Amplitude and Phase Noise in Nano-scale RF Circuits Reza Navid May 14, 2007

CMOS Scaling Since Early 70s 4004 Intel Processor 2,250 10m-MOSFETs 386 Intel Processor 275,000 1m-MOSFETs Pentium IV Intel Processor 169,000,000 90n-MOSFETs Channel Length (Micron) Number of MOSFETs Today, 45nm technology node is available for commercial production design. Several other nano-scale devices are also becoming available.

Scaling Problem at Nanometer Scales Reliability: Mismatch: Physical length Intrinsic Gain: Small output resistance Low intrinsic gain Noise: Short-channel MOSFETs are noisier that Long-channel ones Long-channel prediction 1986 Year 1999 1994 1996 Drain Noise level Ro

Electrical noise strongly impacts the overall performance. Noise in RF Receivers LNA Noise Phase Noise Input Noise Output Noise Mixer IF Filter LNA Transmission Supper heterodyne receiver is a perfect example of the effect of noise in communication. No Signal LO Electrical noise strongly impacts the overall performance.

Outline Amplitude Noise in MOSFET Noise in MOSFETs Physical and Compact Models Noise Performance of Ballistic MOSFETs Jitter and Phase Noise in Oscillators Indirect Noise Characterization Using Phase Noise Time-Domain Formulation of Phase Noise Experimental Results Directions for Further Research Conclusions

Outline Amplitude Noise in MOSFET Noise in MOSFETs Physical and Compact Models Noise Performance of Ballistic MOSFETs Jitter and Phase Noise in Oscillators Indirect Noise Characterization Using Phase Noise Time-Domain Formulation of Phase Noise Experimental Results Directions for Further Research Conclusions

Noise Sources in MOSFETs There are two noise sources in a MOSFET: Drain current noise (ind) Induced gate noise (ing) Gate Drain Drain ing gg Cgs gmvgs go ind Gate Source Source 1/f noise There are two noise sources in a MOSFET working in saturation. White noise Gate Noise: Carrier fluctuations coupled to gate through Cgs 1/f Noise: Unknown origin, believed to be due to traps We study the white noise part of the drain noise in saturation.

Classical MOSFET Noise Formulation Classical long-channel formulation Impedance Field Method [Van Der Ziel, 1970]: Divide the channel into small pieces Calculate noise of each piece (assuming equilibrium noise) Integrate (assuming independence) G S D Noise transfer function (Impedance) N+ N+ dR dx dR The classical formulation of noise in MOSFETs is based on a method called impedance field method. It accurately predicts noise in long-channel MOSFETs.

Deficiency of the Long-Channel Model Excess noise has been reported for 20 years now: g 7.9 Abidi (0.7mm) 3.3 Triantis (0.7mm) 2.9 Jindal (0.75mm) Tedja (1mm) Scholten (0.35mm) 1.1 Long-channel prediction 0.67 The problem with this simple formulation is that …. 1986 1994 1996 1999 Year Several methods are proposed to study this excess noise.

Excess Noise in Short-Channel FETs Researchers have tried to explain excess noise: Local heating effects [Traintis, 1996] Hydrodynamic simulations [Goo, 1999, Jungemann 2002] Montecarlo analysis [Jungemann, 2002] … Usual approach Model revision Our approach Ballistic Mode: Ind=2qId Long-Channel Model: Ind=4kTggdo Short-Channel Model: Ind=4kTgshgdo Short-Channel Model: Ind=ks(2qId) Model revision MOSFETs are moving towards ballistic limit. Several methods are proposed to explain and predict the excess noise in MOSFETs. Long-Channel FETs Today’s FETs, 50% Ballistic Ballistic FETs We present a model based on ballistic MOSFET model.

Outline Amplitude Noise in MOSFET Noise in MOSFETs Physical and Compact Models Noise Performance of Ballistic MOSFETs Jitter and Phase Noise in Oscillators Indirect Noise Characterization Using Phase Noise Time-Domain Formulation of Phase Noise Experimental Results Directions for Further Research Conclusions Now we change gear a little bit and talk about phase noise of CMOS oscillators. We present a formulation of phase noise which has two applications.

Phase Noise in Oscillators Device noise leads to frequency fluctuations. Example: Ring Oscillators Output t Time Domain To see how device noise can lead to phase noise, let’s look at the simple example of a ring oscillator. I Phase Noise fo f t Frequency Domain Phase noise characterizes the frequency fluctuations.

Phase Noise: Formulation and Measurement Phase noise definition: PSD of signal divided by power Hard to formulate Easy to measure PN (dBc/Hz) fo fo+Df f Phase noise measurement helps estimate device noise: The most famous characteristic of phase noise is that it is easy to measure but hard to calculate. Need accurate formulation for specific oscillators. Time-domain phase noise analysis method This method is most suitable for formulation of phase noise in switching-base oscillators.

Time-Domain Phase Noise Analysis Formulation of phase noise: 1) Calculate jitter 2) Calculate phase noise using jitter-phase-noise relationships Jitter characterization: T2 Ti T1 With white noise (presented here) i-j With colored noise (presented elsewhere) Without low-frequency poles In time domain analysis of phase noise we first calculate the jitter in time domain and then calculate the phase noise using exact equation with little or no approximations. Animation here is what we usually face. DTiDTj has necessary and sufficient information for phase noise calculation.

Jitter in Switching-Based Oscillators (1) Energy-injecting elements act like ideal switches. in in vC vout vref vout The method is specially accurate for switching based oscillators. vC Passive noisy network Ideal noise-free switch in C R Calculate jitter during each switching; Add them up to find total jitter.

Jitter in Switching-Based Oscillators (2) Calculation procedure: Calculate voltage variance at the switching time. Divide by the square of voltage slope to get jitter. vc 2Dvc Slope=S vref vref vC in C R 2Dvc 2DT t Once we model an oscillator like a switching based oscillator the rest of the calculations are straightforward. This is suitable for switching-based oscillators.

Jitter-Phase-Noise Relationships (1) If all covariance terms are zero [Navid, 2005], Variance of one period We then need an equation to give phase noise for a given phase noise. PN (dBc/Hz) Df (Hz) Df (Hz) The 1st harmonic The 3rd harmonic Phase noise has peaks around odd harmonics, as expected.

Jitter-Phase-Noise Relationships (2) It can be approximated by a Lorentzian Function. Consistent with the results for sinusoidal signals [Herzel, 1999] Exact phase noise Usually: PN(dBc/Hz) The equation can be approximated by this … Lorentzian Df (Hz) Jitter-phase-noise relationship for nonzero jitter covariance is presented elsewhere [Navid, 2004].

Phase Noise in Ring Oscillators Time-domain phase noise analysis: Treat invertors as ideal switches. Use long-channel noise formulation. A B A B On State: We apply this method to a simple relation oscillator. Off State: Use time-domain jitter analysis for switching-based oscillators.

Phase Noise in Ring Oscillators (cont.) Using jitter-phase-noise relationships [Navid, 2005]: After some simplification and using jitter-phase-noise relationships we get … Dynamic Power Very simple equations, but how accurate?

Phase Noise in Ring Oscillators Measured results form Hajimiri, JSSC 1999 compared to our formulation: DPN (dB) This table compares our prediction to measured results. Lmin (mm) Df=1MHz The difference is only a few dB; it increases in short-channel devices.

Oscillators for Noise Characterization Need an oscillator with predictable phase noise, not necessarily low phase noise: an unsymmetrical ring oscillator. This table compares our prediction to measured results. The unsymmetrical ring oscillator is only one of many possibilities.

The Unsymmetrical Ring Oscillator Chip photo: Ring oscillators for functionality test MIM Capacitors OSC1, L=.18mm OSC2, L=.38mm OSC3, L=.54mm This table compares our prediction to measured results. Fabricated in National Semiconductor’s 0.18mm CMOS process.

MOSFET Noise Characterization Frequency spectrum of the oscillators: This table compares our prediction to measured results. The oscillator with longer transistors has better spectral purity.

MOSFET Noise Characterization (Cont.) Phase noise of the oscillators: This table compares our prediction to measured results. Oscillator with Longer transistors has 7dB smaller phase noise.

Device Noise Parameters Device noise parameters can be extracted from phase noise data. Full shot noise Long-channel prediction OSC3 OSC1 This table compares our prediction to measured results. Extracted device noise parameters are consistent with our prediction.

Further Research on Phase Noise Indirect device noise characterization for Nanotubes and Nanowires: Ring oscillators built with these devices are already available (Z. Chen et al, Science 24 March 2006). Time-domain phase noise analysis: Jitter/phase noise calculation for various oscillators/PLL systems. VCO Fref Charge Pump Loop Filter PFD :N Vb

Noise for Device Engineering Non-equilibrium noise carries unique device information Device engineering based on noise characterization Examples: Examine carrier transport using noise data Nano-tubes, Nano-wires, MOSFETs, … Design new devices based on noise measurement Bio-analytical devices Use noise data to improve existing devices and build new ones.

Other Scaling Problems Reliability: Mismatch: Physical length Intrinsic Gain: Small output resistance Low intrinsic gain Noise: Short-channel MOSFET are noisier that Long-channel ones Long-channel prediction 1986 Year 1999 1994 1996 Drain Noise level Ro

Conclusions Efficient CMOS analog design calls for a careful study of noise in MOSFETs, which has been a mystery for two decades. Time domain phase noise analysis method accurately predicts the phase noise in switching-based oscillators. Device noise can be characterized through phase noise measurement, facilitating process characterization. Noise can be useful.

Acknowledgment This work is supported under an SRC customized research project from Texas Instruments and MARCO MSD center. We would like to thank National Semiconductor Inc. for the fabrication of test chips.