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NOISE N. Libatique ECE 293 2nd Semester 2008-09 Optical Detection: Biomolecular Signaling http://universe-review.ca 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 phosphodiesterase which 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 http://universe-review.ca Optical Detection Opto-electronic Detection vs. Others (Biomolecular Signalling) Limits of communication, bit error rate Shot Noise Shot Noise, Johnson Noise, 1/f Noise Shot Noise ~ Poisson Process Dt very small P(0,Dt) + P(1,Dt) = 1 P(1,Dt) = a(Dt); a = rate constant No arrivals over t + D t ; P(0, t + D t) P(0, t + D t) = P(0,t) P(0,D t) What is P(0, t)? In a pulse of width t, what is the probability of it containing N photons? P(N) t 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,t)/dt = - a P(0, t) P(0, t) = e- a t ; 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 / N! m Poisson Distribution Optical Shot Noise N = 6; Only 16% of pulses have 16 photons; e-6 probability of having no photons P(N) = (Nm)N e –Nm / N! Variation is fundamental Signal to Noise Ratio Shot Noise on a Photocurrent 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 3K 1,000 oC http://en.wikipedia.org/wiki/Black_body 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 • Signal + Noise results in bit errors… • Noise statistics of signal, detector, amplifier determine PDF Output Current A01 2s1 Id s(1) = expectation current value Decision Level 2s0 s(0) = expectation current value A10 Probability 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 p] BER vs Q BER 10-5 10-7 10-9 6 Q Design Assume a perfect quantum detector. Amplifier input impedance is 50 Ohms. Shunt Capacitance 2 pF. Design a 100 Mbps link at 1.5 mm. 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