NOISENOISE

N. LibatiqueN. Libatique

ECE 293ECE 293

22ndnd Semester Semester 2008-092008-09

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Optical Detection: Optical Detection: Biomolecular Biomolecular SignalingSignaling

11-cis-retinal trans-retinal rodopsin changes shape makes opsin sticky to transducin GDP from transducin falls off and replaced by GTP activated opsin binds to phosphodiesterasewhich aqcuires the ability to cut cGMP lower cGMP conc. causes ion channels to close lowering Na concentration in cell and lowers cell potential current transmitted down optic nerve to brain

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Optical DetectionOptical Detection Opto-electronic Detection vs. Others Opto-electronic Detection vs. Others

(Biomolecular Signalling) (Biomolecular Signalling) Limits of communication, bit error Limits of communication, bit error

raterate

Shot NoiseShot Noise

Shot Noise, Johnson Noise, 1/f NoiseShot Noise, Johnson Noise, 1/f Noise Shot Noise ~ Poisson ProcessShot Noise ~ Poisson Process

very small

P(0,) + P(1,) = 1 P(1,) = a(); a = rate constant No arrivals over + ; P(0, + ) P(0, + ) = P(0,) P(0,) What is P(0, )? In a pulse of width what is the

probability of it containing N photons? P(N)

What is the detection limit?

A perfect quantum detector is used to receive an optical pulse train of marks and spaces. If even one photon arrives, it will be detected and counted as a mark. The absence of light over a clock period is a space. Every pulse will have a random number of photons. On average, how many photons should be sent per pulse, if it is desired that only 1 ppb be misinterpreted as a space when in fact it is a mark?

Poisson

dP(0,)/d = - a P(0, ) P(0, ) = e- a ; What about P(N)? N photons at a

time? It can be shown that this is a Poisson

process P(N) = (Nm)N e –N

m / N!

Poisson DistributionPoisson Distribution

P(N) = (Nm)N e –Nm / N!Variation is fundamental

N = 6; Only 16% of pulses have 16 photons; e-6 probability of having no photons

Optical Shot Noise

Signal to Noise RatioSignal to Noise Ratio

Shot Noise on a Shot Noise on a PhotocurrentPhotocurrent

Other Sources

Aside from photon shot noise Background radiation: blackbodies Johnson Noise: thermal motion of

electrons 1/f Noise: conductivity fluctuations Amplifier Noise

Background Radiation

Ptotal = Psignal + Pbackground

MeanSquareCurrentshot proportional to Ptotal

I(W/cm2) = (T/645)4 (T in K) 4.7x10-2 W/cm2 at 300 K Human Body 2 m2 1 kW

Spectrally distributed

http://en.wikipedia.org/wiki/Black_body

1,000 oC

3 K

Spectral Distribution

http://en.wikipedia.org/wiki/Black_body

Bit Error Rates Analog Signals: SNR ratio Digital Signals: BER Telco Links = 10-9

Datacomms and Backplanes = 10-12

Quality Factor Power required to

achieve Q and BER? 0.1 dB significant as fiber losses are low…

http://zone.ni.com/devzone/cda/tut/p/id/3299

Probability Distribution Function

Decision Level

s(0) = expectation current value

s(1) = expectation current value21

20

Id

Output Current

Probability

A10

A01

• Signal + Noise results inbit errors…• Noise statistics of signal, detector, amplifier determine PDF

Probability of Error

p(0) = probability that a space is transmitted

p(1) = probability that a mark is transmitted

A01 = probability that space is seen as mark

A10 = probability that mark is seen as space

P(E) = p(0) A01 + p(1) A10

Assume Gaussian statistics P(E) = Integral[Exp[-x2/2],{x,Q,Infinity}]/Sqrt[2 ]

BER vs Q

Q

BER

6

10-9

10-5

10-7

Design Assume a perfect quantum detector.

Amplifier input impedance is 50 Ohms. Shunt Capacitance 2 pF. Design a 100 Mbps link at 1.5 m. Design for a BER 10-12.

Assume the effective bandwidth required would be 200 MHz (Nyquist Criterion).

Optimize the detector. Minimize the power required to achieve BER. reducing the BW via changing RC, reduce ckt noise, etc……

Show…

Poisson Statistics: Show value of mean: Summation [k p(k,n), {k,0,Infinity}]

Poisson Statistics: Expectation value for k2

(Note: p(k,) = nk e-n / k! Mean[(k-n)^2] = n Simulate a current governed by

Poisson Noise