A general model is introduced which is capable of making accurate, quantitative predictions about the phase noise of different types of electrical oscillators by acknowledging the true periodically time-varying nature of all oscillators. This new approach also elucidates several previously unknown design criteria for reducing close-in phase noise by identifying the mechanisms by which intrinsic device noise and external noise sources contribute to the total phase noise. In particular, it explains the details of how 1/f noise in a device upconverts into close-in phase noise and identifies methods to suppress this upconversion. The theory also naturally accommodates cyclostationary noise sources, leading to additional important design insights. The model reduces to previously available phase noise models as special cases. Excellent agreement among theory, simulations, and measurements is observed.

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A general theory of phase noise in electrical oscillators

We examine the current performance and future demands of interconnects to and on silicon chips. We compare electrical and optical interconnects and project the requirements for optoelectronic and optical devices if optics is to solve the major problems of interconnects for future high-performance silicon chips. Optics has potential benefits in interconnect density, energy, and timing. The necessity of low interconnect energy imposes low limits especially on the energy of the optical output devices, with a ~ 10 fJ/bit device energy target emerging. Some optical modulators and radical laser approaches may meet this requirement. Low (e.g., a few femtofarads or less) photodetector capacitance is important. Very compact wavelength splitters are essential for connecting the information to fibers. Dense waveguides are necessary on-chip or on boards for guided wave optical approaches, especially if very high clock rates or dense wavelength-division multiplexing (WDM) is to be avoided. Free-space optics potentially can handle the necessary bandwidths even without fast clocks or WDM. With such technology, however, optics may enable the continued scaling of interconnect capacity required by future chips.

Device Requirements for Optical Interconnects to Silicon Chips

The various arguments for introducing optical interconnections to silicon CMOS chips are summarized, and the challenges for optical, optoelectronic, and integration technologies are discussed. Optics could solve many physical problems of interconnects, including precise clock distribution, system synchronization (allowing larger synchronous zones, both on-chip and between chips), bandwidth and density of long interconnections, and reduction of power dissipation. Optics may relieve a broad range of design problems, such as crosstalk, voltage isolation, wave reflection, impedence matching, and pin inductance. It may allow continued scaling of existing architectures and enable novel highly interconnected or high-bandwidth architectures. No physical breakthrough is required to implement dense optical interconnects to silicon chips, though substantial technological work remains. Cost is a significant barrier to practical introduction, though revolutionary approaches exist that might achieve economies of scale. An Appendix analyzes scaling of on-chop global electrical interconnects, including line inductance and the skin effect, both of which impose significant additional constraints on future interconnects.

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Rationale and challenges for optical interconnects to electronic chips

A geometric program (GP) is a type of mathematical optimization problem characterized by objective and constraint functions that have a special form. Recently developed solution methods can solve even large-scale GPs extremely efficiently and reliably; at the same time a number of practical problems, particularly in circuit design, have been found to be equivalent to (or well approximated by) GPs. Putting these two together, we get effective solutions for the practical problems. The basic approach in GP modeling is to attempt to express a practical problem, such as an engineering analysis or design problem, in GP format. In the best case, this formulation is exact; when this is not possible, we settle for an approximate formulation. This tutorial paper collects together in one place the basic background material needed to do GP modeling. We start with the basic definitions and facts, and some methods used to transform problems into GP format. We show how to recognize functions and problems compatible with GP, and how to approximate functions or data in a form compatible with GP (when this is possible). We give some simple and representative examples, and also describe some common extensions of GP, along with methods for solving (or approximately solving) them.

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A tutorial on geometric programming

A companion analysis of clock jitter and phase noise of single-ended and differential ring oscillators is presented. The impulse sensitivity functions are used to derive expressions for the jitter and phase noise of ring oscillators. The effect of the number of stages, power dissipation, frequency of oscillation, and short-channel effects on the jitter and phase noise of ring oscillators is analyzed. Jitter and phase noise due to substrate and supply noise is discussed, and the effect of symmetry on the upconversion of 1/f noise is demonstrated. Several new design insights are given for low jitter/phase-noise design. Good agreement between theory and measurements is observed.

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Jitter and phase noise in ring oscillators

Advances in IC fabrication technology, coupled with aggressive circuit design, have led to exponential growth of IC speed and integration levels. For these improvements to benefit overall system performance, the communication bandwidth between systems and ICs must scale accordingly. Currently, communication links in various applications approach Gbps data rates. These applications include computer-to-peripheral connections, local area networks, memory buses, and multiprocessor interconnection networks. Designers are concerned that these links will soon reach the fundamental limits of electrical signaling. In this article, we examine the limitations of CMOS implementations of highspeed links and show that the links' performance should continue to scale with technology. To handle the interconnects' finite bandwidth, however requires more sophisticated signaling methods. CMOS circuits, typically slower than circuits implemented in nonmainstream technologies, are particularly attractive for common applications because of their lower cost. The overall system cost is further reduced when signaling components are implemented as macro cells, integrated on the same die with a microprocessor or signal processing block.

High-speed electrical signaling: overview and limitations

An 8-Gb/s 0.3-/spl mu/m CMOS transceiver uses multilevel signaling (4-PAM) and transmit preshaping in combination with receive equalization to reduce intersymbol interference due to channel low-pass effects. High on-chip frequencies are avoided by multiplexing and demultiplexing the data directly at the pads. Timing recovery takes advantage of a novel frequency acquisition scheme and a linear phase-locked loop that achieves a loop bandwidth of 35 MHz, phase margin of 50/spl deg/, and capture range of 20 MHz without a frequency acquisition aid. The transmitted 8 Gb/s data are successfully detected by the receiver after a 10-m coaxial cable. The 2/spl times/2 mm/sup 2/ chip consumes 1.1 W at 8 Gb/s with a 3-V supply.

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A 0.3-/spl mu/m CMOS 8-Gb/s 4-PAM serial link transceiver

A 4-Gbit/s serial link transceiver is fabricated in a MOSIS 0.5-/spl mu/m HPCMOS process. To achieve the high data rate without speed critical logic on chip, the data are multiplexed when transmitted and immediately demultiplexed when received. This parallelism is achieved by using multiple phases tapped from a PLL using the phase spacing to determine the bit time. Using an 8:1 multiplexer yields 4 Gbits/s, with an on-chip VCO running at 500 MHz. The internal logic runs at 250 MHz. For robust data recovery, the input is sampled at 3/spl times/ the bit rate and uses a digital phase-picking logic to recover the data. The digital phase picking can adjust the sample at the clock rate to allow high tracking bandwidth. With a 3.3-V supply, the chip has a measured bit error rate (BER) of <10/sup -14/.

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A 0.5-/spl mu/m CMOS 4.0-Gbit/s serial link transceiver with data recovery using oversampling

A serial link transmitter fabricated in a large-scale integrated 0.4-/spl mu/m CMOS process uses multilevel signaling (4-PBM) and a three-tap pre-emphasis filter to reduce intersymbol interference (ISI) caused by channel low-pass effects. Due to the process-limited on-chip frequency, the transmitter output driver is designed as a 5:1 multiplexer to reduce the required clock frequency to one-fifth the symbol rate, or 1 GHz. At 5 Gsym/s (10 Gbis), a data eye opening with a height >350 mV and a width >100 ps is achieved at the source. After 10 m of a copper coaxial cable (PE142LL), the eye opening is reduced to 200 mV and 90 ps with pre-emphasis, and to zero without filtering, The chip dissipates 1 W with a 3.3-V supply and occupies 1.5/spl times/2.0 mm/sup 2/ of die area.

A 0.4-/spl mu/m CMOS 10-Gb/s 4-PAM pre-emphasis serial link transmitter

This paper describes two techniques for designing phase-frequency detectors (PFDs) with higher operating frequencies (periods of less than 8x the delay of a fan-out-4 inverter (FO-4)) and faster frequency acquisition. Prototypes designed in 0.25-µm CMOS process exhibit operating frequencies of 1.25 GHz ( = 1/(8 ċ FO-4) ) and 1.5 GHz ( = 1/(6.7 ċ FO-4) ) for two techniques respectively whereas a conventional PFD operates < 1 GHz ( = 1/(10 ċ FO-4) ). The two proposed PFDs achieve a capture range of 1.7x and 1.2x the conventional design.

Chih-Kong Ken Yang

Papers

High-speed electrical signaling: overview and limitations

A 0.3-/spl mu/m CMOS 8-Gb/s 4-PAM serial link transceiver

A 0.5-/spl mu/m CMOS 4.0-Gbit/s serial link transceiver with data recovery using oversampling

A 0.4-/spl mu/m CMOS 10-Gb/s 4-PAM pre-emphasis serial link transmitter

Fast frequency acquisition phase-frequency detectors for GSa/s phase-locked loops