signal degradation in optical fibres - attenuation, dispersion and … · 2016-09-16 · ece 455...

ECE 455 – Lecture 03 1

Signal Degradation in Optical Fibres - Attenuation, Dispersion and their System Impact

• HMY 445 • Lecture 03 • Fall Semester 2016

Stavros Iezekiel Department of Electrical and

Computer Engineering

University of Cyprus

ECE 455 – Lecture 03

SIGNAL DEGRADATION

2


Signal Degradation in Optical Fibres

• The simplest optical fibre communications system is a point-to-point link in which an optical transmitter and receiver are connected to one another via an optical fibre. This simple architecture is typical of those used in trans-oceanic links for example.

Information

source Information

recipient Optical

transmitter Optical receiver

Optical fibre

• Without looking into the detail of the optical fibre itself, in this lecture we will look at how two important parameters – attenuation and dispersion – can affect the above system.


• In an ideal fibre, “what goes in, is what comes out”:

f (t) f (t - )

L

= Ln1/c

In reality, the signal going through the fibre is degraded by: • attenuation (i.e. optical signal loss) • dispersion (i.e. optical signal distortion)

input pulse

Pin Pout

output pulse

Attenuation on its own reduces the power of the pulse. We will see the impact of dispersion later.


5

• In digital communications, the key aim is to minimise the number of bit errors. A typical bit error rate (BER) for many systems is 10-9.

• The other aim is to maximise the repeater spacing L for a given bit rate BT. These two are lumped together to give the bit-rate - repeater spacing product.

• For a given BT, the minimum allowable power at the photoreceiver is called the receiver sensitivity PR.

• If the optical power emitted by the laser diode is given by PS, then the total allowable link loss is given by:

R

Slink

P

Ploss


• In other words, losslink represents the loss allowed between the output of the optical source and the input to the photoreceiver:

Optical transmitter

Optical receiver

Optical fibre loss

= losslink PR (mW) PS (mW)

R

Slink

P

Ploss


• Now, for an optical fibre: attenuation is per unit length, i.e. the longer the fibre, the more the attenuation. • As light travels down an optical fibre, its power (in mW) decreases exponentially according to Beer’s law:

P(z): power at a distance z along the fibre P(0): power at input to fibre A: attenuation constant (per unit length): nepers per m

AzePzP 0

0z Lz

z

zP

0

0P


• Hence for a fibre of length L, the attenuation in dB is:

• Noting that log10 x = ln x / ln 10, we get:

F is the fibre attenuation per unit length, in units of dB/km

Note that attenuation in dB is a positive number. Gain in dB is also a positive number by convention. We have to remember this in link budget calculations.


• If we return to the equation for optical powers along a fibre expressed in mW,

P(L) = P(0) e -AL

and then take logarithms:

10 log10 P(L) = 10 log10 {P(0) e -AL}

= 10 log10 {P(0)} + 10 log10 {e -AL}

= 10 log10 {P(0)} - AL 10 log10 {e}

P(L) in units of dBm

P(0) in units of dBm FL in units of dB


DECIBELS ETC.

10


The dB and dBm units

The dB unit is widely used in optical link design because:

• It allows the various loss and gain contributions to be included via addition/subtraction, rather than by multiplication/division which is what would be required if linear gain/loss units were used.

• The logarithmic nature of the dB also allows large ratios to be expressed with more manageable numbers and allows power levels differing by many orders of magnitude to be easily compared.

• Consider, for example, an optical amplifier with a gain (dimensionless) of G:

• We define gain G in dB as follows:

mWmW INOUT PGP

IN

OUT

P

PG 10log10)dB(


• Examples of decibel measures are listed below:

Ratio dB

10N

10 N

1000 30

100 20

10 10

1 0

0.1 -10

0.01 -20

0.001 -30

10-N

- 10 N

Ratio dB

2N

3.01 N

8 9.03

4 6.02

2 3.01

1 0

0.5 -3.01

0.25 -6.02

0.125 -9.03

2-N

- 3.01 N


• In optical communications, it is useful to have a logarithmic measure of the absolute power at any point in the system. This can be achieved with the dBm unit, which is the decibel level referenced to 1 mW:

• For example:

mW1

)mW(log10)dBm( 10

PP

mW 0.01 0.1 0.5 1 2 10 100

dBm -20 -10 -3.01 0 3.01 10 20


• The usefulness of the dBm comes with it being compatible with the dB unit for gain/loss.

• For example, we know that if we take a power of 1 mW and multiply by a gain of 2, we get 2 mW.

• Now consider the same situation with dB and dBm. The corresponding values of power are 0 dBm and 3 dBm; and the factor 2 corresponds to 3 dB.

• So we could also say that if we take a power level of 0 dBm and pass it through an optical amplifier of 3 dB gain, the output power will be 0 + 3 = 3 dBm.


)mW()mW( INOUT PGP

)mW(loglog

)mW(log)mW(log

1010

1010

IN

INOUT

PG

PGP

mW1

)mW(log10log10

mW1

)mW(log10 101010

INOUT PG

P

• To summarise:

)dBm()dB()dBm( INOUT PGP


LINK POWER BUDGET & ATTENUATION-LIMITED DISTANCE

16


Link Power Budget

• The link power budget determines how much optical power can be lost between the transmitter and the receiver for a given receiver sensitivity (which depends on the bit rate) and transmitter power output.

• The dB ratio and dBm units are used in the link power budget.

PS (dBm) PR (dBm)

FL (dB) LASER PHOTODIODE

FIBRE

Receiver sensitivity Source power

LPP FRS


MLPP TCFRS

System margin

Total connector losses

In practice, we also have to include optical fibre connector losses and also a system margin:

F

TCRS MPPL

max

Total fibre losses

Hence this allows us to calculate the maximum allowed length of link (without using intermediate optical amplifiers):


However, we emphasised in the first two lectures that an important figure of merit is:

Bit-rate - repeater spacing product (bits/s - km)

So how do we include bit-rate in the previous equation?

F

TCRS MPPL

max

We saw in Lecture 02 that the receiver sensitivity is a function of bit rate. Hence knowing how the sensitivity varies with bit rate will allow us to see how attenuation will affect the maximum distance for a particular bit rate.


Receiver sensitivity versus bit rate

In a later lecture on quantum limited receivers, we will show that for a given BER, there must be a minimum average bit energy at the photoreceiver, corresponding to a minimum average number of photons per bit N:

hcNEb

bT

bP

bbb TPE

The receiver sensitivity is given by:

Tb

b

bR BE

T

EP

This is the minimum optical power needed to maintain the specified BER, and is a function of bit rate BT (and also wavelength), i.e.

TbTR BEBP

Bit period


TObTOR BEBP

TO

OTOR

TO

OTObTR

B

BBP

B

BBEBP (Normalisation)

In dBm, we have:

TO

OTORTR

B

BBPBP 10dBmdBm

log10

1 10 100 TO

O

B

B TOR BP

10TOR BP

20TOR BP

dBmTR BP

Sensitivity worsens by 10 dB/dec


Hence for a given wavelength and BER, the maximum fibre length (due to attenuation limits) will depend on bit rate, and it decreases with increasing bit rate:


At “high” bit rates, we notice that the curves of maximum fibre length versus bit-rate change shape:

Attenuation-limited

Limited by???

This is because a different type of signal degradation dominates over attenuation at higher bit rates – this type of degradation is dispersion.


DISPERSION – IMPACT ON PULSES IN THE TIME-DOMAIN

24


z = 0 z = L

Dispersion

z = 0 z = L

Attenuation

Attenuation leads to a reduction of power (which becomes worse with increasing length, i.e. attenuation is specified in dB/km) Dispersion leads to temporal pulse broadening (this too becomes worse with increasing length, so we might expect it to be specified in ns/km for example).


• “What comes out, is not what goes in”

p (t) p(t - )

pIN (t)

t

pOUT (t)

t

t

t

Attenuation only • Reduction in pulse energy

Attenuation & dispersion • Reduction in pulse energy

• Pulse spreading

Fibre

No change in pulse shape


• We can (usually, but not always!) consider the fibre to be a linear system, with an impulse response as shown:

t t

h(t)

(t)

pin(t)

pin(t) pout(t)

pout(t)

pin(t) = (t), hence pout(t) = h(t)

t

t = mean arrival time

= rms pulse spread


t

pout(t)

t

dttpE out

)(

• Energy content • E = area under pulse

dttptE

t out

)(1

• Mean time of pulse arrival

FWHM =

22

22

)(1

)(1

tdttptE

dttpttE

out

out

• is root mean square spread of pulse around mean arrival time • It gives a measure of the dispersion

• An alternative measure is the full width at half maximum (FWHM)

Pulse shape definitions


• If a pulse with an rms pulse width of 1 is applied to a fibre,

then the output pulse spread will be given by:

h(t)

t m2

2

pout(t)

t m1

1

pin(t)

22

1

2

2


In a digital system, inter-symbol interference (ISI) will occur, leading to bit errors:


t

S

SR

1 1 0

bT

1 1 1

Pulses overlap to such an extent as to cause a bit error

R

t

Consider an extreme example: a pulse sequence 101 for which bT

FWHM

Bit stream at fibre input

Bit stream at fibre output

Full width at half maximum

t

50%

100%


For a given bit rate therefore, there will be some upper limit to the possible fibre length before inter-symbol interference starts to have an impact. In other words, we must try to limit the pulse spread relative to the bit duration. A general rule of thumb is that for a bit period Tb, the rms pulse spread should be confined to:

4

bT

Hence the maximum bit rate will be:

4

1TB

Because the pulse spread will be proportional to fibre length, we see that there will be a dispersion-limited value for the bit rate – distance product BTL.

signal degradation in optical fibres - attenuation, dispersion and … · 2016-09-16 · ece 455...

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