NOISE N. Libatique ECE nd Semester

Optical Detection: Biomolecular Signaling

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

Optical Detection Opto-electronic Detection vs. Others (Biomolecular Signalling) Opto-electronic Detection vs. Others (Biomolecular Signalling) Limits of communication, bit error rate Limits of communication, bit error rate

Shot Noise Shot Noise, Johnson Noise, 1/f Noise Shot Noise, Johnson Noise, 1/f Noise Shot Noise ~ Poisson Process Shot 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) = (N m ) N e –N m / N!

Poisson 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 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 P total = P signal + P background MeanSquareCurrent shot proportional to P total I(W/cm 2 ) = (T/645) 4 (T in K) 4.7x10 -2 W/cm 2 at 300 K Human Body 2 m 2  1 kW Spectrally distributed 1,000 o C 3 K

Spectral Distribution

Bit Error Rates Analog Signals: SNR ratio Digital Signals: BER Telco Links = Datacomms and Backplanes = Quality Factor Power required to achieve Q and BER? 0.1 dB significant as fiber losses are low…

Probability Distribution Function Decision Level s(0) = expectation current value s(1) = expectation current value 2121 2020 IdId Output Current Probability A 10 A 01 Signal + Noise results in bit 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 A 01 = probability that space is seen as mark A 10 = probability that mark is seen as space P(E) = p(0) A 01 + p(1) A 10 Assume Gaussian statistics  P(E) = Integral[Exp[-x 2 /2],{x,Q,Infinity}]/Sqrt[2  ]

BER vs Q Q BER

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