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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

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

Reliability:

Mismatch:

Intrinsic Gain:

Small output resistance

Low intrinsic gain

Noise:

Short-channel MOSFETs

are noisier that Long-channel ones

LNA Noise

Phase Noise

Electrical noise strongly impacts the overall performance.

Input Noise

Output Noise

IF Filter

Mixer

LNA

Transmission

No Signal

LO

- 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

- 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

- 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 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)

- Impedance Field Method [Van Der Ziel, 1970]:

G

S

D

N+

N+

dR

It accurately predicts noise in long-channel MOSFETs.

- 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

- 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.

- 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

- 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 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)

- Formulation of phase noise:
- 1) Calculate jitter
- 2) Calculate phase noise using jitter-phase-noise relationships

- 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.

- 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.

- 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.

- 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].

- 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.

- Using jitter-phase-noise relationships [Navid, 2005]:

Dynamic Power

Very simple equations, but how accurate?

- 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.

- 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.

- 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.

- Frequency spectrum of the oscillators:

The oscillator with longer transistors has better spectral purity.

- Phase noise of the oscillators:

Oscillator with Longer transistors has 7dB smaller phase noise.

OSC3

Long-channel prediction

- 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

- 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

- 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

Reliability:

Mismatch:

Intrinsic Gain:

Small output resistance

Low intrinsic gain

Noise:

Short-channel MOSFET

are noisier that Long-channel ones

- 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.

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.