Comunicações Ópticas Noise in photodetectors MIEEC EEC038. Henrique Salgado Receiver operation

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1 Comunicações Ópticas Noise in photodetectors MIEEC EEC038 Henrique Salgado Receiver operation Noise plays a fundamental role in design of an optical receiver Optical data link

2 Receiver performance Noise gives origin to errors at the decision circuit Digital receiver performance measured in terms of Bit Error Rate (BER): BER = N e N t = N e Bτ The power required at the receiver to obtain a desired BER is called Sensitivity. Signal-to-noise ratio (SNR): S N = signal power from photocurrent photodetector noise power + amplifier noise power Photodector noise Sources of Noise

3 Quantum noise Follows a Poisson process Is a result of the random arrival of photons-generation of carriers. Photodiode illuminated by power P(t) N = R q τ 0 P (t)dt = η hν τ 0 P (t)dt = ηe hν N : average value of electron-hole pairs generated over the interval! E: energy received over the same interval of time Quantum noise Probability The effective number of electron-hole pairs over the interval of time! varies according with the Poisson distribution: N n e P r (n) = N n! P r (n) : probability that the number of carriers generated is n in interval! Example: optical link, " = 850 nm, BER = 10-9 What is the energy required in the pulse to have a probability of 10-9 that a logical 0 is detected when a 1 is transmitted.

4 Quantum noise P (n = 0) 10 9 N = 9 ln electron-hole pairs E = ( ) 21 hc η λ (21/!) photons What is the sensitivity of this receiver for a bit rate of Rb=10 Mb/s? ( ) 21 hc/λ P av = = 21 pw = 76 dbm η 2T b Assuming that the number of 1s and 0s are transmitted with equal probability Photodiode noise Quantum noise (or shot noise) If the incident photons per symbol is large the Poisson distribution can be approximated very closely by a Gaussian distribution (white noise) Mean-square noise current I: average photocurrent < i 2 Q >= 2qIB B: bandwidth of the electrical receiver The average photocurrent has three components I = I p + I dark Ip: primary current due to the incident light Idark: output current of device with no illumination

5 Photodiode noise Dark current I dark = I D + I L ID: dark bulk current, thermally generated electrons in the pn junction IL: leakage surface current, due to surface defects Thermal noise < i 2 T >= 4k BT B R L Photodiode noise APD noise signal current is multiplied by the gain of the APD the statistical nature of the avalanche gain introduces additional noise, excess noise factor F(M) < i 2 Q >= 2qIBM 2 F (M) F (M) M x, 0 x 1 Surface current is not multiplied by the gain of the APD < i 2 N >=< I 2 Q > + < i 2 D > + < i 2 L > = 2q(I p + I D )M 2 F (M)B + 2qI L B

6 Signal-to-noise ratio S N = 2q i 2 p M 2 ( I p + I D) M F( M ) B + 2qI LB + 4kBTB / RL 2 <Ip2> : valor quadrático médio da fotocorrente devido ao sinal Ip : valor médio da fotocorrente primária ID : corrente escura M : valor médio do ganho de avalanche B : banda equivalente do ruído q : carga do electrão IL : corrente de fuga RL : resistência de carga Error Probability Gaussian approximation Signal plus noise follows a Gaussian distribution f(s)ds: probability that the signal, in a certain instant, is betwen s and s+ds. f(s) = 1 2πσ 2 e (s m)2 /2σ 2

7 Error probability Calculation of the probability of error at the receiver (BER) At the input of the detector pulses have amplitude V Bit 1: average bon, variance! 2 on Bit 0: average boff variance! 2 off In general!on >! 2 off due to shot noise Error Probability Bit 0 was sent: probability that noise exceeds threshold value v th P 0 (v th ) = = Bit 1 was sent: probability that signal-plus-noise is below threshold P 1 (v th ) = = v th p(y 0)dy 1 2πσoff v th e (v b off ) 2 2σ 2 off dv vth p(y 1)dy 1 2πσon vth e (bon v) 2 2σon 2 dv

8 Error probability Total error probability P e = a P 1 (v th ) + b P 0 (v th ) 1s and 0s with equal probability BER = P e = 1 4 P e = 1 2 [P 1(v th ) + P 0 (v th )] { ( ) ( )} vth b off vth b erfc on + erfc 2σoff 2σon erf(x) = 2 π x 0 e y2 dy Error probability Optimum value for threshold voltage v th b off = v th b on = Q σ off σ on P e = BER = 1 ( ) Q2 2 erfc For Q > 3, For Q = 6, BER e Q2 /2 Q 2π BER = 10 9

9 BER vs Q Bit Error Rate Simplified model Probability distribution with the same variance for 0s and 1s: σ on = σ off From which it follows that v th b off = b on v th v th = b on+b off 2 Threshold voltage is the average of the two logical levels If b off = 0, v th = b on (V is voltage for level 1) 2 = V 2

10 BER-Simplified model b off = 0, Q = V 2σ = 1 2 S N V/s = signal voltage/noise rms = S/N BER = 1 2 erfc ( ( ) S N db = 20 log V 2 2σ ) = 1 2 erfc ( S/N 2 2 ( ) ( ) S V = 20 log N σ ) BER versus SNR

11 Example 1 BER=10-5, Rb = 2 Mb/s, telephone line 1 error in 105 transmitted bits This is an error for every 105/2x106 = 0.05 seconds This is not acceptable Increasing the BER to 10-9 equivalent to 1 error for every 109/2x106 = 8.3 min For higher rates BER should be even lower Calculation procedure 1. For a given BER, SNR is determined BER = 10 9 V σ = 12, SNR = 20 log ( ) V σ = For a known receiver noise,! can be calculated 3. Usually, noise is referred at the input of the receiver V σ = I p < i 2 N > 4. Minimum value for the current required to achieve the specified BER I p,min = S/N 5. Calculation of receiver sensitivity < i 2 N > P min = I p,min R = σ S/N R

12 Example 2 Calculate the receiver sensitivity for BER of 10-6 PIN diode with responsitivity of 0.4 A/W Load resistor R L = 50!, thermal noise dominant ( T = 400 K) Bandwidth of the receiver B = 10 MHz V σ = 9.5 = I p < i 2 T >, < i 2 T > = 4kB T B R L P min = I p R = 9.5 < i 2 T > 0.4 SNR = 19.6 db = 56.6 na = 1.3 µw Analogue receivers Aplications: voice, video (CATV) RF and microwaves Performance of the receiver measured in terms of the signal-to-noise ratio (SNR) Intensity modulation of the optical power An electrical signal is used to directly modulate an optical source about some bias point IB I(t) = I B + I s P (t) = P t + P s

13 Analogue receivers For a semiconductor laser P t = ( dp di P s = ( dp di ( P (t) = P t 1 + P ) ( s = P t 1 + P t = P t (1 + m s(t)) ) (IB I th ) ) Is m is the optical modulation depth (or modulation index) m = I I B I th, I s = I s(t) I s I B I th ) Analogue receivers Photocurrent generated at the receiver i s (t) = RMP r (1 + m s(t)) = I p M (1 + m s(t)) For a sinusoidal signal < i 2 s >= 1 2 (MmI p) 2 Signal-to-noise ratio SNR = (I p Mm) 2 /2 2q(I p + I D )M 2 F (M)B + (4k B T B/R eq )F t Ft noise figure of the amplifier

14 Analogue receivers PIN photodiode M = 1, F(M) = 1 For low incident optical powers the shot noise will be small and the circuit noise will dominate SNR = (I pmm) 2 /2 (4k B T B/R eq )F t = 1 2 (R2 m 2 P 2 r ) (4k B T B/R eq )F t For large optical signals incident on the PIN diode, the quantum (shot) noise associated with the detection process will dominate SNR = I pm 2 4qB = Rm2 P r 4qB APDs Advantage for low signal levels increase in SNR in the region where quantum noise is not dominant there exists an optimum value for the gain of the APD as the gain increases from low value the SNR increases until the quantum noise term becomes comparable to the circuit noise term. No advantage for large optical signal levels the detector noise increases more rapidly with increasing gain that the signal level (see next figure).

15 APD versus PIN Avalanche gain at optimum value