Phase noise and jitter modeling for fractional-N PLLs

Adv. Radio Sci., 5, 313–320, 2007 www.adv-radio-sci.net/5/313/2007/ © Author(s) 2007. This work is licensed under a Creative Commons License.

Advances in Radio Science

Phase noise and jitter modeling for fractional-N PLLs S. A. Osmany, F. Herzel, K. Schmalz, and W. Winkler IHP Im Technologiepark 25, 15236 Frankfurt (Oder), Germany

Abstract. We present an analytical phase noise model for fractional-N phase-locked loops (PLL) with emphasis on integrated RF synthesizers in the GHz range. The noise of the crystal reference, the voltage-controlled oscillator (VCO), the loop filter, the charge pump, and the sigma-delta modulator (SDM) is filtered by the PLL operation. We express the rms phase error (jitter) in terms of phase noise of the reference, the VCO phase noise and the third-order loop filter parameters. In addition, we consider OFDM systems, where the PLL phase noise is reduced by digital signal processing after down-conversion of the RF signal to baseband. The rms phase error is discussed as a function of the loop parameters. Our model drastically simplifies the noise optimization of the PLL loop dynamics.

1

Introduction

Frequency synthesizers are essential components in wireless RF transceivers. A synthesizer provides a stable signal for frequency conversion, modulation and demodulation. A fractional-N PLL gives a greater flexibility than an integerN PLL due to the higher frequency resolution (Perrot et al., 2002). The phase noise is the most important performance criterion of the synthesizer for its stringent requirement in many applications, e.g., in OFDM based systems (Stott, 1998; Herzel et al., 2005). The problem with phase noise is exacerbated in high-frequency applications, since the oscillator phase noise at a given frequency offset typically increases in proportion to the carrier frequency. For this reason, the minimization of the phase noise in frequency synthesizers is of special interest in mm-wave application, e.g., in the 60 GHz band (Winkler et al., 2005). Many publications on phase noise modeling of oscillators and PLLs have Correspondence to: S. A. Osmany ([email protected])

appeared during the last few years, e.g. Lee and Hajimiri (2000)–Rohde (2005). This paper is focussed on problems which are specific to integrated PLLs. They arise mainly from the low quality factor of the available passives as well as from the limited size of filter capacitors. Especially, the low quality factor of integrated inductances causes a high noise level of the voltage-controlled oscillator (VCO). This problem is exacerbated by the fact that variations of the device parameters with process and temperature require a relatively large VCO tuning range affecting oscillator noise and loop filter noise. In integrated PLLs, the values of the integrated capacitances are limited by chip area and, possibly, yield. This can make the filter noise comparable to the VCO noise, if the VCO gain is large. Another problem arises in RF synthesizers for mm-wave applications. The high oscillation frequency results in a large division factor enhancing the reference noise to a level comparable to the phase noise of integrated VCOs. The different dependencies of the noise contribution on the PLL dynamics results in a subtle trade-off for the loop bandwidth. This paper describes the phase noise spectrum of a PLL, where emphasis is placed on the high-pass filtering in OFDM systems due to the correction of the common phase error.

2

PLL phase noise sources

In the literature, two types of phase noise are used, the twosided power spectral density (PSD) of the phase and the single-sideband phase noise. For moderate and large frequency offsets, these quantities are almost equal (Herzel, 2004). For wideband systems, close-in phase noise is less relevant due to a large channel width and/or proper baseband filtering explained below. Therefore, we will not distinguish between the single-sideband phase noise and the two-sided power spectral density of the phase in the remainder of this paper. The phase noise S can be determined from the single-

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