Handbook for Sound Engineers

478 Chapter 15

where,

Ldia equals the loss level of the core’s diameter,

diar is the diameter of the receiving fiber core in μm,

diat is the diameter of the transmitting fiber core in μm.

No diameter mismatch loss occurs when light passes
from a smaller core to a larger core.

Differences in NA also contribute loss when the
input NA of the receiving fiber is less than that of the
output NA of the transmitting fiber:

(15-27)

where,

LNA is the loss level of the numerical aperture,

NAr is the receiving numerical aperture,
NAt is the transmitting numerical aperture.

Calculation of the NA loss requires that the output
NA of the transmitting fiber be known. Since the actual
output NA varies with source, fiber length, and modal
patterns, using the material NA yields misleading
results. No NA mismatch loss occurs when the
receiving fiber has an NA greater than that of the trans-
mitting fiber.

The loss of optical power from mismatches in NA
and diameter between the source and the core of multi-
mode fiber is as follows:

• When the diameter of the source is greater than the
  core diameter of the fiber, the mismatch loss is

(15-28)

where,

Ldia is the level of core diameter mismatch loss.

• No loss occurs when the core diameter of the fiber is
  larger. When the NA of the source is larger than the
  NA of the fiber, the mismatch loss is

(15-29)

where,

LNA is the numerical aperture mismatch loss.

• No loss occurs when the fiber NA is the larger. Area
  or diameter loss occurs when a source’s area or diam-
  eter of emitted light is larger than the core of the
  fiber. (Area is often used instead of diameter because
  of the elliptical beam pattern of edge emitters and
  lasers.) Area or diameter loss is equal to

(15-30)

where,

Larea is the loss level of the area.

Data sheets for sources often give the area and NA of

the output. Although some may not, they may be calcu-

lated from information such as polar graphs that are

often provided. Calculation of the NA loss and area loss

yields an estimate of loss resulting from optical differ-

ences between source and fiber. Additional interconnec-

tion loss comes from connector related loss, which

includes Fresnel reflections and misalignment contrib-

uted by a connector.

As with sources, two main causes of loss in coupling

light from a fiber into the detector results from

mismatches in diameter and NA. When diadet<diafiber ,

then

(15-31)

When NAdet < NAfiber, then (15-32)

(15-33)

where,

Ldia is the loss level of the diameter,

LNA is the loss level of the numerical aperture.

Since detectors can be easily manufactured with

large active diameters and wide angles of view, such

mismatches are less common than with sources. Other

losses occur from Fresnel reflections and mechanical

Figure 15-38. Fiber optic system attenuation.

Transmitter

Receiver

Analog or

digital

interface

Signal

output

LFI fiber

LF 2 fiber

LSP splice

PD = PS (LC 1 + LF 1 + LSP + LF 2 + LC 2 ) dB

PD = Detector power

PS = Source power

LNA 10–

NAr

NAt

©¹§·---------

2

= log

Ldia 10–

diafiber

diasource

©¹§·----------------------

2

= log in dB

LNA 10–

NAfiber

NAsource

©¹§·---------------------

2

= log in dB

Larea – 10

areafiber

areasource

-------------------------

©¹

= log§· in dB

Ldia 10–

diadet

diafiber

©¹§·------------------

2

= log in dB

LNA 10–

NAdet

NAfiber

©¹§·-----------------

2

= log in dB