英文原文.txt

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Noise 

Within the bandwidth of the link, the contribution of 
noise from the various components must also be considered. 
When specifying the noise of a link, the tendency 
is to use equivalent input noise (EIN). EIN is 
defined as the amount of RF noise at the input of a link 
that would be needed to produce the amount of noise 
observed at the output of the link if the total link itself 
were noiseless. Its units can be mW/Hz or dBm/Hz: 

equation 11, 

EINLINK, mW = NoiseOUTPUT, mW/GRATIO 

EINLINK, dBm = NoiseOUTPUT, dBm – GdB 

An alternate measure of noise is the noise figure (NF), 
which is the ratio in dB of the actual noise power to the 
amount that would be produced by a similar device 
with perfect noise performance. It is further defined that 
the inputs of this ideal device are terminated by a passive 
load at the standard temperature of 290 K(TO). 
Since the available noise power from such a load is: 

KTo = (1.38 x 10–20 mW/(k – Hz)) (290 K)

 = 4.0 x 10–18 mW/Hz

 = –174 dBm/Hz 
EIN is related to NF by: 
equation 12, 
NF = 10 log (EINmW/Hz/KTo) 
NF = EINdBm/Hz + 174 dBm/Hz 
The noise also can be specified in terms of the equivalent 
input temperature, T, which is given by: 

equation 13, 

EINmW/Hz = KTo + KT 

10[(EI, dBm/Hz)/10]

T = -------------------------------------------------------

KTO

– 
For example, a link that has an output noise of 
–85 dBm/Hz and a gain of –40 dB would have an EIN 
of –125 dBm/Hz, an NF of 49 dB, and a T of 

2.3 x 107 K. Equations 11 and 12 require that EIN be 
expressed over a 1 Hz bandwidth. 
With these terms defined, the four primary noise 
sources in a fiber-optic link can be defined: 

1. Noise from amplifiers in the transmitter 
2. Noise from the laser diode 
3. Shot noise at the photodiode 
4. Noise from amplifiers and/or matching components 
at the receiver 
Since fiber-optic links typically exhibit a significant 
amount of signal loss, the noise from the transmitter 
amplifiers are generally much less than that from the 
other components, and will be neglected. The calculations 
discussed in this section are also summarized in 
the performance curves in the Appendix, page 28. 

Laser Noise 

Laser noise arises from random fluctuations in the 
intensity of the optical signal. There are two main contributions 
to this effect. The first is the actual fluctuations 
in the intensity of the light as it is generated at the 
laser diode. The second is fluctuations in the frequency 
of the light, which can degrade the signal if the fiber is 
dispersive. This second set of effects will be discussed 
more fully in the sections on Reflections and Interferometric 
Noise, page 24; Polarization Mode Dispersion, 
page 25; and Distributed-Feedback (DFB) vs. Fabry-
Perot (FP) Lasers, page 25. 

The laser noise measured directly at the transmitter is 
often referred to as relative intensity noise (RIN), so 
named because it is the ratio of the mean square 
amplitude of the noise fluctuations per unit bandwidth, 
<P2>, to the square of the dc optical power, Po: 

RINRATIO = <P2>/PO2 

This value is related to EIN by: 

equation 14, 

EINLASER mW/Hz =

, 

2

Mdc

RINRATIO(Idc( – ITH)2 . RIN 

. 1000

ηTx R

, 
EINLASER mW/Hz =

, 

2

Mdc

RINdB10 log

+ 

(Idc – ITH)2(RIN) 

(–30)

ηTx R

, 

where Idc is the dc bias current in mA applied to the 
laser diode, ITH is the laser threshold current, RIN is the 
laser input dc impedance, Mdc is the dc modulation 
gain of the laser diode, and ηTx, RF is the RF efficiency 
of the transmitter at the frequency of interest. 

As an example, a laser biased 60 mA above threshold 
with an RIN of –153 dB/Hz, an input impedance of 
50 Ω, and a modulation gain ratio Mdc/ηTx, RF of 1 
would have an EINLASER of –130 dBm/Hz. In general, 
both RIN and EIN vary with the bias current and frequency. 


Agere Systems Inc. 


Application Note 
RF and Microwave Fiber-Optic Design Guide April 2001 

Link Design Calculation (continued) 

Shot Noise 

The second main contributor to link noise is from a subtle 
effect called shot noise. Shot noise occurs because 
light is composed of discrete packets of energy called 
photons, which convey a signal not as a smooth flow of 
energy but instead as a stream of infinitesimal quanta 
of energy. The randomness of the arrival time of each 
photon generates a random noisiness in the current at 
the output of the photodiode: 

equation 15, 

iSHOT = (2 . e . Idc . BW)1/2 

where iSHOT is the rms value of the shot noise at the 
photodiode chip; e is 1.6 x 10–19 Coulombs; Idc is the 
dc electrical current through the photodiode, and BW is 
the channel or resolution bandwidth of the measurement. 


The amount of shot noise that leaves the receiver, 
iSHOT, OUT will depend on the ratio of the photodiode 
responsivity and the efficiency of the total receiver: 

ηRx, RF

iSHOT, OUT = iSHOT ..-------------------. 

.RPD . 

The contribution from shot noise per unit bandwidth 
can be referred back to the input of the total link to give: 
equation 16, 

PLASER .RIN

EINSHOT, mW = 2e 

.LOPT, RATIO 
(ηTx R)2(RPD

,) 

where PLASER is the optical power launched into the 
fiber immediately after the laser. 

For example, if PLASER is 4 mW, R is 50 Ω, ηTx, RF is 

0.1 W/A, RPD is 0.75 A/W, and LOPT,RATIO is 2 (i.e., 
3 dB) then: 
equation 17, 

EINSHOT, mW = 
(4 mW)(50 Ω)

21.6(×10 –19C) 
2

() 

(0.1 W/A)2(0.75A/W) 
EINSHOT, mW = 1.71 x 10-14 mW/Hz 

EINSHOT, dBm = –137 dBm/Hz. 

Receiver Noise 

The receiver also will add noise from any amplifiers or 
resistive matching elements incorporated in or immediately 
after the receiver. Since it is necessary to have 
such amplifiers in most situations, it is important to 
carefully consider its contribution as well. The receiver 
noise is referred back to the input just as in equation 10 
on page 7. 

EINRx, dBm = NoiseRx, OUTPUT, dBm – GLINK, dB 

Receiver noise often is specified by the equivalent 
noise current. Similar to EIN, the equivalent noise current 
is the theoretical amount of rms current at the photodiode 
that would be required to create the actual 
amount observed noise leaving the photodiode, imagining 
that all other components in the receiver had no 
noise. 

equation 18, 

RPD

iENC = iNOUTPUT.
------------------. 

, .ηRx,RF. 

where iENC is the rms equivalent noise current at the 
photodiode and iN,OUTPUT is the actual rms noise out of 
the receiver. 

As an example, consider the 50 Ωresistively-matched 
receiver in Figure 7 on page 7. The thermal noise of a 
resistor, here RPD, can be modeled as a current source 
in parallel with the resistor with an rms current of: 

1/2

4 KT B)

(

iRESISTOR NOISE = 

R 

iRESISTOR NOISE = 18 pA/Hz 

In Figure 7, half of this 18 pA/Hz will pass through the 
matching resistor, RPD, and half will pass through the 
load, thus the output noise current is 9 pA/Hz (or in 
power is –174 dBm/Hz). Using equation 17 and 
remembering from section on Resistively Matched 
Components, page 7, that the ratio of RPD/ηRx, RF = 2 
for a resistively-matched receiver, the equivalent noise 
current for a resistively-matched 50 Ωreceiver is simply 
18 pA/Hz. 

To convert this equivalent noise current into EIN of the 
link use the following: 

EINLINK, mW/Hz = EINLASER, mW/Hz + EINSHOT, mW/Hz + 
EINTH, mW/Hz 

Agere Systems Inc. 


Application NoteApril 2001 RF and Microwave Fiber-Optic Design Guide 

Link Design Calculation (continued) 

Total Link Noise 

When the laser noise and photodiode shot noise are 
added together with receiver thermal noise, as in Figure 
9, each noise source obeys a different law with 
respect to the amount of optical loss in a given system. 

Specifically, the laser EIN stays constant, the photodiode 
EIN grows proportional to the optical loss, and 
the receiver thermal EIN grows proportional to the 
square of the optical loss (Of course, the actual thermal 
noise is constant, but since it is referred back to the link 
input its contribution relative to the input signal grows 
as the losses of the link increase.) 

equation 19, 

EINLINK, mW/Hz = EINLASER, mW/Hz + EINSHOT, mW/Hz + 
EINTHERMAL, mW/Hz 

–100 

Figure 10 shows the benefits that can be achieved 
when reactive matching is used. Reactive matching at 
the transmitter decreases the level of all three components 
of the link noise, which means that lower gain 
pre-amps are needed to achieve the same signal to 
noise ratio. Reactive matching at the receiver further 
reduces amplification requirements by increasing the 
link gain, but it also specifically lowers the relative contribution 
of receiver thermal noise, which is often the 
limiting factor in longer links.The Appendix, page 28 
includes a more complete set of EIN curves. High-
power photodiodes also can improve the noise performance 
of a link because generally they do not require 
extra optical attenuation for protection, thus the optical 
losses of link can be lower. 

74 

SHOT EIN 
THERMAL EIN 
TOTAL EIN 
LASER EIN 

–110 


64 

EIN (dBM/Hz) 

NOISE FIGURE (dB) 

–120 

54 
–130 

44 
–140 

34 
–150 

24 
–160 

14 

1 3 5 7 9 11 13 15 17 19 21 
OPTICAL LOSS (dB) 

1-1220F 

Figure 9. Cumulative Loss Effects of Laser Noise, Photodiode Shot Noise, and Receiver 
Thermal Noise on Total Link Performance 

–100 74 REACTIVELY MATCHED 
–110 64 RESISTIVELY MATCHED 
NF 
–120 54 
–130 44 
–140 34 
–150 24 
–160 14 
1 3 5 7 9 11 13 15 17 19 21 

OPTICAL LOSS (dB) 

1-1221F 

EIN (dBM/Hz) 

Figure 10. Reactive Matching at the Transmitter and Receiver Imparts Improved Noise Performance 

Agere Systems Inc. 


Application Note 
RF and Microwave Fiber-Optic Design Guide April 2001 

Link Design Calculation (continued) 

Cascading Noise Figures 

Once the noise contributions of an optical link are calculated 
and reduced to a single quantity for the 
EINLINK, this noise can be cascaded with other microwave 
components in the system. Friis’ formula states 
that if a single component with a noise figure of NF1 
and gain of G1 is followed by another component with 
a noise figure of NF2, then the total noise figure will be: 

equation 20, 
NF, RATIO – 1 

, ---------------


NFTOTAL RATIO, = NF1RATIO .------------------. 

. G1, RATIO . 

where both the NF and G must be expressed as ratios