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## Amplitude and Phase Noise in Nano-scale RF Circuits

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**Amplitude and Phase Noise in Nano-scale RF Circuits**Reza Navid May 14, 2007**Today, 45nm technology node is available for commercial**production design. Several other nano-scale devices are also becoming available. Channel Length (Micron) Number of MOSFETs 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**Physical length**Drain Noise level Ro Long-channel prediction 1986 1994 1996 1999 Year Scaling Problem at Nanometer Scales Reliability: Mismatch: Intrinsic Gain: Small output resistance Low intrinsic gain Noise: Short-channel MOSFETs are noisier that Long-channel ones**LNA Noise**Phase Noise Noise in RF Receivers Electrical noise strongly impacts the overall performance. Input Noise Output Noise IF Filter Mixer LNA Transmission No Signal LO**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 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.**Noise transfer**function (Impedance) dx dR 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 N+ N+ dR 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) Jindal (0.75mm) 2.9 Scholten (0.35mm) Tedja (1mm) 1.1 Long-channel prediction 0.67 1996 1986 1994 1999 Year Several methods are proposed to study this excess noise.**Our approach**Ballistic Mode: Ind=2qId Today’s FETs, 50% Ballistic Ballistic FETs Long-Channel FETs Model revision Short-Channel Model: Ind=4kTgshgdo 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 Short-Channel Model: Ind=ks(2qId) Long-Channel Model: Ind=4kTggdo Model revision • MOSFETs are moving towards ballistic limit. 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**Phase Noise in Oscillators**• Device noise leads to frequency fluctuations. • Example: Ring Oscillators Output t Time Domain I Phase Noise f fo Frequency Domain t 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: • 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.**Jitter characterization:**Without low-frequency poles T1 Ti T2 0 i-j 0 i-j DTiDTjhas necessary andsufficient information for phase noise calculation. With white noise (presented here) With colored noise (presented elsewhere) Time-Domain Phase Noise Analysis • Formulation of phase noise: • 1) Calculate jitter • 2) Calculate phase noise using jitter-phase-noise relationships**Jitter in Switching-Based Oscillators (1)**• Switching-based oscillators: • Energy-injecting elements act like ideal switches. in in vC vout vref vout vC in C R Passive noisy network Ideal noise-free switch 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. 2Dvc vc Slope=S vref vref vC in C R 2Dvc 2DT t This is suitable for switching-based oscillators.**Jitter-Phase-Noise Relationships (1)**• If all covariance terms are zero [Navid, 2005], Variance of one period 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) 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 B A On State: Off State: Use time-domain jitter analysis for switching-based oscillators.**Phase Noise in Ring Oscillators (cont.)**• Using jitter-phase-noise relationships [Navid, 2005]: 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) 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. 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 Fabricated in National Semiconductor’s 0.18mm CMOS process.**MOSFET Noise Characterization**• Frequency spectrum of the oscillators: The oscillator with longer transistors has better spectral purity.**MOSFET Noise Characterization (Cont.)**• Phase noise of the oscillators: Oscillator with Longer transistors has 7dB smaller phase noise.**OSC3**Long-channel prediction Device Noise Parameters • Device noise parameters can be extracted from phase noise data. Full shot noise OSC1 Extracted device noise parameters are consistent with our prediction.**Charge**Pump 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 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.**Physical length**Drain Noise level Ro Long-channel prediction 1986 1994 1996 1999 Year Other Scaling Problems Reliability: Mismatch: Intrinsic Gain: Small output resistance Low intrinsic gain Noise: Short-channel MOSFET are noisier that Long-channel ones**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.