Download chapter 04 -- Photodetector and Optical Receiver

Chapter 4
Photo-detectors and Optical Receiver
 4-1 Introduction
 4-2 Optical Sensible Semiconductor Material
 4-3 Photodiode
 4.3.1 PIN photodiode
 4.3.2 APD photodiode
 4.3.3 Noise Analysis of photodiode
 4-4 Detector
 4.4.1 Detector circuit
 4.4.2 Basic characteristic of detector circuit
 4.4.3 Noise Analysis of detector circuit
 4-5 Optical Receiver
 4.5.1 Digital optical receiver
 4.5.2 Main parameters of digital receiver
 4.5.3 Analog optical receiver
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4-1 Introduction
 Photo-sensitive devices
 photomultiplier、phototransistor、pyroelectric detector
 photoconductor、photodiode
 Photodiode
 small size、proper material、high sensitivity、rapid response
 Commercial Photodiodes
 PIN photodiode、APD photodiode
 Photo-detector
 detect weak optical signal and amplify with low noise
 Optical Receiver
 amplify、reshape、re-timing and re-generate the distorted
electronic signals
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4.2 Optical Sensible Semiconductor Material
 Photo-Electro effect (Einstein)




Photon absorption & ionization when l < lC
photo electron– electron-hole pair generation by photon
ionization energy for semiconductor ~1 eV (lC=1.24 mm)
IR < lC < UV, by controlling the composition and proportion
in compound semiconductor
 l for optical communication : 1.3 mm &1.55 mm
 Value electron and conduction band ~ energy band
 Energy barrier or forbidden gap (Eg)
 The energy gap between the trough of conduction band and
the peak of the value electron band
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4.2 Optical Sensible Semiconductor Material
 Electron transition (due to photon absorption)
 with proper energy (photon absorption) and
momentum, the electron will transit from value
electron band up to conduction band as a free
current carrier
 Possible when hc/l > Eg
 Low probability for indirect energy gap with
unmatched momentum : must be matched by
the phonon generated by thermal perturbation,
a low probability
 High probability for direct energy gap with
matched momentum : easy momentum
conservation when transition
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4.2 Optical Sensible Semiconductor Material
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4.2 Optical Sensible Semiconductor Material
 Indirect energy gap:
Si & Ge in IV group
 Direct energy gap:
GaAs & InGaAs in III-V group
 1.3 mm：
Ge (Eg = 0.67 eV) & InGaAsP (Eg = 0.89 eV)
 1.55 mm：
InGaAs (Eg = 0.77 eV)
 Tri-compound semiconductor :
by controlling the energy band distribution, the energy band and
the operating l can be tuned, and the momentum can be matched
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4.2 Optical Sensible Semiconductor Material
 Spectral sensitivity for common semiconductor
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4-3 Photodiode
 Intrinsic Semiconductor : Si & Ge
 P-type Semiconductor :
 Doped with III group (Acceptor)，free electric hole as the major current
carrier
 NP-type Semiconductor :
 Doped with V group (Donor)，free electron as the major current carrier
(with reverse direction)
 Space charge layer/depletion region
 At the PN junction，the major electric holes diffuse from P layer to N layer
and combine with its major electrons with the unmoved negative ions holes
left in P layer
 On the other hand， the major electrons diffuse from N layer to P layer and
combine with its major electric holes with the unmoved positive ions left in N
layer
 A space charge layer formed by two parallel different ions near the PN
junction
 Depletion region: all the major carriers are run out near the PN junction
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4-3 Photodiode
 Depletion electric field
 An electric field, directed from N to P, is formed by the two
different static charges groups
 When equilibrium, no diffusion occur due to energy barrier from
the depletion electric field
 When an electron-hole pair is generated by a photon absorption
in the depletion layer, the electron (hole) will be driven into N(P)
layer with a saturation drift speed.
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4.3.1 PIN photodiode
 To enhance the depletion electric field effect (from architecture)
 Inserting wide intrinsic (I) layer
 PN junction with double-hetero structure
 PIN structure :
 Thin P and N layers(1018~1019 ) to pass the photon into the I layer
 Thick I layer(N-type:1013~1014) as the photon absorption layer
 What happen to the Intrinsic layer
 Photons absorbed, and electron-hole pairs generated
 Photo-current formed when electrons are drifted to N layer and holes
to P layer, accelerated by the depletion electric field
 Only slow diffusion process outside the depletion region (I layer)
 Wider/Thicker Intrinsic layer
 Most absorption here
 Due to E field acceleration, carriers move quickly, ease photon absorption,
and achieve high quantum efficiency
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4.3.1 PIN photodiode
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4.3.1 PIN photodiode
 Double-heterostructure PIN photodiode
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4.3.1 PIN photodiode
 Double-heterostructure
 The material of intrinsic layer (InGaAs) is different
from those of P and N layers (InP)
 Eg = 1.35 eV for InP，
all photons l > 0.92 mm are transparent
 Eg = 0.75 eV for In53Ga0.47As，lC = 1.65 mm
all photons are absorbed in 1.3 < l < 1.6 mm
 All absorption occur in intrinsic layer, no slow
carriers outside the depletion layer
 Absorption efficiency ~ 100% with anti-reflection
coating and 4~5 mm width of intrinsic layer
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4.3.1 PIN photodiode
 Reverse bias voltage (several tens of volts)
 The electric holes in P layer
• Diffuse to PN junction
• drived to cathode with negative ions left in P layer
The depletion region are enlarged!
 The electron in N layer do in the same way, so the
positive depletion region are also enlarged!
 Both positive and negative charges near PN junction
are increased, so the width of depletion layer is
broadened.
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4.3.1 PIN photodiode
 The width of depletion layer is broadened as
W = {2ε[(1/ND)+(1/NA)].[(VD+Vb)/e]}1/2
where,
ε: the dielectric constant,
ND and NA : the concentration of Donor and Acceptor,
VD and Vb: depletion and bias voltages
 From energy level,
 The reverse bias voltage tear off the Fermi level of the PN
junction provide electrons (holes) more energy to drift
 From circuit’s view,
 Without major carrier, I layer has the higher resistance
than both sides, and take most voltage drop.
A higher E field can be expected.
 The bias circuit enable current flow, and is photo-conductive.
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4.3.1 PIN photodiode
 Reverse bias voltage
 In ideal case, optocurrent flows to both
ends as soon as the
electron-hole pairs
are generated;
 Opto-current flow is
proportional to the
incident optical
power.
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4.3.1 PIN photodiode
 Reverse bias voltage
 Square waveform distortion due to diffusion
and drift.
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4.3.2 APD photodiode
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4.3.2 APD photodiode
 I-V curve
The dashed line is the I-V curve of diode
The solid line is the I-V curve of photodiode
 Empirical multiplication (M) equation
When Vb < V < VB, VB(T) = VB(To)[1 + a(T-To)]
n(T) = n(To)[1+b(T-To)], a, b got from experiment
M = 1/[1-(V/VB)n]
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4.3.2 APD photodiode
 Avalanche Breakdown
Increasing bias voltage up to 50 ~hundreds of volts, E
field will achieve up to 106~108V/m)
In I layer, the photo-generated electron (hole) will drift
toward N (P) layer.
Gaining giant energy when drifting into the
multiplication region, the electron will impact and ionize
the second electron-hole pair, and continue the drift and
impact-ionization process.
The second electron-hole pair may proceed the same
process.
As a result, one incident photon can generate hundreds
of electrons-hole pairs and form current multiplication.
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4.3.2 APD photodiode
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4.3.2 APD photodiode
 Ionization rate (ae, ah)
The generated no. of electron-hole pair by the
electron (ae)/hole (ah) in unit distance.
When bias ~100V, E~4x107V/m, ae & ah ~10-4cm-1。
 Reach-Through Si-APD
The depletion region reach through the electrode
All photon are absorbed in I layer, and the first
electron-hole pair are generated.
Accelerated by the weak E field in depletion region,
the electron drift toward multiplication region were
the impact-ionization of the second electron-hole pair.
High doped (P+) incident layer can lessen the contact
resistance and benefit electrode contact.
The separation of E-field can decrease the required bias
except original acceleration and avalanche process.
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4.3.2 APD photodiode
 Ionization rate (ae, ah)
Assume Ie(x=0) = 0, only electron drift through
multiplication region, then Id(x=d) = 0，
Assume ae , ah indep. of x, and ae > ah, then :
M = (1 - kA)/{exp[1 - (1 - kA)aed] - kA}
where, kA= ah / ae
If ah = 0, then M = exp(aed);
If ah = ae, then M = 1/(1-aed);
When ah = ae = 1/d, then M→∞ (avalanche).
For noise-proof, single carrier ae >> ah is better.
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4.3.2 APD photodiode
 Ionization rate (ae, ah)
Assume Ie(x=0) = 0,
only electron drift
through multiplication
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4.3.2 APD photodiode
 Statistical Multiplication
The time of the second pair generation must be
added to the drift time, so the multiplication M
will be a function of frequency：
M(w) = Mo/{1+(wteMo)2}1/2
 Where Mo is the DC value, te the drift time of electron
as a function of kA.
 When ah < ae, te= kAtt. Assume tRC << te , we have
the bandwidth Df ~ (2pte /Mo)-1 ~ 1/Mo
 kA << 1 for larger Df .
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4.3.2 APD photodiode
 Characteristic table of APD
APD gain < 10 for 1.3 < l < 1.6 mm due to noise
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4.3.3 Noise of Photodiode
Introduction
Noise is a kind of output disregarding signal
Photo-current are generated together with quantum noise,
dark current noise and thermal noise.
The quantum noise includes shot noise and excess noise (APD).
Shot noise current
The incident photon is random with Poisson distribution,
and the output photo-current should be statistical.
The photo-current I = Ip + Is, where Ip is the average value
and Is the current perturbation.
The shot noise current, or the variance of current perturbation is
ss2 = <Is2> =∫-∞∞ Ss(f)df = 2qIpDf
where, Df is the equivalent noise bandwidth, Ss(f) = qIp
(white noise)
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4.3.3 Noise of Photodiode
Dark current noise
Dark current exists under bias voltage without optical input,
including buck and surface dark currents
Bulk dark current
In PN junction, electron-hole pair may be generated due to
random thermal excitation and side radiation.
Dark current will double when temperature increases 10 times
High energy barrier with lower dark current.
~nA for Si, InGaAs next, Ge ~hundreds of nA
Dark current is shot noise basically. With noise current
sd2 = 2qIdDf, should be amplified by APD gain
Surface dark current
due to dirty, defective surface and bias, decreased by guard ring
Independent of APD gain
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4.3.3 Noise of Photodiode
Excess noise current
Multiplication process is also random.
With the average gain <M>,
we have the square-average gain <M2>:
<M2> = <M>2*F(<M>)
Where, the excess noise factor is,
F(<M>) = kA<M> + (1-kA)(2-1/<M>) ≡ <M>x
x = 0.3 for Si, 0.6~0.1 for Ge-APD,
0.7 for InGaAs,
1.0 for Ge,
0.5~0.7 for InGaAsP-APD。
Higher kA, higher F(<M>)
For kA= 0, F ≦ 2, for kA= 1, F ~ kA
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4.3.3 Noise of Photodiode
Excess noise current
Both shot and dark noises will be multiplied,
the total noise current is s2 = 2qDf <M>(2+x) (Ip+Id)
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4.3.3 Noise of Photodiode
Thermal noise current
Without bias, the thermal perturbation of electron
in resistor become a current variation, Johnson noise
or Nyquist noise.
A steady Gaussian distribution with a constant
spectral density function for f < 1012 Hz:
ST(f) = 2kBT/RL
where RL is load resistor
The current variance due to thermal noise
sT2 = <(IT2)> =∫-∞∞ ST(f)df
= 4kBTDf/RL
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4.4.2 Basic Properties of APD Detector
 The higher bias of APD detector means that high power
consumption, short lift time and noisy, larger size, hard to
couple with fiber
 Avalanche multiplication is high temperature-sensitive,
and need expensive temperature compensation circuit.
 quantum efficiency h
h = total generated electrons / incident photon
= (I/e)/(P/hn) = (I/P)(hn/e)
where I, e, P are opto-current, electron charge, optical power
h is Plank’s constant, n is the optical frequency
h is dependent on the material, structure and associated optical
device.
 The steep drop at long wavelength (Fig. 4.21) implies
the energy barrier, and the slowly decreasing at short
wavelength means the recombination on the surface.
 Higher intrinsic layer width of PIN diode means higher h.
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4.4.2 Basic properties of APD detector
 Sensitivity
The minimum required incident optical power for
specified BER.
The sensitivity of APD is 6-dB higher than that of PIN
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4.4.2 Basic properties of APD detector
 Responsibility
Defined as current output per unit optical power:
R = I/P = (h/n)(e/h)
= hl/1.24 Ampere/Watt
(1) R ∞ h, R ∞ 1/n
(2) R ~ 1 A/W for l = 1.55 mm
By responsibility, the optical power noise can be
transformed into current noise
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4.4.2 Basic properties of APD detector
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4.4.2 Basic properties of APD detector
Response time
 The time interval between optical incident and current output
 Rise time
T = Tdrift + Tdiffusion + TRC
TRC：RC time constant (load resistance and junction capacitance)
For A= 250 mm, W= 30 mm, Cj = eA/W = 0.17 pF, and RL= 50Ω,
we have TRC= RLCj = 8.5 ps, fcut = 1/(2pTRC) = 18 GHz。
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4.4.2 Basic properties of APD detector
 Response time
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4.4.2 Basic properties of APD detector
 Response time
Tdiffusion：diffusion time outside depletion region,
~ 1/doping, ~ diffusion width
Without E-field, the region should be shorten to
avoid optical absorption here
Vdiffusion = 103 m/s for general photodiode
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4.4.2 Basic properties of APD detector
 Response time
Tdrift : drift time in depletion region
W = 30mm for Si, the scatter-limited saturation
drift velocity is about 8.6x104 m/s,
or Tdrift =0.3ns,
fcut=1.5 GHz (<< 18GHz)
Bandwidth is drift-dependent
Edrift≒ 2x104 V/cm,
Circuit cannot response
immediately to higher
bit rate (1/T)
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4.4.2 Basic properties of APD detector
 Response time
For APD, response time includes avalanche
build-up, i.e., the drift time in avalanche t.
We have the multiplication gain <M> as the
function of angular frequency:
M(w) = Mo/{1+(w+Mo)2}1/2 ,
For optimum 10 < M < 100, the drift time is
1ps < t < 10 ps
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4.4.2 Basic properties of APD detector
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4.4.3 Amplifier Noise Figure
 Amplifier noise figure Fn
Except photodiode noise, we have noises from
pre-amplifier and main amplifier which are
called amplifier noise figure (Fn)
Fn is the noise factor due to amplifier’s resistors
All thermal noises from amplifier’s resistors
sT2 = (4kBT/RL) FnDf
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4.5.1 Digital Optical Receiver
 Digital optical receiver
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4.5.1 Digital Optical Receiver
 Digital optical receiver
Optical signal →detection →amplifying →re-shaping
→ regenerating → de-multiplexing → electric signal
Optical repeater
Optical signal →detection →amplifying →re-shaping
→regenerating → re-timing → Optical signal
PIN and APD detector
Output current of PIN detector is about several nA
The noise of pre-amplifier is the main noise source
because the back-end amplifier tends to amplify both
signal and noise output from the pre-amplifier.
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4.5.1 Digital Optical Receiver
 Pre-amplifier
The balance between sensitivity and response
time High impedance and Trans-impedance preamplifiers with ultra high S/N value (low noise).
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4.5.1 Digital Optical Receiver
 Front end
High RL (sum of photodiode series resistor, load resistor and input
resistor of pre-amplifier) can increase the input voltage of the preamplifier, and then reduce the thermal noise.
But it will increases the input RC constant of the amplifier and
then reduce the response bandwidth Df .
If Df is far less than the optical bit rate, we can use a equalizer
to depress the low frequency response to enlarge the equivalent
bandwidth.
Trans-impedance amplifier can keep both low-noise and high
bandwidth properties simultaneously
Taking RL as a negative feedback resistor of a amplifier, high load
resistor keeps low thermal noise and the equivalent input resistor
of amplifier is reduced by factor of amplifier gain, which results
in high bandwidth.
The main problem is the stability of feedback circuit.
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4.5.1 Digital Optical Receiver
 Linear section
With a high-gain amplifier and LPF
Two functions of main amplifier:
1). to amplify the pre-amplifier output to the required
level for decision circuit
2). to automatic gain control to adapt the variation of
detected signal to maintain specified level required by
decision circuit.
Due to pulse dispersion, the detected and amplified
waveforms have inter-symbol interference (ISI)
phenomenon.
A LPF-type equalizer is used to shape the pulse
waveforms so that the main peak of the neighboring
pulse will be decided accurately.
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4.5.1 Digital Optical Receiver
 Linear section
A linear transfer function constituted by pre-amplifier,
main amplifier and equalizer：
Where, Ip is the detected current, Vout is the amplified
voltage waveform.
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4.5.1 Digital Optical Receiver
 Linear section
The total impedance is the united impedance transfer function
by all components of the receiver：
ZT(w)=GP(w)GA(w)HF(w)/Yin(w)
where Yin(w) is the input admittance, GP(w)、GA(w) and HF(w)
are the transfer functions of pre-amplifier, main amplifier and
filter respectively.
The normalized transfer function is
HT(w)= ZT(w)/ZT(0) = Hout(w)/HP(w)，
where Hout(w) and HP(w) are spectral function of output voltage
and detected current respectively.
If the bandwidth of LPF is larger than that of amplifier, the final
transfer function HT can be approximated by HF.
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4.5.1 Digital Optical Receiver
 Linear section
We can prove that if the spectra of output voltage is raised-cosinefilter like
where h(t) is the ideal waveform for decision circuit
At the decision point t=0, h(t)=1; meanwhile, at the decision point
of the neighboring pulse, t = m/B (m is integer), h(t)=0; therefore,
no ISI occur.
In practice, ISI is inevitable due to un-perfect square input
optical pulses.
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4.5.1 Digital Optical Receiver
 Data recovery end
Decision circuit and clock recovery circuit
Data recovery process：
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4.5.1 Digital Optical Receiver
 Data recovery end
For Return-Zero format, the spectral component of
Df = B (bit rate) is mixed in received signal.
For Non-Return-Zero format, the spectral
component of Df = B (bit rate) is obtained by passing
the signal through HPF and taking square of it.
According to the specified decision level, the output
signal of equalizer is decided at the time specified
by timing signal.
‘1’ data is got when the signal level is larger than
critical level; otherwise, ‘0’ data is got.
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4.5.1 Digital Optical Receiver
 Data recovery end
The eye diagram, built up by 2 or 3 recovered bits stream,
is used to judge the receiver performance which is usually
better than a BER of 10-9
The more open the eye diagram, the better the receiver
performance
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4.5.2 Parameter of Digital Receiver
 Sensitivity -- to judge receiver performance:
BER (Bit Error Rate), Minimum received power, or Quantum
limit of optical detection.
The sensitivity S (in dBm) is defined by the minimum received
power when BER < 10-9 .
Quantum limit is used as an ideal reference for receiver
improvement.
Considering the noises included in transmitter and optical
amplifier, the minimum received power should be larger than
the estimated value above.
 The power difference is called power penalty.
There are some degradation factors for sensitivity: such as
extinction ratio, intensity noise and time jitter.
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4.5.2 Parameter of Digital Receiver
1) Bit Error Rate (BER)
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4.5.2 Parameter of Digital Receiver
BER = P(1)P(0|1) + P(0)P(1|0)
= [P(0|1)+P(1|0)]/2
where P(1) and P(0) are the probability of receiving
bit 1 and 0 respectively.
P(0|1) is the conditional probability when bit 1 is
received but bit 0 is decided;
P(1|0) is the conditional probability when bit 0 is
received but bit 1 is decided.
In general, P(1) = P(0) = 1/2, and all noise are
approximated by Gaussian distribution.
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4.5.2 Parameter of Digital Receiver
Assume the sampled current value I = I1 + I0,
where I1 is bit ‘1’ current, I0 is bit ‘0’ current, and s1
and s0 are their variances, we have the conditional
probability (with ID being the threshold current) :
The Bit-Error Rate then is
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4.5.2 Parameter of Digital Receiver
The optimum threshold current to minimize the BER
If s1～s0,
ID = (s0I1 + s1I0)/(s1 + s0)
= ( I1 + I0)/2
is the mean value, this is suitable for PIN detector
where thermal noise dominates and is independent of
average current
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4.5.2 Parameter of Digital Receiver
If define Q = (I1- I0)/(s1+s0), we have
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4.5.2 Parameter of Digital Receiver
2) Minimum received power (Prec)
The bit ‘0’ current is I0 = 0,
The bit ‘1’ current is I1 = MRPin = MRPrec,
where Prec= (P1+P0)/2, M=1 for PIN.
For ‘0’ bit, only thermal noise exists, s0 = sT.
For ‘1’ bit, s1= (sT2 + sS2)1/2.
Then
Q = (I1 - I0) / (s1 + s0)
= 2MRPrec/[(sT2 + sS2)1/2 + sT]
or
Prec = (Q/R)[qFQDf + sT/M]
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4.5.2 Parameter of Digital Receiver
2) Minimum received power (Prec)
a) For PIN, M=1, sT2 >> sS2 ,
then Prec ~ QsT/R ~ B1/2 (∵sT2 ~ B).
Example: With l = 1.55 mm, when R = 1 A/W,
Q = 6 (BER = 10-9), sT = 100 nA,
then Prec = 0.6 mW = -32.2 dBm。
b) For APD,
if sT2 >> sS2, Prec ~ QsT/(RM) ~ 1/M, a benefit of APD
if sT2 ~ sS2, then we have the optimal Mopt for the Prec
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4.5.2 Parameter of Digital Receiver
2) Minimum received power (Prec)
b) Example: InGaAs APD:
For smaller kA, Prec decrease by 6~8dB, a benefit of APD;
Prec ~ B is the feature of shot-noise dominating receiver.
c) The average no. of received photon in bit ‘1’:
For thermal noise-dominated,
s0~s1, I0=0, then Q = (I1-I0)/(s1+s0) = I1/2s1
SNR= I12/s12 = 4Q2 = 144 for BER = 10-9 (Q=6);
For shot noise-dominated,
s0~0, I0=0, then Q = I1/s1,
SNR= I12/s12 = Q2 = 36 for BER = 10-9 (Q=6)
NP = 36 for SNR = hNP and h=100%
NP ~ 1000 in practice due to serious thermal noise.
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4.5.2 Parameter of Digital Receiver
3) Quantum limit of optical detection
 For weak optical input, only Poisson distribution is valid for
the behavior of incident photon
 The probability of m pairs generated by NP photons in bit ‘1’ is
Pm = exp(-Np)Npm/m!
 P(1|0) = 0 if NP = 0, then no decision for ‘1’
P(0|1) = P(m=1) = exp(-NP) for one electron generated
BER = [P(1|0)+P(0|1)]/2 = exp(-NP)/2 <10-9 for NP = 20
 Quantum limit is named by the incident photon perturbation
Prec = (P1+ P0)/2 = P1/2 = NPhnB/2
 Quantum limit is the average photon number per bit
(including ‘1’ and ‘0’), i.e., Np will be divided by 2.
 With l = 1.55 mm, and B = 10 Gbps,
Prec = 13 nW = -48.9 dBm for Np’=10 limit,
but most receivers operate at NP’ > 1000.
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4.5.2 Parameter of Digital Receiver
4) Degradation to Sensitivity -- Extinction ratio (rex)
 When the bias current operates at more than
threshold, semiconductor laser will emit some power
even for bit ‘0’.
 rex = P0/P1 , where P1 is the power for bit ‘1’.
 For PIN, I1 = RP1, I0 = RP0, Prec = (P1+P2)/2,
for Q = (I1- I0)/(s1+s0) we have
Q = [(1-rex)/(1+rex)].[2RPrec/(s1+s0)]
 For thermal noise dominated, s1 = s0 = sT, then
Prec(rex) = [(1-rex)/(1+rex)].[sTQ/R]
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4.5.2 Parameter of Digital Receiver
4) Degradation to sensitivity -- Extinction ratio (rex)
 Define the power penalty for rex
δex = 10 log[Prec(rex)/Prec(0)]
= 10 log[(1+rex)/(1-rex)]
 For under threshold, rex < 0.05, and δex < 0.4dB
 For over threshold, Mopt(APD) will decrease by 2,
and δex will double for the same rex .
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4.5.2 Parameter of Digital Receiver
4) Degradation to Sensitivity -- Intensity noise
 Noise from the semiconductor laser output
 Define incident optical noise level rI, and RIN (relative
intensity noise) of source
In fact, rI = 1/SNR. For SNR > 20dB, rI < 0.01.
sI2 = RPinrI is the current variance from incident intensity
Assume zero extinction ratio, I0=0, I1=RPin=2RPrec,
we have
Q = 2RPrec/[(sT2 + sS2 + sI2)1/2 + sT]
where, sI = 2rIRPrec and ss = (4qRPrecDf)1/2
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4.5.2 Parameter of Digital Receiver
4) Degradation to Sensitivity -- Intensity noise
 Expressed by Prec and its power penalty dI
For most emitter, rI < 0.01 and dI < 0.02 dB is negligible
Another three intensity noise from transmission
1). in-line optical amplifier.
2). mode-partition noise from interaction between
multimode laser and fiber dispersion.
3). scattering and reflection from the fiber link.
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4.5.2 Parameter of Digital Receiver
4) Degradation to Sensitivity -- Time jitter

With noise, the input signal of clock recovery circuit will lead to
the variation of sampling point, a perturbation called time jitter.
 If the bit can not be sampled at the peak, there exists a current
perturbation Dij dependent of the random time jitter Dt.
Dij = I1[hout(0) – hout(Dt)]
where decision output h(t)=cos2(pBt/2) for BDt << 1
~ (2p2/3 - 4).(BDt)2I1
 Assume Dt is Gaussian distribution with standard variation tj
then we have probability distribution for Dij
p(Dij) = 1/(pbDijI1)1/2. exp(-Dij/bI1)
where b = (4p2/3 - 8).(Btj)2, <Dij> = bI1/2, sj = bI1/√2
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4.5.2 Parameter of Digital Receiver
4) Degradation to Sensitivity -- Time jitter
 For I1 = 2RPrec,
 For (time drift to bit period ratio) Btj < 0.1, dj < 0.3dB.
 For non-Gaussian time jitter, Dij will be higher.
 For APD, dl is higher.
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4.5.2 Parameter of Digital Receiver
5) Dynamic range
There exists a maximum input power, Pmax, without
saturating the photodiode, then the dynamic range is
DR (dB) = 10 log(Pmax/Prec)
AGC circuit and optical attenuator can be tuned to
adapt to the emitter power degradation, fiber loss
increase due to temperature variation or aging.
For input optical power within this range, the BER
requirement of the system will be kept a long time.
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4.5.2 Parameter of Digital Receiver
6) Signal-Noise Ratio for PIN

For any electric signal
SNR≡(average signal power)/(noise power)
= Ip2/s2 = RPin/s2
 For sT >> sS thermal noise limit
1) SNR = (RLR2Pin2)/(4kBTFDf) ~ RL
2) Thermal noise as a Noise-Equivalent-Power (NEP):
3) NEP = 1 ~ 10 pW/Hz, the required minimum optical power
per unit bandwidth for SNR=1;
4) Detectivity ≡ 1/NEP;
5) NEP is used to estimate the required the incident optical power
for a given bandwidth and SNR.
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4.5.2 Parameter of Digital Receiver
6) SNR for PIN
 For sS >> sT, shot-noise limit
1) SNR = RPin/2qDf
= hPin/2hnDf ∞ Pin
2) define Np as required photon number for bit ‘1’,
and Pin = NphnB, where B = 2Df.
Since SNR = hNp,
for SNR = 20dB and h=100%, Np = 100 per bit
3) but thermal noise limit,
SNR = 20dB, Np > 1000 per bit
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4.5.2 Parameter of Digital Receiver
6) SNR for APD
 IP = MRPin where M is the statistically average
 The shot noise currents including dark current noise is
ss2 = 2eM2F(RPin + Id)Df
For thermal noise limit,
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4.5.2 Parameter of Digital Receiver
6) SNR for APD
For shot noise limit,
The optimum Mopt to get the maximum SNR satisfy
Mopt is independent of noise bandwidth Df and
decreases with the increasing Pin.
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4.5.2 Parameter of Digital Receiver
6) SNR for APD
For 1.55 mm InGaAs-APD,
RL = 1 kW, Fn = 2,
R = 1 A/W, Id = 2 nA,
For Si-APD,
kA << 1, Mopt ~ 100
For InGaAs-APD,
kA : 0.3~0.5, Mopt ~ 10
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4.5.2 Parameter of Digital Receiver
 Receiver performance evaluation
Two straight lines are the quantum limit.
Most systems are 20 dB worse.
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4.5.3 Analog optical Receiver
 Performance evaluation : SNR
 SNR : a ratio of <is2> to <in2>
 Neglecting dispersion effect, and with original
sinusoidal modulation index m, then
<is2> = (mIp<M>)2/2 = m2Ip2<M>2/2
<in2> = 4kBTB/RL + 2eB(Ip + Id)<M>2+x
where B is bandwidth of detector.
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4.5.3 Analog optical Receiver
 Performance evaluation


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input power↑, signal current ↑, shot noise ↑
When <M> increase until shot_noise = thermal_noise
SNR has its maximum.
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4.5.3 Analog optical Receiver
 Performance evaluation

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For small Pr, SNR of APD is larger than that of PIN.
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4.5.3 Analog optical Receiver
 Performance evaluation : CNR


CNR = PC/sn2 (after detector, before RF receiver)
For FSK digital transmission,
BER=10-9 (10-15), CNR=15.6 (18)dB
 For analog, the criterion is 525 scan_lines TV signal
so CNR = 56dB for AM analog signal, but
CNR = 15-18dB for FM analog signal
 CNR of total system: 1/CNR = Si=1N (1/CNRi)
Noises for single channel analog transmission:
Laser intensity perturbation, laser chirping, detector noise
and ASE noise from optical amplifier.
Noises from multi-channels with different carriers:
Harmonic noise, inter-modulation noise.
In practice, most noises can be easily decreased except:
Shot noise, optical amplifier noise, laser chirping.
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4.5.3 Analog optical Receiver
 Single channel AM baseband analog transmission

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P(t) = Pdc(1 + ms(t)), m = Pdc/Ppeak = 0.25 ~0.5
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4.5.3 Analog optical Receiver
1) Carrier power:
C = (mRMPrec)2/2 A2
2) Noise of detector: sN2 ~ 2e(Ip + Id)M2FtB
3) Noise of pre-amplifier: sT2 = 4kBTBFt/Req
where Ft is the noise factor of pre-amplifier,
Req is the equivalent resistance of PD and Pre-AMP
4) Relative Intensity Noise:
RIN = Noise/signal = <(DPL)2>/PL2
~ -150 to -158 (dB/Hz) for 1.55 mm DFB
neglected when I/Ith ≧1.2
For laser output random perturbation by DT or ASE
sRIN2 = RIN (RPr)B
5) Reflection effects on RIN:
Back-reflected signals can increase the RIN by 10-20dB
To keep RIN≦-140dB, reflection ≦-60dB (when I=1.33Ith).
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4.5.3 Analog optical Receiver
6) Limiting Condition
a) For small Pr,
CNR~0.5(mRMPr)2/[4kBT.
(BF/Req)] ~ P2rec
b) For medium Pr,
CNR~0.5(m2RPr)/(2eFB)
~ Pr
c) For strong Pr,
CNR~0.5(mM)2/(RIN*B)
indep. of Pr
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4.5.3 Analog optical Receiver
 Multi-channel analog transmission
 In CATV, there exists 40 VSB-AM in a fiber, each
channel is sensitive to noise and nonlinear distortion
 N channels are carried by N sub-carriers which are
electrically multiplexed into a mix signal which is
used to drive the laser source.
 After detector, a series of parallel BPFs are used to
recovery each signal by standard RF techniques.
 The operating frequency ranges of CATV are
50~88MHz and 120~550 MHz band.
 The intermediate band is revered for FM broadcast
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