Download Transmitter, Amplifier and Receiver Design

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
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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.
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ISI is minimized when:
Vout (t ) 
sin( 2Bt )
1
Vmax
2Bt 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 )
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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)
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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  MRPin1
I 0  MRPin0
 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 Qf   T / M )
R
Shot noise limited
PIN
Q qf / R
APD
sen
(Q qf / R)2(k A M opt
 1  k A ) (worse)
Thermal noise limited
Q T / R ~ f
(Q T / R) / M (better)
2
2
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