Transcript EE 230: Optical Fiber Communication Lecture 12

EE 230: Optical Fiber Communication
Lecture 12
Receivers
From the movie
Warriors of the Net
Receiver Functional Block Diagram
Fiber-Optic Communications Technology-Mynbaev & Scheiner
Receiver Types
+Bias
+Bias
+Bias
Is
Is
Is
Output
RL
50 
Output
Output
RL
Amplifier
Rf
Ct
Ct
Amplifier
Equalizer
Amplifier
Low Impedance
High Impedance
Transimpedance
Low Sensitivity
Easily Made
Wide Band
Requires Equalizer for high BW
High Sensitivity
Low Dynamic Range
Careful Equalizer Placement Required
High Dynamic Range
High Sensitivity
Stability Problems
Difficult to equalize
Equivalent Circuits of an Optical
Receiver
High Impedance Design
Transimpedance Design
Transimpedance with Automatic Gain Control
Fiber-Optic Communications Technology-Mynbaev & Scheiner
Receiver Noise Sources
Photodetector without gain
•Photon Noise
Also called shot noise or
Quantum noise, described by
poisson statistics
•Photoelectron Noise
Randomness of photodetection
process leads to noise
•Gain Noise
eg. gain process in APDs or
EDFAs is noisy
•Receiver Circuit noise
Resistors and transistors in the
the electrical amplifier contribute
Photodetector with gain (APD)
to circuit noise
Johnson noise (Gaussian and white)
Vn
Noise Power=4kTB 
R
 in 2 R
Frequency
4kTB

R
Noise Power
Vrms  4kTRB
Shot noise (Gaussian and white)
rms noise current  in 2
1/ 2
  2qIB 
“1/f” noise
spectral density=
K
f
V 2 /Hz
1/ 2
Frequency
Noise Power
irms
2
Noise Power
Noise
1/f noise
Fc
for FETs
Frequency
4kT
K=
fc
gm
where fc is the FET corner frequency and  is the channel noise factor
Johnson (thermal) Noise
Noise in a resistor can be modeled as due to a
noiseless resistor in parallel with a noise current
source
The variance of the noise current source is given by:
s i2 = i 2 »
4kBTB
R
Where kB is Boltzman's constant
T is the Temperature in Kelvins
B is the bandwidth in Hz (not bits/sec)
Photodetection noise
The electric current in a photodetector
circuit is composed of a superposition of
the electrical pulses associated with
each photoelectron
Noise in photodetector
The variation of this current is called shot
noise
If the photoelectrons are multiplied by a gain
mechanism then variations in the gain
mechanism give rise to an additional
variation in the current pulses. This variation
provides an additional source of noise, gain
noise
Noise in APD
Circuit Noise
Signal to Noise Ratio
Signal to noise Ratio (SNR) as a function of the
average number of photo electrons per receiver
resolution time for a photo diode receiver at two
different values of the circuit noise
Signal to noise Ratio (SNR) as a function of the
average number of photoelectrons per receiver
resolution time for a photo diode receiver and an
APD receiver with mean gain G=100 and an excess
noise factor F=2
At low photon fluxes the APD receiver has a better
SNR. At high fluxes the photodiode receiver has
lower noise
Dependence of SNR on APD
Gain
Curves are parameterized by
k, the ionization ratio between
holes and electrons
Plotted for an average
detected photon flux of 1000
and constant circuit noise
Receiver SNR vs Bandwidth
Double logarithmic plot showing the receiver bandwidth dependence of the
SNR for a number of different amplifier types
Basic Feedback Configuration
Ii
Is
A Vi +
Is
If
Ri
Ro
Parallel Current Feedback
Lowers Input Impedance
is  i f  ii
bVo
V
is  b AVi  i
Ri
Zin 
Vi
Ri

is 1  Rm b
Parallel Voltage Sense:
Voltage Measured and held
Constant
=> Low Output Impedance
Zo 
Vtest
Ro
Ro


I test 1  b ARi 1  b Rm
Stabilizes Transimpedance Gain
Vo  Aii Ri
ii  is  i f  is  b Vo
Ii
ZtIi +
Vo  ARi  is  b Vo 
Zt 
Vo
ARi
Rm


is 1  ARi b 1  Rm b
Zi
-
Zo
Transimpedance Amplifier
Design
i
+
Zi
Output Voltage
Proportional to
Input current
Zero
Input
Impedance
Vi
A Vi +
Ri
Ro
Typical amplifier model
With generalized input impedance
And Thevenin equivalent output
is
+
Vi
-
A Vi +
Ri
-
Vo  AVi  ARi ii
Calculation of
Openloop transimpedance gain: Rm V  ARi  Rm
is
Ro
Vo
Transimpedance Amplifier Design
Example
Vcc1
Controls open loop gain
of amplifier, Reduce to decrease
“peaking”
Vcc2
See Das et. al. Journal of Lightwave Technology
Vol. 13, No. 9, Sept.. 1995
Rc
Q2
Q1
Out
Photodiode
Most Common Topology
Vbias
Has good bandwidth
and dynamic Range
Rf
For an analytic treatment of the design of maximally flat
high sensitivity transimpedance amplifiers
Transimpedance approximately equals Rf
low values increase peaking and bandwidth
“Off-the-shelf” Receiver Example
i2
i2
Detector
Re sistor
 2qId I2B  1.8x1017 A2

4kT
2
I2B  i Detector
 1.9 x1012 A2
Rs
NF
i
2
i
2
Re sistor  Amp1
1
4kT
2
10

10 I2B  iDetector
 7.5x1012 A2
Rs
Re sistor  Amp1 Amp 2
4kT

10
Rs
NFTotal
10
2
I2B  i Detector
 7.6x1012 A2
Sensitivity
45.22dBm
20.14dBm
16.63dBm
16.59dBm
Bit Error Rate
BER is equal to number of errors divided by
total number of pulses (ones and zeros).
Total number of pulses is bit rate B times
time interval. BER is thus not really a rate,
but a unitless probability.
Q Factor and BER
Q
Vth  Voff
 off

Von  Vth
 on
1
 Q 
BER  1  erf 

2
 2 
BER vs. Q, continued
When off = on and Voff=0 so that Vth=V/2, then
Q=V/2. In this case,
1
 V 
BER  1  erf 

2
 2 2 
Sensitivity
The minimum optical power that still gives a
bit error rate of 10-9 or below
(Smith and Personick 1982)
Receiver Sensitivity
Sensitivity= Average detected optical power for a given bit error rate
P


  hv Q
 q 


i2
1/2
Probability of error vs. Q is to good approximation:

For pin detectors
i2  i2
amplifier
 2qId I2B

Q2 /2
P E   1 e
 
2 Q
eg. for a SNR = Q = 6


Bit Error Rate= P(E)=10-9
Dynamic Range and Sensitivity
Measurement
Dynamic range is the Optical power difference
in dB over which the BER remains
within specified limits (Typically 10-9/sec)
Input
Optical
Power
Dynamic Range
The low power limit is determined by the
preamplifier sensitivity
The high power limit is determined by the nonlinearity and gain compression
High Rf
Feedback Resistance
Low Rf
(High Impedance Preamplifier)
(Transimpedance Preamplifier
Patten
Generator
Transmitter
Adjustable
Attenuator
Optional Clock
Experimental Setup
Optical
Receiver
Bit Error
Rate Counter
Eye Diagrams
Transmitter
“eye” mask
determination
Formation of eye diagram
Eye diagram
degradations
Computer Simulation of a distorted eye diagram
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Power Penalties
• Extinction ratio
• Intensity noise
• Timing jitter
Extinction ratio penalty
Extinction ratio rex=P0/P1
 1  rex  2RP

Q  
 1  rex   on   off
 1  rex 

 ex  10 log 
 1  rex 
Intensity noise penalty
rI=inverse of SNR of transmitted light
 I  R PrI
 I  10 log 1  r Q
2
I
2

Timing jitter penalty
Parameter B=fraction of bit period over which
apparent clock time varies
 4 2

2
b  
 8 B 
 3



1 b / 2

 J  10 log 
2
2 2

 1  b / 2  b Q / 2 