082-Engineering-Mathematics-Anthony-Croft-Robert-Davison-Martin-Hargreaves-James-Flint-Edisi-5-2017

2.4 Review of some common engineering functions and techniques 89
And so
10 1.5 =
(
Po
10 −3 )
Therefore the actual power is
P o
= 10 1.5 ×10 −3 = 10 −1.5 = 0.0316 ∼ = 32 mW
ThisisthetypicalamountofRFpowerthatmightbetransmittedbyalaptopcomputer
with WiFicapability.
Engineeringapplication2.12
Attenuationinastep-indexopticalfibre
Fibre optical cables are used to guide high-bandwidth light signals generated by
lasers. One design is the step-index optical fibre. This consists of a glass core of
silicondioxidewithahighrefractiveindex,obtainedbydopingtheglasswiththeelementgermanium.Asurroundingsheathoflowerrefractiveindexglassensuresthat
nearly all of the light remains within the core. Transmission occurs by total internal
reflection atthe interfacebetween the two typesofglass.
The losses that do occur in the optical fibre can be described by the following
equation:
I(z) =I 0
e −αz
where the intensity of the light I(z) is a function of the distance along the fibre, z,
fromthelightsource.TheintensityofthelightsourceattheinsertionpointisI 0
and
α is anattenuation factor.
Note that α varies with the wavelength of the light and so the rate of attenuation
dependsonthecolourofthelight.Itispossibletoobtainplotsforthevariationofthe
attenuationfactorwithwavelengthfromthemanufacturers.Theattenuationfactoris
often expressed in units of dB km −1 . A typical value for a cable operating at a light
wavelength of1550 nmis0.3 dBkm −1 .
An alternative measure for gain/attenuation is that of the neper (Np). Like the
decibel this is also a dimensionless ratio that has a logarithmic form. Whereas the
decibel is defined in terms of base 10 logarithms, the neper is defined in terms of
natural logarithms, that is base e logarithms. The gain measured in Np is defined by
the following expression:
voltage gain (Np) = ln V o
V i
=lnV o
−lnV i
whereV o
is the signal value in volts after gain/attenuation andV i
is the reference
signal value involts.
It is possible to derive a conversion factor between Np and dB by considering
the case whenV o
is a factor of 10 greater thanV i
. Using the neper measurement this
corresponds to
voltage gain (Np) = ln 10V i
V i
=ln10
➔