Phase Noise In LC Oscillators Research Articles

Closed-form and technology independent phase noise relation for LC oscillators

PurposeThe purpose of this paper is to find a closed relation for the phase noise of LC oscillators.Design/methodology/approachThe 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.FindingsThis 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 gm/ID method.Originality/valueA technology-independent method using the gm/ID method and the closed relationship is provided to calculate phase noise.

A Transformational Framework for Analysis of Phase Noise in LC Oscillators

Phase noise has become the single most critical factor to be addressed in the design of modern communication systems. Facing the challenging requirements of 5G cellular communication, our paper describes a new theoretical framework to calculate the phase noise of LC oscillators, relying on easy to implement closed form solutions for phase noise calculations. Using closed form phase noise solutions enables oscillator designers to easily implement multiple phase noise calculation options for a number of oscillator circuits, which would be very difficult to implement with the existing mathematically complex phase noise theories. The analytic methods of our theory rely on modeling all real oscillators as having non-ideal or latent behaviors in addition to their primary nature for generating a carrier wave operating at a single frequency with a single amplitude. It is a cascade of these non-ideal transformation processes that produce non-ideal oscillator outputs containing the phase noise sidebands. Enhanced qualitative and quantitative insights into oscillator phase noise performances are achieved by using this approach. We validate our methods by comparing their results with phase noise simulations carried out for a sample CMOS LC voltage-controlled oscillator in 90 nm RFCMOS process using SpectreRF simulator. The results for the oscillator's output 1/f2 thermal phase noise, 1/f noise upconversion into 1/f3 phase noise and the 1/f3 corner frequency of phase noise spectrum using our theory yields −136 dBc/Hz at 10 MHz offset, −21.3 dBc/Hz at 1 kHz offset and 2.6 MHz respectively. The corresponding values obtained with SpectreRF simulation are −135.9 dBc/Hz, −23.4 dBc/Hz and 2.1 MHz. The carrier frequency is 5.4 GHz with output power of 9.78 dBm.

A 170-GHz 23.7% Tuning-Range CMOS Injection-Locked LO Generator With Third-Harmonic Enhancement

This article proposes a harmonic-extraction technique to enhance the amplitude and the phase noise of LC oscillators at the third-harmonic frequency. By leveraging this technique, a cascaded subterahertz (sub-THz) injection-locked local oscillator (LO) generator is proposed, which consists of a fundamental voltage-controlled oscillator (VCO) and a millimeter-wave (mm-wave) injection-locked frequency multiplier (ILFM). Fabricated in a 65-nm CMOS process, the VCO prototype concurrently generates two output signals: the first output at the fundamental frequency from 17.1 to 21.7 GHz with a 10-MHz-offset phase noise from −120.6 to −126 dBc/Hz, the second output at the third-harmonic frequency from 51.3 to 65.1 GHz with a 10-MHz-offset phase noise of −116.3 dBc/Hz, and the third-harmonic output power of −19.1 dBm. The VCO prototype consumes 1.4 mW from a 0.3-V supply, resulting in an FoM from −186 to −189.6 dBc/Hz at the fundamental frequency. The sub-THz injection-locked LO generator achieves a frequency tuning range of 23.7% from 153.9 to 195.3 GHz with a 10-MHz-offset phase noise of −106.8 dBc/Hz and the output power of −14.6 dBm, and consumes 8.4 mW, which corresponds to an FoM of −181.2 dBc/Hz and an ${\mathrm {FoM}}_{T}$ of −188.7 dBc/Hz at 153.9 GHz.

Modeling the Impact of Phase Noise on the Performance of Crystal-Free Radios

We propose a crystal-free radio receiver exploiting a free-running oscillator as a local oscillator (LO) while simultaneously satisfying the 1% packet error rate (PER) specification of the IEEE 802.15.4 standard. This results in significant power savings for wireless communication in millimeter-scale microsystems targeting Internet of Things applications. A discrete time simulation method is presented that accurately captures the phase noise (PN) of a free-running oscillator used as an LO in a crystal-free radio receiver. This model is then used to quantify the impact of LO PN on the communication system performance of the IEEE 802.15.4 standard compliant receiver. It is found that the equivalent signal-to-noise ratio is limited to ~8 dB for a 75- ${\mu }\text{W}$ ring oscillator PN profile and to ~10 dB for a 240- ${\mu }\text{W}$ LC oscillator PN profile in an AWGN channel satisfying the standard’s 1% PER specification.

Design of LC Resonator for Low Phase Noise Oscillators

The effects of resonator topology on the phase noise of LC oscillators are studied in this paper. It is shown that there is a neglected factor that can considerably influence the phase noise behavior of the oscillator. We designate this factor as the Inductance Energy Factor (IEF), which directly depends on the topology of the resonator. It is shown that through proper design of the resonator for a better IEF, the oscillator phase noise can be improved. It is also shown that by modifying the resonator structure to improve IEF, the phase noise does not have to be constrained by the minimum realizable inductance and its maximum quality factor. Therefore, the power-phase noise trade-off remains effective beyond this point. In the following, a general method to design the resonator circuit by a so-called evolutionary modification of the conventional LC tank is given. Illustrated simulations further help to confirm that phase noise improvements of more than 10 dB can be readily achieved by judicious design of the resonator circuit.

An Analytic Circuit-Based Model for White and Flicker Phase Noise in <emphasis emphasistype="italic">LC</emphasis> Oscillators

A general circuit-based model of LC oscillator phase noise applicable to both white noise and 1/f noise is presented. Using the Kurokawa theory, differential equations governing the relationship between amplitude and phase noise at the tank are derived and solved. Closed form equations are obtained for the IEEE oscillator phase noise for both white and 1/f noise. These solutions introduce new parameters which take into account the correlation between the amplitude noise and phase noise and link them to the oscillator circuit operating point. These relations are then used to obtain the final expression for voltage noise power density across the output oscillator terminals assuming the noise can be modeled by stationary Gaussian processes. For white noise, general conditions under which the phase noise relaxes to closed-form Lorentzian spectra are derived for two practical limiting cases. Further, the buffer noise in oscillators is examined. The forward contribution of the buffer to the white noise floor for large offset frequency is expressed in terms of the buffer noise parameters. The backward contribution of the buffer to the 1/Delta f2 oscillator noise is also quantified. To model flicker noise, the Kurokawa theory is extended by modeling each 1 /f noise perturbation in the oscillator as a small-signal dc perturbation of the oscillator operating point. A trap-level model of flicker noise is used for the analysis. Conditions under which the resulting flicker noise relaxes to an 1/Delta f3 phase noise distribution are derived. The proposed model is then applied to a practical differential oscillator. A novel method of analysis, splitting the noise contribution of the various transistors into modes is introduced to calculate the Kurokawa noise parameters. The modes that contribute the most to white noise and flicker noise are identified. Further, the tail noise contribution is analyzed and shown to be mostly up-converted noise. The combined white and flicker noise model exhibits the presence of a number of corner frequencies whose values depend upon the relative strengths of the various noise components. The proposed model is compared with a popular harmonic balance simulator and a reasonable agreement is obtained in the respective range of validity of the simulator and theory. The analytical theory presented which relies on measurable circuit parameters provides valuable insight for oscillator performance optimization as is discussed in the paper.

A filtering technique to lower LC oscillator phase noise

Based on a physical understanding of phase-noise mechanisms, a passive LC filter is found to lower the phase-noise factor in a differential oscillator to its fundamental minimum. Three fully integrated LC voltage-controlled oscillators (VCOs) serve as a proof of concept. Two 1.1-GHz VCOs achieve -153 dBc/Hz at 3 MHz offset, biased at 3.7 mA from 2.5 V. A 2.1-GHz VCO achieves -148 dBc/Hz at 15 MHz offset, taking 4 mA from a 2.7-V supply. All oscillators use fully integrated resonators, and the first two exceed discrete transistor modules in figure of merit. Practical aspects and repercussions of the technique are discussed.

Phase noise in LC oscillators

Analytical methods for the phase-noise analysis of LC-tuned oscillators are presented. The fundamental assumption used in the theoretical model is that an oscillator acts as a large-signal LC-tuned amplifier for purposes of noise analysis. This approach allows us to derive closed-form expressions for the close-to-carrier spectral density of the output noise, and to estimate the phase-noise performance of an oscillator from circuit parameters using hand analysis. The emphasis is on an engineering approach intended to facilitate rapid estimation of oscillator phase noise. Theoretical predictions are compared with results of circuit simulations using a nonlinear phase-noise simulator. The analytical results are in good agreement with simulations for weakly nonlinear oscillators. Complete nonlinear simulations are necessary to accurately predict phase noise in oscillators operating in a strongly nonlinear regime. To confirm the validity of the nonlinear phase-noise models implemented in the simulator, simulation results are compared with measurements of phase noise in a practical Colpitts oscillator, where we find good agreement between simulations and measurements.