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Transmission media Cables

! A transmission medium is known once we give:

!

! the frequency response (f ) (and/or)

ch

! the power gain (f )

g ch

! Examples of transmission media: telephone networks

! cables (twisted pairs, coaxial cables)

! optical fibers

! radio links

! also power lines, underwater links, ... tv, computer networks

Cables Cables

! !

For cables, it is typical to give impedance Both input and output impedances

pedances

parameters (resistance, inductance, are therefore equal to:

capacitance, conductance) per unit length. (characteristic impedance)

nce)

! Scheme per each infinitesimal length dx ! The frequency response can be written as

–d (α(f ) + j β(f ) )

(f ) = e

!

ch

where d is the length of the line

! If matching for max power transfer holds:

–2d α (f )

2

(f )| = e

(f ) = |!

g ch

ch

Cables Cables

! Instead of (f ), often (f ) (in dB) is given:

g a f K f f K f f

( ) , ( ) 2π

α β

= = + ℓ

! c

Usually

ch ch 2d )

α(f

e

(f ) = 1/g (f ) =

a with constant K

ch ch 2d )

α(f

(f ) = 10 log e

a π

!

ch (dB) 10 ( )

!

(f ) = exp - (1+j) f / f – j 2 f t

c c

= (20 log e) d )

α(f

10 ! g (t) = g (t – t )

ch c c

8.68 -1

)

( π π

3 "

f t exp(1/4 f t) (t)

where: g (t) = 2 c c

c

f

∝

! )

α(f

In general, we have that

98 Optical fibers

Examples

p of parameters

p ! They typically employ very high frequencies.

! Actually, wavelength is used in lieu of f.

! Recall: f = v = c / n, with n being the refraction

λ

index (≈1.55 for glass, 1.35 for plastic)

very wide bands can be achieved

!

! The electrical TX and RC signals are

mapped to light signal powers P (t) and P (t).

1 2

optical electrical

electrical domain domain

domain

Optical fibers Optical fibers

(attenuation

enuation per unit length)

! The h (t) yielding (t) = (h ) (t) is ~Gaussian.

F 2 F 1 2

1 (t - t )

-1

g (t) = A exp

! F [dB/km]

Ch F 2 window 1 window 2 window 3

π

2 2

σ σ

F F

where:

t = delay A = attenuation = dispersion

σ (λ)

F F F F

Ã

2

-2

2 ) ]

exp [ - (2

(f ) = | ) | = A f

π σ

! !(f

g F

Ch F attenuation

(if equal matched in/out impedances)

! Delay = speed of light in the fiber times distance

! Dispersion = proportional to wavelength and distance

! σ

System bandwidth set by (inv. prop. to) F λ

wavelength [µm]

Optical fibers Radio links

! Typically, one of the three windows is used: ! Several bands for diverse purposes

attenuation per unit length is known

! also, dispersion is (120, ~0, 15 ns/nm/km

! in the first, second, third window, respectively)

fiber wavelength [nm] source bandwidth at 1 km [MHz]

multimode SI 850 LED 30

multimode GRIN 850 LD 500

multimode GRIN 1300 LD/LED 1000

monomode 1300 LD >10000

monomode 1550 LD >10000

used for very high distance links (low attenuation, low dispersion) 99

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