This document is a quick reference to some of the formulas and
important information related to optical technologies. This document focuses on
decibels (dB), decibels per milliwatt (dBm), attenuation and measurements, and
provides an introduction to optical fibers.
There are no specific requirements for this document.
This document is not restricted to specific software and hardware
versions.
The information in this document was created from the devices in a
specific lab environment. All of the devices used in this document started with
a cleared (default) configuration. If your network is live, make sure that you
understand the potential impact of any command.
Refer to
Cisco
Technical Tips Conventions for more information on document
conventions.
A decibel (dB) is a unit used to express relative differences in signal
strength. A decibel is expressed as the base 10 logarithm of the ratio of the
power of two signals, as shown here:
dB = 10 x Log_{10} (P1/P2)
where Log_{10} is the base 10 logarithm, and P1 and
P2 are the powers to be compared.
Note: Log_{10} is different from the Neparian Logarithm
(Ln or LN) base e logarithm.
You can also express signal amplitude in dB. Power is proportional to
the square of the amplitude of a signal. Therefore, dB is expressed as:
dB = 20 x Log_{10} (V1/V2)
where V1 and V2 are the amplitudes to be compared.
1 Bell (not currently used) = Log_{10}
(P1/P2)
1 decibel (dB) = 1 Bell / 10 = 10 * Log_{10}
(P1/P2)
dBr = dB (relative) = dB = 10 * Log_{10}
(P1/P2)

Log_{10} (AxB) = Log_{10} (A)
+ Log_{10} (B)

Log_{10} (A/B) = Log_{10} (A)
 Log_{10} (B)

Log_{10} (1/A) =  Log_{10}
(A)

Log_{10} (0,01) =  Log_{10}
(100) = 2

Log_{10} (0,1) = 
Log_{10}(10) =  1

Log_{10} (1) = 0

Log_{10} (2) = 0,3

Log_{10} (4) = 0,6

Log_{10} (10) = 1

Log_{10} (20) = 1,3
Log_{10} (2 x 10) =
Log_{10} (2) + Log_{10} (10) = 1 +
0,3

Log_{10} (100) = 2

Log_{10} (1000) = 3

Log_{10} (10000) =
4
This table lists the Logarithm and dB (decibel) power ratios:
Power Ratio 
dB = 10 x Log_{10} (Power
Ratio) 
AxB 
x dB = 10 x Log_{10}(A) + 10 x
Log_{10}(B) 
A/B 
x dB = 10 x Log_{10}(A)  10 x
Log_{10}(B) 
1/A 
x dB = + 10 x Log_{10} (1/A) =  10 x
Log_{10} (A) 
0,01 
 20 dB =  10 x Log_{10}(100) 
0,1 
 10 dB = 10 x Log_{10} (1) 
1 
0 dB = 10 x Log_{10 }(1) 
2 
3 dB = 10 x Log_{10} (2) 
4 
6 dB = 10 x Log_{10} (4) 
10 
10 dB = 10 x Log_{10} (10) 
20 
13 dB = 10 x (Log_{10} (10) +
Log_{10} (2)) 
100 
20 dB = 10 x Log_{10} (100) 
1000 
30 dB = 10 x Log_{10} (1000) 
10000 
40 dB = 10 x Log_{10 }(10000) 
dBm = dB milliwatt = 10 x Log_{10} (Power in mW / 1
mW)
Power 
Ratio 
dBm = 10 x Log_{10} (Power in mW / 1
mW) 
1 mW 
1 mW/1mW=1 
0 dBm = 10 x Log_{10} (1) 
2 mW 
2 mW/1mW=2 
3 dBm = 10 x Log_{10} (2) 
4 mW 
4 mW/1mW=4 
6 dBm = 10 x Log_{10} (4) 
10 mW 
10 mW/1mW=10 
10 dBm = 10 x Log_{10} (10) 
0,1 W 
100 mW/1mW=100 
20 dBm = 10 x Log_{10} (100) 
1 W 
1000 mW/1mW=1000 
30 dBm = 10 x Log_{10} (1000) 
10 W 
10000mW/1mW=10000 
40 dBm = 10 x Log_{10} (10000) 
dBW = dB Watt = 10 x Log10 (Power in W / 1 W)
Power 
Ratio 
dBm = 10 x Log_{10} (Power in mW / 1
mW) 
1 W 
1 W / 1 W = 1 
0 dBW = 10 x Log_{10} (1) 
2 W 
2 W / 1 W = 2 
3 dBW = 10 x Log_{10} (2) 
4 W 
4 W / 1 W = 4 
6 dBW = 10 x Log_{10} (4) 
10 W 
10 W / 1 W = 10 
10 dBW = 10 x Log_{10} (10) 
100 mW 
0,1 W / 1 W = 0,1 
10 dBW = 10 x Log_{10} (10) 
10 mW 
0,01 W / 1 W = 1/100 
20 dBW = 10 x Log_{10 }(100) 
1 mW 
0,001W/1W=1/1000 
30 dBW = 10 x Log_{10} (1000)

This table compares the power and voltage gains:
dB 
Power Ratio 
Voltage Ratio 
dB 
Power Ratio 
Voltage Ratio 
0 
1,00 
1,00 
10 
10,00 
3,16 
1 
1,26 
1,12 
11 
12,59 
3,55 
2 
1,58 
1,26 
12 
15,85 
3,98 
3 
2,00 
1,41 
13 
19,95 
4,47 
4 
2,51 
1,58 
14 
25,12 
5,01 
5 
3,16 
1,78 
15 
31,62 
5,62 
6 
3,98 
2,00 
16 
39,81 
6,31 
7 
5,01 
2,24 
17 
50,12 
7,08 
8 
6,31 
2,51 
18 
63,10 
7,94 
9 
7,94 
2,82 
19 
79,43 
8,91 
10 
10,00 
3,16 
20 
100,00 
10,00 
With this information, you can define the formulas for attenuation and
gain:
Attenuation (dB) = 10 x Log_{10}(P
in/P out) = 20xLog_{10}(V in/V out)
Gain (dB) = 10 x Log_{10}(P out/P
in) = 20 x Log_{10}(V out/V in)
Optical fiber is a medium to carry information. Optical fiber is made
of silicabased glass, and consists of a core surrounded by cladding. The
central part of the fiber, called the core, has a refractive index of N1. The
cladding that surrounds the core has a lower refractive index of N2. When light
enters the fiber, the cladding confines the light to the fiber core, and the
light travels down the fiber by internal reflection between the boundaries of
the core and the cladding.
Figure 1 – Optical Fiber Structure
Singlemode (SM) and multimode (MM) fibers are the mainstream fibers
that are manufactured and marketed today. Figure 2
provides information on both these fiber types.
Figure 2 – SM and MM Fibers
A small amount of light is injected into the fiber. This falls into
visible wavelength (from 400nm to 700nm) and near infrared wavelength (from
700nm to 1700nm) in the electromagnetic spectrum (see Figure 3).
Figure 3 – The Electromagnetic Spectrum
There are four special wavelengths that you can use for fiber optic
transmission with low optical loss levels, which this table lists:
Windows 
Wavelength 
Loss 
1^{st} wavelength 
850nm 
3dB/km 
2^{nd} wavelength 
1310nm 
0.4dB/km 
3^{rd} wavelength 
1550nm (C band) 
0.2dB/km 
4^{th} wavelength 
1625nm (L band) 
0.2dB/km 
In order to measure optical loss, you can use two units, namely, dBm
and dB. While dBm is the actual power level represented in milliwatts, dB
(decibel) is the difference between the powers.
Figure 4 – How to Measure Optical Power
If the optical input power is P1 (dBm) and the optical output power is
P2 (dBm), the power loss is P1  P2 dB. In order to see how much power is lost
between input and output, refer to the dB value in this power conversion
table:
dB 
Power Out as a % of Power In 
% of Power lost 
Remarks 
1 
79% 
21% 
 
2 
63% 
37% 
 
3 
50% 
50% 
1/2 the power 
4 
40% 
60% 
 
5 
32% 
68% 
 
6 
25% 
75% 
1/4 the power 
7 
20% 
80% 
1/5 the power 
8 
16% 
84% 
1/6 the power 
9 
12% 
88% 
1/8 the power 
10 
10% 
90% 
1/10 the power 
11 
8% 
92% 
1/12 the power 
12 
6.3% 
93.7% 
1/16 the power 
13 
5% 
95% 
1/20 the power 
14 
4% 
96% 
1/25 the power 
15 
3.2% 
96.8% 
1/30 the power 
For example, when direct line (LD) optical input into the fiber is 0dBm
and output power is 15dBm, optical loss for the fiber is calculated as:
Input Output Optical Loss
0dBm  (15dBm) =15dB
In the power conversion table, 15dB for optical loss equals 96.8
percent of lost optical power. Therefore, only 3.2 percent of optical power
remains when it travels through the fiber.
In any fiber optic interconnection, some loss occurs. Insertion loss
for a connector or splice is the difference in power that you see when you
insert the device into the system. For example, take a length of fiber and
measure the optical power through the fiber. Note the reading (P1). Now cut the
fiber in half, terminate the fibers and connect them, and measure the power
again. Note the second reading (P2). The difference between the first reading
(P1) and the second (P2) is the insertion loss, or the loss of optical power
that occurs when you insert the connector into the line. This is measured
as:
IL (dB) = 10 Log_{10} (P2 / P1)
You must understand these two important things about insertion loss:

The specified insertion loss is for identical
fibers.
If the core diameter (or the NA) of the side that transmits data is
larger than the NA of the fiber that receives data, there is additional
loss.
Ldia = 10 Log_{10}
(diar/diat)^{2}
LNA = 10 Log_{10}
(NAr/NAt)^{2}
where:
Additional loss can occur from Fresnel reflections. These occur when
two fibers are separated so that a discontinuity exists in the refractive
index. For two glass fibers separated by an air gap, Fresnel reflections are
0.32 dB.

The loss depends on the launch.
The insertion loss depends on the launch, and receives conditions in
the two fibers that are joined. In a short launch, you can overfill the fiber
with optical energy carried in both the cladding and core. Over distance, this
excess energy is lost until the fiber reaches a condition known as equilibrium
mode distribution (EMD). In a long launch, the fiber has already reached EMD,
so the excess energy is already stripped away and is not present at the
connector.
Light that crosses the fibertofiber junction of an interconnection
can again overfill the fiber with excess cladding modes. These are quickly
lost. This is the shortreceive condition. If you measure the power output of a
shortreceive fiber, you can see extra energy. However, the extra energy is not
propagated far. The reading is therefore incorrect. Similarly, if the length of
the receive fiber is long enough to reach EMD, the insertion loss reading can
be higher, but it reflects actual application conditions.
You can easily simulate EMD (long launch and receive). For this, you
must wrap the fiber around a mandrel five times. This strips the cladding
modes.
You can make a rough estimate of a link power budget. For this, you
must allow 0.75 dB for each fibertofiber connection, and assume that fiber
loss is proportional with length in the fiber.
For a 100meter run with three patch panels and 62.5/125 fiber that
have a loss of 3.5 dB/km, the total loss is 2.6 dB, as shown here:
Fiber: 3.5 dB/km = 0.35 dB for 100 meters
Patch Panel 1 = 0.75 dB
Patch Panel 2 = 0.75 dB
Patch Panel 3 = 0.75 dB
Total = 2.6 dB
The measured loss is normally less. For example, the average insertion
loss for an AMP SC connector is 0.3 dB. In this case, the link loss is only 1.4
dB. Regardless of whether you run Ethernet at 10 Mbps or ATM at 155 Mbps, the
loss is the same.
Optical timedomain reflectometry (OTDR) is a popular certification
method for fiber systems. The OTDR injects light into the fiber, and then
graphically displays the results of detected backreflected light. The OTDR
measures elapsed transit time of reflected light to calculate the distance to
different events. The visual display allows determination of loss per unit
length, evaluation of splices and connectors, and fault location. OTDR zooms in
to certain locations for a closeup picture of portions of the link.
While you can use power meters and signal injectors for many link
certifications and evaluations, OTDRs provide a powerful diagnostic tool to get
a comprehensive picture of the link. But OTDR requires more training and some
skill to interpret the display.