ECE594_

Noise In Electronics.
Mark Rodwell

UPDATE: Please see more updated noise analysis notes from the following courses:

ece218b

This is a Ph.D.-level seminar course in noise in electrical engineering, with an emphasis on covering material significant to Ph.D. students whose research is experimental and is in semiconductor devices, integrated circuits, or optical communications. The intent is to teach it once every ~4 years, so as to  be available once for each set of Ph.D. students. I am considering offering it again in Fall term 2005. I would be grateful of feedback from Mishra, York, Bowers, Blumenthal, Coldren, and Long group Ph.D. students as to whether this would be of interest.

Notes

# Notes

## Notes set 1: Scope of topics

noise_notes_set1.pdf

math, physics, devices, circuits, systems

## Notes Set 2: Math

Sets, probability, conditional probability, Bayes theorem, independence.
Bernoulli trials, random variables, density and distribution functions .

Binomial distributions and Gaussian and Poisson as limiting cases thereof.

Transformations.

## Notes Set 3: Statistical Thermodynamics

noise_notes_set3.pdf

System configurations, multiplicity functions, entropy, temperature.

Boltzmann law, velocity distribution of a gas.

## Notes set 4: More math

noise_notes_set4.pdf

Expectations, mean, variance, distribution functions of multiple RVs.
Conditional densities, sums of RVs and convolution, central limit theorem.

Covariance, correlation, Jointly Gaussian RVs and correlation matrix.

Linear operations on JGRV's and relationship to filtered random processes.

Linear Estimation .

## Notes Set 5: Yet More Math

noise_notes_set5.pdf

Random processes, sample space, orders of stationarity, ergodicity.

time and ensemble averages.

correlation functions as complete description of stationary ergodic JGRP.
spectral densities, cross spectral densities.

## Noise Notes Set 6: Thermal Noise

noise_notes_set6.pdf

Thermal noise derivation from stat thermo.

Available noise power
circuit noise relationships.

## Noise Notes Set 7: First Look at Noise in Circuits

noise_notes_set7.pdf

Pre-introduction of transistor noise models.

Circuit noise analysis

Total input referred noise voltage.

Total input referred noise current.

Short-circuit input noise voltage, open-circuit input noise current.

Noise figure, minimum noise figure, optimum source impedance.

Friss Formula, available gain, noise measure, noise temperature.

## Noise Notes Set 8: Shot Noise and Diffusion Noise

noise_notes_set8.pdf

Independent events and shot noise derivation
Ultraviolet crisis and shot noise

Counting arguments.
Schottky diode: thermionic emission,  shot noise vs. bias, 2kTR relationship.

Diffusion noise: variation of fluxes

diffusive transport and diffusive noise in PN junctions: physics and circuit models

shot noise of GR currents.

Transit times, diffusion capacitance

## Noise Notes Set 9:  Bipolar Transistor Noise

noise_notes_set9.pdf

BJT operation: DC and high frequency inclusive of diffusion and space charge effects.

Small signal noiseless model. Addition of diffusion noise terms.

Full (correlated) base and collector noise
Simplified (normal , zero correlation) BJT noise model.

## Noise notes set 10: Noise in Field-Effect Transistors

noise_notes_set10.pdf

Velocity-field curves, ad-hoc electron temperature model

gradual channel model. integrals. Derivation of channel noise current.

Modification for velocity saturated case.

Gate current noise and correlation with channel noise.

Simplified, pragmatic noise model.

## Noise Notes Set 11:  Noise of Miscellaneous devices

noise_notes_set11.pdf

Schottky and PN diode noise models. Transmission lines. Antenna noise temperature.

Friss formula in temperature form.

## Noise Notes Set 12:  Physics and Noise of Resonant Tunnel diodes.

noise_notes_set12.pdf

Contents exactly as stated. Topic now only of specialized interest; will likely be skipped.

## Noise Notes Set 13: Circuit Noise analysis: overview and benchmarks

noise_notes_set13.pdf

Total input referred noise voltage.

Total input referred noise current.

Short-circuit input noise voltage, open-circuit input noise current.

Noise figure, minimum noise figure, optimum source impedance.

Friss Formula, available gain, noise measure, noise temperature.

Signal/noise ratio expressed in various terminologies: by voltage, by current, by noise figure, by noise temperature; equivalence thereof.

## Noise Notes Set 14: Circuit Noise analysis methods.

noise_notes_set14.pdf

Method of transposition of sources. Many examples worked.

En-In model of FET. Noise figure circles.

Strong discrepancy between impedance matching and noise matching.

## Noise Notes Set 15: FET minimum noise figure

noise_notes_set15.pdf

Proof (and some corrections to) Fukui noise figure relationship for FETs.

Impact of impedance and power consumption  limits on achievable noise with square-law MOSFET front-ends.

## Noise Notes Set 16: Bipolar Transistor Noise Analysis

noise_notes_set16.pdf

HBT / BJT noise figure at low frequencies

Resistive feedback amplifier noise figure.

## Noise Notes Set 17: Approximate BJT Minimum Noise figure derivation

noise_notes_set17.pdf

Derivation of very long expression for noise figure vs. source impedance.

Derivation of very approximate expression for minimum noise figure.

## Noise Notes Set 18: Mixers and Analog Communications Systems

noise_notes_set18.pdf

Superhet receivers. Diodes as mixers. Diode Design.

Diode mixer noise models. Noise figure and effect of image response on noise.

Elimination of image noise by image termination.

Harmonic mixers and sampling circuits.

2-port mixer description.

## Noise Notes set 19: Baseband, AM, and FM analog receivers.

noise_notes_set19.pdf

Signal/noise ratio. Microphone preamp example. AM and DSB receiver example.

Nonlinear and twisted modulation: SNR enhancement. Threshold effect.

FM and PM as twisted modulation.

## Noise notes set 20: Noise in signal sources

noise_notes_set20.pdf

Hand waving treatment of 1/f noise.

Small angle PM. Spectral descriptions of AM and PM.

AM and PM/FM sidebands. Energy relationships and timing deviation.

Phase noise in oscillators. Van Der Pohl method.

Example: PLL for laser timing control.

## Noise notes set 21:  Sensitive Experiments: Noise in the Physics Lab.

noise_notes_set21.pdf

How to measure *tiny* things.

Integration bandwidth. Minimum detectable signal.

Period of observation and integration bandwidth. Averaging as a form of filtering.

Limit of observation times on 1/f^N  noise processes.

Limits *to* observation times by drift.

Examples: finding little green men from alpha centari (CETI), electro optic sampling, atomic force microscopy.

## Noise notes set 22:  Digital communications systems

noise_notes_set22.pdf

Linear algebra. Waveforms as vectors in N-space.

Delta functions and sinusoids as orthonormal basis sets --> the Fourier transform.

Modulation formats and channel codes.

Example: sending data from Saturn to Earth.

## Noise Notes Set 23: Fiber Optic Communication Links

noise_notes_set23.pdf

Receiver in colored noise. Whitening filter.  Intersymbol interference.  Intractability.

Simplified practical  non-optimum receivers. Eye diagrams. Personik noise integrals.  Optical receiver sensitivity.

Design of low-noise optical receiver front-ends.

## Noise Notes Set 24: A sketch of information theory

noise_notes_set24.pdf

Statistical entropy. Typical sequences. Conditional distributions and conditional entropy.

Mutual information. Entropy of a signal sequence.

Channel capacity. Capacity of band limited additive Gaussian channel.