A general method for deriving the describing functions for a certain class of nonlinearities

Purdue University, Lafayette, IN, USA
IRE Transactions on Automatic Control 07/1960; DOI: 10.1109/TAC.1960.1104997
Source: IEEE Xplore

ABSTRACT Since Goldfarb's original work on describing functions, a considerable number of papers have been published in which the describing functions of particular nonlinearities have been derived. It appears however that little effort has been made to classify the nonlinearities. Since the describing function method is one of the more powerful methods available at present to analyze nonlinear feedback systems, it appears desirable to collect the expressions for the describing functions of a few different types of nonlinearities in one paper. It is the purpose of this paper to derive the describing functions of two general types of nonlinearities and show how the describing functions of many other practical types of nonlinearities for which the describing function analysis is valid naturally follow.

  • [Show abstract] [Hide abstract]
    ABSTRACT: A novel harmonic Class-C CMOS VCO architecture with improved phase noise performance and power efficiency is presented in this paper. The VCO is based on the widely adopted topology consisting in a crossed pair of NMOS devices refilling a symmetric resonator with a center tapered inductor and biased by a top PMOS current generator. The Class-C operation mode is obtained through a low frequency feedback loop constituted by an operational transconductance amplifier operating the difference between the inductor center tap voltage and a reference voltage, pushing gate polarization voltage of VCO crossed pair devices well below their threshold voltage. The Class-C VCO achieves a theoretical 2.9 dB phase noise improvement compared to the standard differential-pair LC-tank oscillator for the same current consumption. A prototype of the VCO is implemented in a standard RF 55 nm CMOS technology and compared to both a standard and an optimized VCO implemented in the same technology. All these VCOs share a copy of a unique resonator. The Class-C VCO is tunable over the frequency band 6.5–7.8 GHz and displaying an average phase noise lower than $-$127 dBc/Hz @ 1 MHz offset with a power consumption of 18 mW, for a state-of-the-art figure-of-merit of $-$ 187 dBc/Hz @ 1 MHz and $-$ 191 dBc/Hz @ 10 MHz offsets, respectively.
    Circuits and Systems I: Regular Papers, IEEE Transactions on 07/2014; PP(99):1-13. DOI:10.1109/TCSI.2014.2332268 · 2.30 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: The shunt regulator (SR) is a key part of the power conditioning unit, which is a kind of power supply system for spacecrafts. SR is a strong nonlinear system due to the hysteresis control adopted, but the stability analysis for SR is still ground on the approximate linearization. In this paper, a novel stability analysis method for strong nonlinear systems is proposed based on describing function, which is used to model the nonlinear link of SR. Further, two different conclusions about the stability of SR are drawn, obtained by the approximate linearization method and the describing function (DF) method, respectively. Finally, the simulation and experimental results prove the correctness of the stability analysis method proposed in this paper and discover the limitation of the linearization method for analyzing the stabilities of the nonlinear systems.
    Energy Conversion Congress and Exposition (ECCE), 2013 IEEE; 01/2013
  • [Show abstract] [Hide abstract]
    ABSTRACT: Many Class-C CMOS VCOs have been introduced in the last decade claiming to achieve improved phase noise performance and power efficiency with apparently no tradeoff, however only in the past two years implementation efforts have been focused on stability related issues of such oscillator architectures. In fact, oscillators exploiting time-varying bias techniques may present several stability points and for this reason dedicated start-up circuits are needed to reach the desired periodic steady state regime. In this paper we introduce a novel stabilization technique for a CMOS VCO polarized in Class-C via a common mode feedback loop with the aim to ensure a robust start-up with no significant phase-noise and power efficiency degradation. The VCO core is based on a crossed pair of NMOS devices refilling a symmetric resonator with a center tapered inductor and biased by a top PMOS current generator. The proposed Class-C VCO is implemented in a RF 55nm CMOS technology and is tunable over the frequency band 6.6–8.2 GHz with average phase noise lower than −127 dBc/Hz @ 1 MHz offset and mean power consumption of 18mW, for a state-of-the-art figure-of-merit of −190 dBc/Hz @ 1 MHz offset.
    European Solid State Circuits Conference (ESSCIRC), ESSCIRC 2014 - 40th, Venice Lido, Italy; 09/2014


Available from