated operation), fabricated in a SiGe BiCMOS process and tested to resolve approximately 4 mV/° from 35° to 55° and approximately 5 mV/° from 80° to 100° at 12 GHz. Instances of this phase detector are used to measure the phase of nominal 45° differential transmission line sections of an 18-GHz RTWO. The phase alignment algorithm mitigates differences between these measurements by iteratively adjusting varactors placed differentially across the RTWO transmission line sections.

A 2-GHz Pulse Injection-Locked Rotary Traveling-Wave Oscillator

This paper proposes a scalable and efficient frequency multiplication technique that synthesizes a multi-phase clock with finely adjustable output taps. It uses a pulse injection locked rotary traveling-wave oscillator (RTWO) with switched capacitors and complementary varactor pairs to achieve a 1.7–2-GHz tuning range and to implement the fine phase adjustment. The worst case phase-tuning resolution is 0.36°. The design is implemented in IBM’s 130-nm CMOS technology, and consumes a total power of 28.4 mW. Locked to a clean 679-MHz reference, it has a phase-noise performance of $-{\text {132 dBc/Hz}}$ at 100-kHz offset from 2.039 GHz. It achieves 39-fs integrated root mean square (rms) jitter from 1 kHz to 40-MHz offset, for a ${\text {Jitter}}^{2} \ast {\text {Power Figure of Merit}}$ (FOM) of $-{\text {251 dB}}$ .

Frequency Domain Phase Shift Measurement Technique Applied to a Multiphase Rotary Travelling-Wave VCO

In this letter, the design of a multiphase 18.5 GHz Rotary Travelling-Wave Oscillator (RTWO) is presented. Lack of symmetry in such a structure can result in oscillation in a standing wave rather than the travelling wave mode. In order to determine the mode of the signal, before going through the time consuming steps of time domain phase shift measurement, we have proposed a preliminary phase shift measurement technique in the frequency domain for a high frequency RTWO. This new technique was verified against direct phase measurements for a multiphase RTWO fabricated in a 0.25 $\mu{\rm m}$ BiCMOS process with good agreement. In other measurements, the VCO achieved a tuning range of 1.1 GHz and output power of $-$ 5.3 ${\rm dBm}$ .

Low-Phase Noise Clock Distribution Network Using Rotary Traveling-Wave Oscillators and Built-In Self-Test Phase Tuning Technique

This brief describes a built-in self-test (BIST) technique used to verify and tune the timing integrity of a clock distribution system implemented with injection-locked rotary traveling-wave oscillators (RTWOs). The die is fabricated in a 130-nm CMOS process and occupies 4.4 mm $\times$ 2.25 mm and is limited by the outer diameter of the RTWOs, leaving internal space for other circuits. The BIST circuits take a chip area of only 0.025 $\hbox{mm}^{2}$ . The measured frequency tuning range of the RTWOs is from 1.7 to 2.0 GHz. The measured RTWO phase tuning range is 58.56 $^{\circ}$ with a worst case 0.34 $^{\circ}$ phase tuning resolution. The injection-locked clock multiplication and distribution network achieves a single-sideband integrated RMS jitter of 66.8 fs from 10-kHz to 40-MHz offset frequencies at 2.04-GHz output. The BIST circuit allows testing of the integrity of the clock distribution system at speed by determining if the system clock skew can be tolerated or needs adjustment. To the authors' knowledge, the implementation of this BIST technique to determine clock integrity of an injection-locked clock distribution network has not been explored previously.

Design of a 30 GHz rotary traveling wave oscillator with improved frequency tuning range in 0.18 μm CMOS technology

In this paper, the operation of rotary traveling wave oscillators is analyzed, the general oscillation condition is derived, and analytical formula for the oscillator loss is presented. Based on this analysis, switched transmission line is employed to extend the output frequency tuning range. Post-layout simulation shows a frequency tuning range of 3.1GHz in the vicinity of 30GHz. The proposed half-quadrature VCO exhibits a phase noise better than −102.2dBc/Hz at 1MHz offset frequency. The VCO provides an output power level ranging from −6 to −2.5dBm with drawing 15.2mA of dc current from a 1.8V power supply.

Rotary Traveling-Wave Oscillator With Differential Nonlinear Transmission Lines

A methodology for the harmonic-balance analysis and design of rotary-traveling wave oscillator is presented. Two different implementations are compared. The first one is the standard configuration based on a distributed transmission lines. The second one is a new configuration based on a differential nonlinear transmission line (NLTL), which enables the generation of square waveforms with reduced number of stages, while still maintaining the capability to produce multiphase signals. The possible coexistence of oscillation modes is investigated with a detailed bifurcation analysis versus practical parameters such as the device bias voltage. The phase-noise spectrum is predicted from the variance of the common phase deviation. The parameters that determine this variance are identified with the conversion-matrix approach. The two prototypes, based on a distributed transmission line and a differential NLTL, have been manufactured and characterized experimentally, obtaining very good agreement between simulations and measurements.

Analysis and Design of a 54 GHz Distributed “Hybrid” Wave Oscillator Array With Quadrature Outputs

An array of distributed oscillators for millimeter-wave phased arrays combines local oscillator (LO) generation and distribution, leading to a phase noise improvement proportional to the number of array elements. The unit “hybrid wave” oscillator (HWO) consists of a rotary traveling-wave oscillator with quadrature outputs, coupled to the other units through standing-wave oscillators. A phase noise analysis for distributed oscillators based on impulse-sensitivity functions (ISF) is introduced and applied to study the proposed oscillator and arrays of it. A standalone oscillator and a 4-elements array implemented in a 65 nm CMOS technology have a measured phase noise of -125 dBc/Hz and -131 dBc/Hz respectively at 10 MHz from the 52 GHz carrier. Each unit consumes 36 mW corresponding to a FoM of -183.7 dBc/Hz. The tuning range is from 51.9 to 56.5 GHz.