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Chapter 6
Noise
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• Noise is a term generally used to refer to any
  undesired disturbances that mask the received
  signal in a communication system.
• Thermal noise
• Shot noise

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6.1 Thermal Noise

• Also known as Johnson Noise or Nyquist noise
• The thermal noise current it in a resistor R may
  be expressed by its mean square value and is
  given by
• where K is Boltzmann's constant, T is the
  absolute temperature and B is the
  post-detection bandwidth.

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• Electrons within any resistor never remain
  stationary and this constitutes a randomly
  varying current known as thermal current.
• Motion due to their thermal energy.

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SHOT NOISE

• Discrete nature of electrons causes a signal
  disturbance called shot noise.
• Deviation of the actual number of electrons from
  the average number is known as shot noise.
• Present for BOTH current Signal and dark current.

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6.2 Shot Noise due to Dark Current

• When there is no optical power incident on the
  photodetector a small reverse leakage current
  still flows from the device terminals and this
  contributes to the total system noise
• The shot noise due to the dark current, id is
  given by
• where e is the charge of an electron and
  Id is the dark current.

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6.3 Shot Noise on the Photocurrent

• The shot noise, is on the photocurrent Ip is
  given by

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6.4 Overall Receiver Noise

• Figure 6.1 shows a block schematic of the front
  end of an optical receiver and the various noise
  sources associated with it.
• The majority of the noise sources shown apply to
  both main types of optical detector (p-i-n and
  avalanche photodiode).
• The avalanche photodiode receiver is the most
  complex case as it includes noise resulting from
  the random nature of the internal gain mechanism
  (dotted in Fig. 6.1).

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Figure 6.1
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6.4.1 p-n and p-i-n Photodiode Receiver

• The total shot noise iTS is given by

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• The thermal noise due to the load resistance RL
  is given by

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• The signal to noise ratio (SNR) for the p-n or
  p-i-n photodiode receiver may be obtained by
  summing all the noise contributions.
• It is given by

where iamptotal noise from amplifier
circuit
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The noise associated with the amplifier, iamp
can be combined with the thermal noise from the
load resistor it using the noise figure, Fn for
the amplifier to give The expression for the
SNR can now be written in the form
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6.4.2 Receiver Capacitance

• The total capacitance to the front end of an
  optical receiver is given by
• CT Cd Ca
• where Cd is the detector capacitance and
  Ca is the amplifier input capacitance.
• Need to minimize in order to preserve the post
  detection bandwidth B. To increase B it is
  necessary to reduce RL

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Figure 6.4
Equalizer compensates for distortions
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• However, a thermal noise penalty is introduced
  when B is increased by decreasing RL
• A trade-off therefore exists between the maximum
  bandwidth and the level of thermal noise which
  may be tolerated.
• This is especially important in receivers which
  are dominated by thermal noise.

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Example

• A silicon p-i-n photodiode connected into an
  optical receiver has a quantum efficiency of 60
  when operating at a wavelength of 0.9 micometer.
  The dark current in the device at this point is 3
  nA and the total resistance is 4 k ohms. The
  incident optical power at this wavelength is 200
  nW and the post detection bandwidth of the
  receiver 5 MHz. compare the shot noise generated
  in the PD with the thermal noise in the load
  resistance at 20 C

Ans 3.79 e-10 A (rms shot noise current)
4.49E-9 A (rms thermal noise current)
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6.4.3 Avalanche Photodiode (APD) Receiver

• The internal gain mechanism in an APD increases
  the signal current into the amplifier and so
  improves the SNR.
• However, the dark current and quantum noise are
  increased by the multiplication process and may
  become a limiting factor.
• This is because the random gain mechanism
  introduces excess noise into the receiver in
  terms of increased shot noise above the level
  that would result from amplifying only the
  primary shot noise.

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• Thus if the photocurrent is increased by a factor
  M, then the shot noise is also increased by an
  excess noise factor Mx, such that the total shot
  noise is is given by
• where x is between 0.3 and 0.5 for silicon
  and between 0.7 and 1.0 for germanium or III-V
  alloy.

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• The total SNR for the avalanche photodiode may be
  obtained as
• This can be rewritten

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• It may be seen that the first term in the
  denominator increases with increasing M whereas
  the second term decreases.
• For low M the combined thermal and amplifier
  noise term dominates and the total noise power is
  virtually unaffected when the signal level is
  increased, giving an improved SNR.
• However, when M is large, the thermal and
  amplifier noise term becomes insignificant and
  the SNR decreases with increasing M at the rate
  of Mx.

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• An optimum value of the multiplication factor Mop
  therefore exists which maximizes the SNR.
• It is given by
• The variation in M, for both silicon and
  germanium APD is illustrated in Fig. 6.5.
• This shows a plot SNR versus M with Fn equal to
  unity and neglecting the dark current.

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Figure 6.5
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6.5 Receiver Structures

• There are 3 basic configurations for optical
  receivers
• a) Low Impedance Front End
• b) High Impedance Front End
• c) Transimpedance Front End

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6.5.1 Low Impedance Front End

• Simplest and most common
• Low impedance front end allows thermal noise to
  dominate within the receiver
• Impractical for long-haul, wideband optical fiber
  communication systems.

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Low Impedance Front End
Rb
Ra
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6.5.2 High Impedance Front End

• High input impedance amplifier with large
  detector bias resistor to reduce thermal noise.
• Degraded frequency response
• Needs equalizer
• Improvement in sensitivity over the low impedance
  front end design, but creates a heavy demand for
  equalization and has problems of limited dynamic
  range.

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High Impedance Front End
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6.5.3 Transimpedance Front End

• Overcomes the drawbacks of the high impedance
  front end by utilizing a low noise, high input
  impedance amplifier with negative feedback.
• Operates as a current mode amplifier where the
  high input impedance is reduced by negative
  feedback (vout IpRL)
• Provides a far greater bandwidth without
  equalization than the high impedance front end.
• Has a greater dynamic range.
• Preferred for use in wideband optical fiber
  communication receivers

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Transimpedance Front End
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Exercise 1
The bandwidth was 10 MHz. The detected signal
power was 2x10-12 W, and the thermal-noise power
was 1.66x10-13 W at 300 K. Suppose the the
photodetector is followed by an amplifier giving
the power gain 10 dB and having the noise
temperature 454 K. Compute the SNR.
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Exercise 2
A 1-Mbps NRZ link uses a 100? load at 300 K. The
wavelength is 0.82 µm, and the desired error rate
is 10-4. The PIN detector quantum efficiency is
unity. Compute the optic power incident on the
photodetector. Given that
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Example A good silicon APD (x0.3) has a
capacitance of 5 Pf, negligble dark current and
is operating with a post detection bandwidth of
50 MHz. When the photocurrent before gain is
10-7 A and the temperature is 18 C determine
the maximum SNR improvement between M1 and MMop
assuming all operating conditions are maintained