Chapter 4 Optical Receivers Configuration Requirements high sensitivity fast response low noise low cost & high reliability optical signal voltage supply O/E pre-amplifier automatic gain control amplifier filter decision circuit clock recovery PIN or APD data Front End Linear Channel Data Recovery 2018/11/12 OE of HUST

Chapter 4 Optical Receivers Basic Concept Common Photodetectors Receiver Design Receiver Noise Receiver Sensitivity Sensitivity Degradation 2018/11/12 OE of HUST

4.1 Basic Concepts 4.1.1 Detector Responsivity Stimulated absorption: photon an electron-hole pair Photon current: , R: responsivity Quantum efficiency: 2018/11/12 OE of HUST

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4.1.2 Rise time and Bandwidth Pin Vout(t) 90% 10% V0 Tr input voltage: 0~V0 output voltage: rise time: Tr For photodiode: τRC: time constant of the RC circuit, τtr: transit time of carriers Vd: drift velocity 2018/11/12 OE of HUST

Bandwidth of a photodiode Trade-off between Dark current Caused by stray light or thermally generated electron-hole pairs 2018/11/12 OE of HUST

Chapter 4 Optical Receivers Basic Concept Common Photodetectors Receiver Design Receiver Noise Receiver Sensitivity Sensitivity Degradation 2018/11/12 OE of HUST

4.2 Common photodetectors 4.2.1 p-n photodiodes a reverse biased p-n junction 2018/11/12 OE of HUST

the presence of a diffusive component distorts the temporal response of a photodiode. solution: decreasing the widths of the p- and n- regions; increasing the depletion-region width. 2018/11/12 OE of HUST

4.2.2 p-i-n photodiodes 2018/11/12 OE of HUST

Double-heterostructure design i-layer → high resistance → large electric field → the depletion region throughout it → drift component dominates over the diffusion component → Double-heterostructure design p-InP n-InP InGaAs absorption can only occur in the middle of i-layer diffusive component is eliminated completely 2018/11/12 OE of HUST

4.2.3 Avalanche Photodiodes Basic concepts 2018/11/12 OE of HUST

a photon a single primary electron many secondary electrons & holes Impact ionization: an accelerating electron can acquire sufficient energy to generate a new electron-hole pair. a photon a single primary electron many secondary electrons & holes i-layer: absorption p-layer: multiplication through impact ionization impact-ionization coefficients: ( : electrons; : holes ) depend on material and on the electric field. 2018/11/12 OE of HUST

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ie, ih: electron & hole current respectively Multiplication factor the current flow within multiplication layer ie, ih: electron & hole current respectively the total current: 2018/11/12 OE of HUST

where is ionization coefficient ratio assuming that: , the electric field across the gain region is uniform ( are constants), only electrons cross the boundary to enter the n-region. boundary condition: where is ionization coefficient ratio 2018/11/12 OE of HUST

Avalanche process: intrinsically noisy, gain factor fluctuates around an average value. Responsivity avalanche breakdown! when M: average APD gain 2018/11/12 OE of HUST

the effective transit time Bandwidth the low frequency gain the effective transit time 2018/11/12 OE of HUST

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SAM-APD (Separate Absorption & Multiplication) APD structures Reach-through APD SAM-APD (Separate Absorption & Multiplication) Absorption & Multiplication materials is the same bandgap. 1) 0.85um: Si, KA<<1 2) 1.31um, 1.55um: Ge, InGaAs p+-InP n+-InP n-InP i-InGaAs M A - + 2018/11/12 OE of HUST

large bandgap → can be applied high reverse voltage InP: large bandgap → can be applied high reverse voltage 2018/11/12 OE of HUST

Problem: large bandgap difference between InP & InGaAs Eg-Inp=1.35eV Eg-InGaAs=0.75eV 1) holes generated are trapped at the heterojunction 2) slow response & small bandwidth Solution: 2018/11/12 OE of HUST

SAGM-APD (Separate Absorption Grading & Multiplication) p+-InP n+-InP n-InP InGaAs M A - + InGaAsP G 2018/11/12 OE of HUST

SAGCM-APD (C-charge layer) p+-InP N+-InP n-InP InGaAs M A - + InGaAsP G C 2018/11/12 OE of HUST

Chapter 4 Optical Receivers Basic Concept Common Photodetectors Receiver Design Receiver Noise Receiver Sensitivity Sensitivity Degradation 2018/11/12 OE of HUST

4.3.1 光接收机的前端 光接收机前端由光电二极管和前置放大器两部份组成，其作用是将光纤线路末端的光比特流转换为时变电流信号，然后进行预放大，以便后级电路作进一步处理。 2018/11/12 OE of HUST

(a)高（低）阻抗前端；(b)跨阻抗前端 图4.10 光接收机前端的等效电路 (a)高（低）阻抗前端；(b)跨阻抗前端 2018/11/12 OE of HUST

光接收机前端的设计应折衷考虑速度和灵敏度这两个指标。由于采用较大的负载阻抗RL可以提高输入到前置放大器的电压，因而高阻抗前端经常被采用，如图4.10(a)所示。同时大的负载阻抗可以降低热噪声，提高接收机灵敏度。但高阻抗前端的主要缺点在于其带宽较低，由带宽表达式 可知，负载电阻越大，带宽越小，其中 表示光电二极管和用于放大的晶体管带来的总电容。 2018/11/12 OE of HUST

接收机的带宽受它的低频分量所限制，如果带宽小于信号的比特率，则这种高阻抗前端不能被采用。有时需要采用均衡器来提高带宽，均衡器对低频分量的衰减比对高频分量的多，因而可以有效地提高前端的带宽。对于接收机的灵敏度不是最关键指标的通信系统，当然，可以简单地采用减小RL的方法来增加带宽，但必然会引起灵敏度的降低，热噪声的增加。这种小负载阻抗的前端称为低阻抗前端。 2018/11/12 OE of HUST

跨(互)阻抗前端能同时具备以上两种前端的优点，在具备高灵敏度的同时，也具有大的带宽。如图4 跨(互)阻抗前端能同时具备以上两种前端的优点，在具备高灵敏度的同时，也具有大的带宽。如图4.10(b)所示，这种前端将负载电阻连接为反相放大器的反馈电阻，因而又称互阻抗前端，它是一个性能优良的电流—电压转换器，即使RL很高，而负反馈使有效输入阻抗降低了G倍，G是前置放大器增益，从而使其带宽比高阻抗前端增加了G倍。 2018/11/12 OE of HUST

4.3.2 光接收机的线性通道 光接收机的线性能道由一个高增益放大器(称为主放大器)和一个低通滤波器组成。有时在主放大器前接入一个均衡器以校正前端有限的带宽。主放大器的增益可以自动调整以使平均输出电压限制在固定电平而不随输入平均光功率而变。低通滤波器对电压脉冲进行整形，降低噪声，以避免引起码间串扰(ISI)。由后面一节中对噪声的分析可知，接收机噪声正比于接收机带宽，可采用带宽 小于比特率B的低通滤波器来降低噪声。在接收机设计中其他部件的带宽均大于该低通滤波器的带宽，因此接收机带宽主要由线性通道的低通滤波器决定。当 时，电脉冲展宽超过了规定的比特时隙，将可能干扰相邻比特时隙的检测，引起码间串扰。滤波器设计时应使码间串扰减小到最低程度。 2018/11/12 OE of HUST

前置放大器，主放大器和滤波器起一个线性系统的作用，故可称为线性通道，线性通道的输出电压可写为 (4.3.1) (4.3.2) 前置放大器，主放大器和滤波器起一个线性系统的作用，故可称为线性通道，线性通道的输出电压可写为 式中Ip(t)为光电二极管的输出光电流（ ）。经傅里叶变换，在频域可得 式中ZT是频率ω处的总阻抗；“～”对应傅里叶变换结果， 2018/11/12 OE of HUST

ZT (ω)由接收机各组成部分对应的传递函数决定，可表示为 式中， 是输入导纳； 、 和 分别为前置放大器、主放大器和滤波器的传递函数。将式(4.3.2)中的 和 作归一化处理，得到归一化谱函数 和 ，这两个谱函数分别与输入和输出脉冲的傅里叶变换相关。 (4.3.3) 2018/11/12 OE of HUST

式中， 为线性通道的总传递函数，与总阻抗 的关系为 = 。若放大器的带宽远大于低通滤波器的带宽，则有 。 式(4.3.2)可改写成 式中， 为线性通道的总传递函数，与总阻抗 的关系为 = 。若放大器的带宽远大于低通滤波器的带宽，则有 。 研究表明，当对应升余弦滤波器的传递函数时 码间串扰(ISI)最小，式中 ，B为比特率。 (4.3.4) (4.3.5) 2018/11/12 OE of HUST

对上式作傅里叶逆变换，得线性通道的响应为 对应于线性通道输出判决电路接收到的电压脉冲 的形状。在t=0判决时刻， =1，信号最大，而当t=m/B，m为整数时， =0，t=m/B对应于相邻比特的判决时刻。所以式(4.3.6)对应的电脉冲不会干扰相邻比特。 (4.3.6) 2018/11/12 OE of HUST

(4.3.7) （4.3.8） 线性通道的输出波形由（4.3.6）式决定，进而由（4.3.4）式可以得到线性通道的传递函数 ，并可写成 线性通道的输出波形由（4.3.6）式决定，进而由（4.3.4）式可以得到线性通道的传递函数 ，并可写成 对于非归零（NRZ）格式的理想比特流（脉宽TB＝1／B的矩形脉冲）， ，则有 （4.3.8）式表示为了理想情况下线性通道的频率响应。但必须注意，输入脉冲通常都不是理想矩形脉冲，输出脉冲波形也不与（4.3.6）式相对应，因而不可避免地会发生一定程度的码间串扰。 (4.3.7) （4.3.8） 2018/11/12 OE of HUST

图4.11 非归零格式的理想和退化眼图 2018/11/12 OE of HUST

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Chapter 4 Optical Receivers Basic Concept Common Photodetectors Receiver Design Receiver Noise Receiver Sensitivity Sensitivity Degradation 2018/11/12 OE of HUST

Wiener-Khinchin theorem 4.4.1 Noise Mechanisms Shot noise: electrons are generated at random times Photodiode current　 A stationary random process with Poisson statistics (approximated by Gaussian statistics) Wiener-Khinchin theorem 2018/11/12 OE of HUST

considering the dark current Id, the two-sided spectral density the one-sided spectral density considering the dark current Id, 2018/11/12 OE of HUST

Thermal noise: At a finite temperate, electrons move randomly in a resistor in the absence of an applied voltage. iT(t): a current fluctuation induced by thermal noise A stationary random process with Gaussian statistics Fn: factor by which thermal noise is enhanced by various resistors used in pre and main amplifier 2018/11/12 OE of HUST

is(t), iT(t), are independent random processes Total noise is(t), iT(t), are independent random processes 2018/11/12 OE of HUST

4.4.2 p-i-n Receivers Noise-equivalent power (NEP): optical power per unit bandwidth required to produce SNR=1 Detectivity: (NEP) -1 Thermal-noise limit 2018/11/12 OE of HUST

Shot-noise limit SNR can be written in term of the number of photon Np contain in the “1” bit by choosing 2018/11/12 OE of HUST

4.4.3 APD Receivers Shot – noise enhancement Secondary electron-hole pairs generates at random times through the process of input ionization. FA(M): the excess noise factor 2018/11/12 OE of HUST

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Thermal – noise limit Shot – noise limit: Optimum APD gain 2018/11/12 OE of HUST

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Chapter 4 Optical Receivers Basic Concept Common Photodetectors Receiver Design Receiver Noise Receiver Sensitivity Sensitivity Degradation 2018/11/12 OE of HUST

4.5 Receiver Sensitivity 4.5.1 Bit - Error Rate BER (bit - error rate) : probability of incorrect identification of a bit by the decision circuit of the receiver. Sensitivity: the minimum average received power Prec required by the receiver to operate at a BER of 10 -9 . 4.5.1 Bit - Error Rate Threshold value ID and bit error (Fig.4.18) When bit error will occur? BER (assuming p(1)=p(0)=1/2) 2018/11/12 OE of HUST

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(complementary error function) 2018/11/12 OE of HUST

decision threshold ID should be optimized to minimize the BER. The minimum occurs when ID is chosen such that: 2018/11/12 OE of HUST

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4.5.2 Minimum Received Power Average received power 2018/11/12 OE of HUST

PIN: APD: 2018/11/12 OE of HUST

4.5.4 Quantum limit of photodetection 4.5.3 BER & SNR Thermal–noise limit Shot–noise limit 4.5.4 Quantum limit of photodetection DIY! 2018/11/12 OE of HUST

Chapter 4 Optical Receivers Basic Concept Common Photodetectors Receiver Design Receiver Noise Receiver Sensitivity Sensitivity Degradation 2018/11/12 OE of HUST

4.6 Sensitivity Degradation Power penalty: The increase in the minimum average received power because of non-ideal conditions: extinction ratio; intensity noise; timing jitter; mode-partition noise; parasitic reflections 2018/11/12 OE of HUST

4.6.1 Extinction Ratio ideal: rex =0 in fact: rex ≠0 Ib<Ith, P0=0, relaxation oscillation and electro-optical delay rise up. Ib>Ith, P0≠0, rex ≠0, modulation bandwidth rises up. For a PIN receiver, in the thermal noise limit: Power penalty: For a APD receiver, δex is larger by a factor of about 2 2018/11/12 OE of HUST

4.6.2 Intensity Noise Power fluctuation current fluctuation mode partition noise; parasitic reflection 2018/11/12 OE of HUST

BER floor! 2018/11/12 OE of HUST

4.6.3 timing jitter 2018/11/12 OE of HUST

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Chapter 5 Lightwave Systems 5.1 System Architectures 5.1.1 P2P 2018/11/12 OE of HUST

5.1.2 Distribution Networks 2018/11/12 OE of HUST

5.2 Design Guidelines 5.2.1 Power Budget 2018/11/12 OE of HUST

5.2.2 Rise-time Budget The rise time of RC circuit Tr 2018/11/12 OE of HUST

5.2.2 Rise-time Budget 2018/11/12 OE of HUST

思考题 某单模光纤通信线路长90km，工作在1550nm，色散系数D＝16ps/nmkm。若已知光发射机和光接收机的上升时间分别为Ttr＝50ps和Trec＝20ps，考虑单纵模激光器的半高全宽谱宽Δλ＝0.2nm，输入信号为RZ格式，按照上升时间预算线路允许工作速率为多少？ 2018/11/12 OE of HUST