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Transmitter, Amplifier and Receiver Design 1. Transmitter design Transmitter function: E-O conversion a) Laser package b) Transmitter configuration Current Driver Electrical Data In Optical Data Out DC Bias Power Control Temperature Control Thermister TEC Warning 2. Amplifier design Amplifier function: direct optical amplification without O-E-O conversion EDFA amplifier configuration Optical Signal Input EDF ISO Optical Signal Output ISO PhotoDetector Pump Laser PhotoDetector Gain Control Unit 1 3. Receiver design Receiver function: O-E conversion a) Receiver configuration +V Optical Signal Preamp. Equalizer Amp. Electrical Signal Decision Clock Recovery AGC Recovered Data Signal Linear Channel b) Linear channel design The photo-detector can be viewed as a current source, the linear channel converts the current pulse to the voltage pulse (through the preamplifier), then shapes and amplifiers the voltage pulse (through the main amplifier and the equalizer). The receiver noise is proportional to the receiver bandwidth and can be reduced by using a band-limited linear amplification channel. However, if the linear channel bandwidth f B (in-coming signal bit rate), the voltage pulse spreads beyond the allocated bit slot. Such a spreading can interfere with the detection of neighboring bits, a phenomenon referred to as inter-symbol interference (ISI). Our goal is then to design a band-limited amplification channel in such a way that ISI is minimized. The output voltage can be written as: Vout (t ) zT (t t ' ) I p (t ' )dt ' where I p (t ) is the photodiode current, zT (t ) is the transfer response (impedance) of the linear channel. Or: Vout ( ) Z T ( ) I p ( ) where Z T ( ) can be further written as: Z T ( ) G p ( )G A ( ) H F ( ) / Yin ( ) where Yin ( ) is the input admittance and G p ( ), G A ( ), H F ( ) are transfer functions of the preamplifier, the main amplifier and the equalizer. 2 ISI is minimized when: Vout (t ) sin( 2Bt ) 1 Vmax 2Bt 1 (2 Bt ) 2 or: Vout ( ) V {1 cos[ /( 2 B)]} / 2, /( 2 ) B 0, /( 2 ) B For an ideal bit stream with NRZ format: I p ( ) I sin( 2B )/ 2B which corresponds to rectangular input pulses of duration TB 1 / B . Hence the optimized impedance transfer response should be: Z T ( ) V cot( ) 4B I 4B c) Receiver noise Shot noise (from O-E counting process in PIN): I (t ) I p i s (t ) RPin is (t ) where I p RPin is the average current, i s (t ) is a stationary random process with Poisson statistics. If the total received photon numbers are significant (received average optical power Pin is not very small), i s (t ) can be approximated by the Gaussian statistics with its variance given by: s2 is2 (t ) S s ( f )df 2qI p f according to the Wiener-Khinchin theorem and the fact that the shot noise is “white”: S s ( f ) qI p where q is the electron charge. Thermal noise (from carrier moving in any conductor): I (t ) I p i s (t ) iT (t ) 3 where iT (t ) is current fluctuation induced by thermal noise which can be modeled as a stationary Gaussian random process with a nearly constant spectral density (“white noise”) given by: ST ( f ) 2k BT / RL with k B , T , RL as the Boltzmann constant, the absolute temperature and the load resistor, respectively. Thermal noise variance can then be derived as: T2 iT2 (t ) ST ( f )df 4k B T f RL Considering the dark current from PIN and the enhancement to thermal noise from the components other than the load resistor in the linear channel, the total noise variance is: 2 [ I (t ) I p ]2 s2 T2 [2q( I p I d ) 4k BT Fn ]f RL where I d , Fn are the PIN dark current and the amplifier noise figure, respectively. d) Receiver signal to noise ratio PIN receiver: R 2 Pin2 SNR 4k T [2q( RPin I d ) B Fn ]f RL APD receiver: M 2 R 2 Pin2 SNR 4k B T Fn ]f RL where M , FA are the APD gain and the APD excess noise factor, respectively. ( FA k A M (1 k A )(2 1/ M ) , where k A is the ionization-coefficient ratio.) [2qM 2 FA ( RPin I d ) Shot noise limited PIN SNR ~ Pin APD SNR ~ Pin / FA (worse) Thermal noise limited SNR ~ Pin2 (large load impedance required) SNR ~ M 2 Pin2 (better) e) Receiver sensitivity The bit error rate can be computed as: BER p(1) P(0 / 1) p(0) P(1 / 0) 4 where: P(0 / 1) P(1 / 0) 1 1 2 1 0 ID exp[ ( I I1 ) 2 I ID 1 ]dI erfc( 1 ) 2 2 2 1 1 2 (I I 0 ) 2 I I0 1 exp[ ]dI erfc( D ) 2 ID 2 2 0 2 0 2 and: I 1 MRPin1 I 0 MRPin0 12 [2qM 2 FA ( I 1 I d ) 4k B TFn / RL ]f 02 [2qM 2 FA ( I 0 I d ) 4k B TFn / RL ]f I D is the decision threshold, it should be such chosen that minimizes the BER . We may find: I1 I D I D I 0 Q 1 0 and: p(1) p(0) 1 / 2 Therefore: 1 Q BER erfc( ) 2 2 where: I I Q 1 0 1 0 and: I 1I 0 ID 0 1 0 1 Receiver sensitivity can be calculated by letting P0 0, P1 2P min and neglecting the dark current: Q P min (qFA Qf T / M ) R Shot noise limited PIN Q qf / R APD sen (Q qf / R)2(k A M opt 1 k A ) (worse) Thermal noise limited Q T / R ~ f (Q T / R) / M (better) 2 2 5