Mabel Ponton

Phase-Noise Analysis of Injection-Locked Oscillators and Analog Frequency Dividers

In-depth investigation of the phase-noise behavior of injection-locked oscillators and analog frequency dividers is presented. An analytical formulation has been obtained, which allows a better understanding of the shape of the output phase-noise spectrum of these circuits. The simplicity of this formulation is also helpful for circuit design. Approximate expressions for the corner frequencies of the spectrum are determined, identifying the most influential magnitudes and deriving design criteria. In particular, a technique has been developed to shift the frequency of the first corner of the phase-noise spectrum, up to which the output phase noise follows the input one. The expressions for the corner frequencies can be introduced in either in-house or commercial harmonic-balance software, thus allowing an agile design, as no separate phase-noise analysis is required. The validity of the analytical techniques is verified with the conversion-matrix approach and with measurements using two field-effect-transistor-based circuits: a 4.9-GHz injection-locked oscillator and a frequency divider by 2 with 9.8-GHz input frequency.

Stability Analysis of Oscillation Modes in Quadruple-Push and Rucker's Oscillators

Oscillator systems composed by N sub-oscillators coupled through a symmetric linear network enable the combination of output power at the first or Nth harmonic component of the oscillation frequency of each sub-oscillator. However, they have the drawback of a possible coexistence of different oscillation modes, which limits their practical application. This paper presents an in-depth stability analysis of coexisting steady-state solutions in Ruckers oscillator and N -push oscillators. Criteria are provided to avoid undesired oscillation modes. The coupled system is described by means of a semianalytical formulation based on numerical models of the active subcircuits, extracted from harmonic-balance (HB) simulations. Each active subcircuit is composed by the transistor(s), feedback elements, and termination load. The use of the HB numerical models allows a realistic prediction of the behavior of the globally coupled oscillator. Alternatively, a graphical technique is provided to obtain the different oscillation modes using full HB simulations. The perturbation of the reduced-order nonlinear system enables the stability and phase-noise analysis of the steady-state oscillatory solutions. In the derived formulation for phase-noise analysis, both flicker- and white-noise perturbations are considered. The different techniques have been applied to a Ruckers oscillator at 3.9 GHz and a quadruple-push oscillator at 15.6 GHz.

Optimized Design of Pulsed Waveform Oscillators and Frequency Dividers

A technique is presented for the optimized design of oscillators and frequency dividers based on nonlinear transmission lines (NLTLs). The oscillator design relies on a closed-loop configuration containing a high-efficiency amplifier, with the loop output matched to a short NLTL. Attention is paid to the oscillator phase noise. A simple and general-application method is presented for an accurate calculation of the phase sensitivity functions with respect to specific noise sources. The predictions obtained when considering stationary and cyclo-stationary noise-source models are compared. The influence of crucial design parameters on the oscillator efficiency, pulse amplitude, and duty cycle is analyzed, as well as their impact on the phase-noise behavior. An efficient simulation technique enables the evaluation of the injection-locking capabilities during this global optimization of the oscillator in the free-running regime. The phase-noise spectrum in injection-locked conditions is analyzed in detail, considering the influence of flicker noise. A frequency division by 2 is observed in the amplifier stage loaded by the NLTL. The origin of this division is investigated, as well as the influence of the number of cells on the pulsed waveform and the division bandwidth. The techniques have been successfully applied to the design of a pulsed oscillator at 900 MHz.

Nonlinear-optimization techniques for quadruple-push oscillators

A systematic procedure for the design of quadruple-push oscillators is presented. The 4th-harmonic output power is maximized through load-pull optimization of the sub-oscillator circuit. Two variants of the technique are considered: the use of ideal harmonic terminations, defined by their reflection coefficients, and the use of a substitution generator at the output frequency. The latter enables a direct control of the output amplitude at the 4th-harmonic component. A further global optimization of the entire quadruple-push configuration is performed, connecting one auxiliary generator to each sub-oscillator to impose the required 90deg phase shift and preventing undesired oscillation modes. A statistical analysis of the design sensitivity to discrepancies between the four sub-oscillator elements is also presented. The proposed techniques have been applied to the design of a quadruple-push oscillator operating at 20 GHz.

Applications of Pulsed-Waveform Oscillators in Different Operation Regimes

In this paper, following previous works, a pulsed-waveform oscillator is made up of a feedback loop containing an amplifier stage and a nonlinear transmission line. Efficient simulation techniques are applied for the correction of waveform nonidealities. A global stability analysis of the pulsed-waveform oscillator is performed, considering two relevant circuit parameters. All the possible oscillation modes are taken into account in this analysis, with the aim to guarantee operation in the desired mode only. The jitter in the pulsed waveform is quantified with a phase-noise analysis, and the uncommon form of variation of the phase-noise spectral density is understood with the aid of a semianalytical formulation. The injection-locked operation of the pulsed-waveform oscillator is also investigated, examining its robustness and possible advantages and applications. In particular, we will consider the injection-locked mode at a subharmonic frequency and analyze the resulting phase-noise spectrum, which will be compared with that of the free-running pulsed-waveform oscillator. The application as a frequency multiplier will be considered. The techniques have been applied to a prototype at 1 GHz with very good agreement with the measurement results.

Pulsed-waveform generator based on coupled oscillators

Waveform sharpening in nonlinear transmission lines (NLTL) is analyzed in detail and applied to the design of a pulse-generator based on two coupled oscillators. The maximum propagation frequency through the NLTL is calculated with a realistic numerical technique, which enables an optimized design. By coupling two NLTL oscillators terminated in grounded stubs of different length, three design parameters are available, which enables a flexible mechanism for pulse formation. A reduced-order model is proposed for the efficient determination of the tuning voltage in one of the oscillator elements. The analysis and design techniques have been applied to a prototype at 0.8 GHz.

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.

Design of pulsed waveform oscillators with a short nonlinear transmission line

In this paper we present a new methodology for the design of pulsed-waveform oscillators. The design is based on the use of a short section of nonlinear transmission line (NLTL), constituting the load of a transistor-based subnetwork exhibiting negative resistance. The oscillation start-up conditions are imposed at a transistor port different from the one at which the NLTL is connected, to increase the optimization flexibility. The NLTL is ended in a reactive termination which is optimized in order to reduce the duty cycle of the voltage waveform. Compared with previous works, the new methodology enables a smaller duty cycle with less varactor diodes and no need for adaptive gain in the transistor stage. The methodology has been applied to obtain a pulsed-waveform oscillator at 1.2 GHz, achieving a 5% duty cycle. Good agreement has been obtained in the comparison with the experimental results.

Analysis of Injection Pulling in Phase-Locked Loops With a New Modeling Technique

A new formulation is presented for the analysis of phase-locked loops (PLL). It is based on the use of a realistic reduced-order model for the voltage-controlled oscillator, extracted from harmonic-balance (HB) simulations. An HB formulation of the reduced-order PLL equations enables an efficient analysis of the PLL in unlocked conditions, and therefore, prediction of common hysteresis phenomena. The injection-pulling effects in the presence of interference signals are analyzed taking into account the nonlinearity of the phase detector. The interfered PLL in locked conditions is analyzed with a single-tone HB formulation of the reduced-order system, whereas a two-tone HB analysis is used for the analysis in unlocked conditions. The frequency-domain formulation enables an accurate and efficient prediction of the effect of the interferer on the hold-in and lock-in ranges, here investigated, to our knowledge, for the first time. The analysis has been successfully applied to a PLL operating at 5.3 GHz.

Optimized design of pulsed waveform oscillators

We present a technique for the optimized design of pulsed-waveform oscillators. This design is based on a closed-loop configuration, with the transistor output matched to a short nonlinear transmission line (NLTL). Class E and Class D operation classes, providing different waveforms at the NLTL input, are compared. Attention is paid to the oscillator phase noise, describing a simple procedure for an accurate calculation of the phase sensitivity functions with respect to specific circuit noise sources. The influence of crucial design elements on the oscillator efficiency, pulse amplitude and duty cycle is analyzed, as well as the effect on the phase noise behaviour. The predictions obtained when using stationary and cyclostationary noise-source models are compared with the measurement results. The techniques have been successfully applied to the design of a pulsed oscillator at 900 MHz.