英文原文.txt

毕业论文全套~ 本课题主要设计一种气体泄漏检测系统。

when computing the algebra. 

Friis’ formula also can be converted to EIN and T by 
using the definitions in equation 12 and equation 13 on 
page 9: 

equation 21, 

EINTOTAL, mW/Hz = 

EIN2 mW/Hz – KTO

EIN1, mW/Hz + .
. ------------------------------------------------..

G1, RATIO 

equation 22, 
T1+ T2

TTOTAL = ------------------------


G1, RATIO 

Unconverted Noise and SNR 

The noise phenomena described in the previous section 
all occur independent of the presence of an RF signal; 
however, there is another class of noise 
phenomena that occur only when a signal is present. 
Such noise is present at low frequencies even without 
a signal, but is translated to the neighborhood of the 
signal when the light is modulated, as shown in Figure 

11. This upconverted noise may reduce the signal to 
noise ratio (SNR, C/N, or CNR) below what would be 
calculated if only the EIN was considered. Fabry-Perot 
lasers are especially susceptible to this noise and this 
is reflected in their SNR specification. 
For a Fabry-Perot laser, this low-frequency noise 
results largely from mode partition noise, which 
increases with fiber length and modulation frequency. 
For DFB lasers there is only one optical mode (or 
wavelength) so these effects are absent. The remaining 
low-frequency noise for DFBs primarily results from 
Rayleigh scattering in the fiber, which only becomes 
apparent for links on the order of 20 km or more and for 
high SNRs. These upconverted noise sources are 
described in more detail in the sections on Reflections 
and Interferometric Noise, page 24, and Distributed-
Feedback (DFB) vs. Fabry-Perot (FP) Lasers, page 25. 

POWER

SIGNAL 

LOW-FREQUENCY 

SIDEBOARD 

NOISE 

NOISE 


1 GHz 10 GHz 
FREQUENCY 
1-1222F 

Figure 11. Effects of Unconverted Low-Frequency Noise on SNR 

Agere Systems Inc. 


Application NoteApril 2001 RF and Microwave Fiber-Optic Design Guide 

Link Design Calculation (continued) 

Noise-Equivalent Bandwidth 

The SNR of the link depends not only on the RF signal 
level outlined above, but also on the noise-equivalent 
bandwidth. Wider channel widths will include more 
noise power and thus reduce the SNR. Although the 
link may be passing many channels over a wide band, 
the receiver can be tuned to a single channel within this 
band. This single-channel bandwidth is important in 
determining the SNR and, in the next section, the 
dynamic range. 

equation 23, 

NoiseCHANNEL = EINdBm/Hz + BWdB, Hz 

Dynamic Range and Distortion 

While the noise floor determines the minimum RF signal 
detectable for a given link, non-linearizes in the 
laser and amplifiers tend to limit the maximum RF signal 
that can be transmitted. For links transmitting a single 
tone where there is little concern for it interfering 
with other signals, the 1 dB compression point is generally 
used to specify the dynamic range. For links transmitting 
a larger number of signals, the third-order 
intercept point is frequently used to calculate the spur-
free dynamic range. Both definitions are discussed 
below. 

1 dB Compression Point 

The most straightforward limitation on the power of an 
input signal is the 1 dB compression point, P1dB. At this 
RF input power, the output signal is 1 dB less than 
what would be predicted by the small signal gain of the 
link. Returning to the L-I curve of the transmitter, Figure 
2 on page 4, it can be seen that once the magnitude of 
the signal approaches that of the bias current, the signal 
will clip at the lower level of the curve. This limit 
defines the 1 dB dynamic range, DR1dB, as follows: 

equation 24, 

DR1dB = P1dB – NoiseCHANNEL 

DR1dB = P1dB – EINdBm/Hz – 10 log (BWHz) 

Third-Order Intercept and Spur-Free Dynamic 
Range 

A more precise treatment for a large number of carriers 
uses the third-order intercept. Even in the middle of the 
linear portion of a laser’s L-I curve, non-idealities distort 
the output and cause higher order, intermodulation 
signals. In particular, if two equilevel sinusoidal tones 
at f1 and f2 modulate the fiber-optic link, third-order distortion 
products are generated at 2f1– f2 and at 2f2 – f1, 
as shown in Figure 12. The magnitude of these distortion 
products expressed in dBm has a slope of three 
when plotted against the input or output power level, as 
shown in Figure 13 on page 14. 

2f1 – f2 f1 f2 2f2 – f1 
f2 – f1 
INTERMODS 
CARRIER 
SIGNALS 
C/IRF POWER (dB) 
FREQUENCY 
1-1223F 

Figure 12.Third-Order Intermodulation Distortion Spectrum 

Agere Systems Inc. 

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

Link Design Calculation (continued) 

NOISE LEVEL 
THIRD-ORDER 
DISTORTION 
THIRD-ORDER 
INTERCEPT 
1 dB COMPRESSION 
FUNDAMENTAL 
SDFR 
–104 dBm 35 dBm 
(INPUT TOI OR IIP3) 
–144 dBm 
–5 dBm (OUTPUT TOI) 
1-1224F 

Figure 13. Third-Order Intercept and Spur-Free Dynamic Range 

To quantify this effect, the slopes of the output signal 
and distortion terms are extrapolated to higher power 
until they intercept. The input power corresponding to 
this intersection is defined as the input third-order intercept 
point (IIP3 or input TOI), which can be calculated 
by: 

equation 25, 

, ----------


IIP3dBm = SIN dBm + .
. -------C --------.
. /2

I2 TONE, dB 

SIN, dBm is the input power of one of the carriers and 
C/IdB is the ratio of the output power of the carrier to 
that of one of the intermodulation distortion signals. 
(For Agere Systems’ components, the input TOI rather 
than the output TOI is usually specified because the 
input TOI will be independent of the link gain. To find 
the output TOI, simply add the input TOI to the link gain 
in dB.) Equation 25 also can be used to approximate 
the worst-case distortion terms for a given input power. 
For example, if the IIP3 of a transmitter is 35 dBm and 
a pair of signals is input with –5 dBm in each, then the 
third-order terms will be 80 dB below these at 
–85 dBm. 

equation 26, 

C/I2 TONE, dB = 2 (IIP3dBm –SIN, dBm) 

C/I2 TONE, dB = 2 (35 dBm – (–5 dBm)) 

C/I2 TONE, dB = 80 dB 

An important note to make is that this IIP3 power level 
is never measured directly because it is strictly a small 
signal linearity measurement. The IIP3 of a laser also 
does not follow the traditional relationship observed in 
amplifiers because it is roughly 10 dB above the 1 dB 

compression point. For lasers, the difference between 
these two powers is very dependent on both the frequency 
and the dc bias current. Additionally, some 
transmitters include predistorters, which specifically 
improve the IIP3 without necessarily affecting the 1 dB 
compression point. 

Once the IIP3 is determined, the spur-free dynamic 
range (SFDR) can be calculated. The SFDR corresponds 
to the case of a link transmitting two input signals 
of equal power. The SFDR is defined as the range 
of the two input signals in which the signals are above 
the noise floor and the third-order products are below 
the noise floor. Graphically, this is shown in Figure 13. 
If the noise floor is lowered either by using a quieter 
laser or by operating over a narrower frequency band 
then the SFDR will increase at a 2/3 rate, which is the 
difference between the slope of the output signal and 
distortion curves. In dB this gives: 

equation 27, 

SFDR = 2/3 (IIP3dBm – NoiseCHANNEL) (dB – BW)2/3 

SFDR = 2/3 (IIP3dBm – EINdBm/Hz – 10 log BW) (dBHz2/
3) 

For example, a link with an IIP3 of 35 dBm and an EIN 
of –130 dBm/Hz would have a SFDR of 110 dB-Hz2/3 
over a 1 Hz bandwidth. If the same link had a bandwidth 
of 1 kHz, then its SFDR would be 90 dB-kHz2/3. 
The SFDR value that results from these calculations 
can be applied to either the input or output. 

Agere Systems Inc. 


Application NoteApril 2001 RF and Microwave Fiber-Optic Design Guide 

Link Design Calculation (continued) 

Large Number of Carriers 

If a large number of carriers (or channels) are transmitted 
through a link, then, in certain situations, the distortion 
products can be higher than those predicted by the 
two-tone IIP3 and SFDR. In particular, when the input 
channels are evenly spaced, several different inter-
modulation tones may add together at the same frequency, 
creating a stronger third-order term than what 
would be produced by only two carriers. To approximate 
the increase in the C/I, the following equation is 
commonly used: 

equation 28, 

C/ITOTAL, dB = C/I2 TONE, dB – [6dB + 10 log (x)] 

where x is a counting term that accounts for the overlap 
of intermods, and the 6 dB term normalizes the result 
to the two-tone case. This equation assumes that all of 
the input carriers are equally spaced, add in power (not 
voltage), and have equal powers. If they are not 
equally spaced, then the two-tone calculations of the 
section on Third-Order Intercept and Spur-Free 
Dynamic Range, page 13, will be more appropriate. 

Table 1. Carrier and Counting Term Calculations 

Carriers x 6 dB + 10 log (x) 
2 0.25 0 dB 
3 1 6 dB 
4 2.3 9.6 dB 
5 4.5 12.5 dB 
6 7.5 14.8 dB 
7 11.5 16.6 dB 
8 15.5 17.9 dB 
9 20 19.0 dB 
10 26 20.1 dB 
11 33 21.2 dB 
12 40 22.0 dB 
13 48 22.8 dB 
14 57 23.6 dB 
15 67 24.3 dB 
16 77 24.9 dB 
n > 16 ~ (3/8) n2 6 dB + 10 log ((3/8) n2) 

Placement of Amplifiers 

For optical links that incorporate amplifiers, the amount 
of distortion produced will be affected by where the 
amplifiers are placed. Specifically, a trade-off must be 
made between the noise and distortion performance of 
the link. Placing an amplifier before the transmitter 
raises the signal above the noise floor and, therefore, 
lessens the noise figure of the link. However, if the 
amplification is too large, then the transmitter or the 
amplifier itself may begin to distort the signal. To avoid 
such distortion some intermediate level pre-amp is 
chosen appropriate to the given application. If necessary, 
another amp after the receiver can then be used 
to provide any additional gain. 

Example 

With all of the critical quantities defined, the perfor-
mance for a typical link can now be predicted. As an
example, consider an X-band antenna that needs to be
remotely operated 5 km from the receiver electronics
and has the following RF requirements:


Frequency range: 7.9 GHz to 8.4 GHz,
Five channels,
Channel width = 35 MHz,
SCHANNEL, RF(MIN) = –60 dBm,
SCHANNEL, RF(MAX) = –35 dBm,
SNR = 12 dB,
Total link gain = 0 dB,
Input and output impedances = 50 Ω.


Transmitter and Receiver Choice 

Several transmitter/receiver pairs cover the range of 
interest. For this example, the minimum data sheet 
specifications for a typical DFB transmitter are used. 
(Because performance varies for different products, 
other values can be appropriate, depending on the 
specific transmitter chosen.) 

EINLASER < –120 dBm/Hz 
PLASER > 2.4 mW 
IIP3 > +25 dBm 
P1 dB > +13 dBm 
dc modulation gain > 0.06 mW/mA 

For the receiver, consider one that is resistively 
matched to 50 Ω and has no built-in amplifiers: 

RPD > 0.75 mA/mW 

ηRx, RF > 0.375 mA/mW 

Throughout the example, these minimum specification 
values will be used with the understanding that the 
actual link would be expected to perform better than 
the final answers. 

Agere Systems Inc. 

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

Link Design Calculation (continued) 

Gain 

The first thing to consider is the gain. Since the transmitter 
is resistively matched for broadband operation, 
its RF efficiency will be approximately equal to the 
modulation gain of 0.06 mW/mA. The optical losses 
can be determined with: 

equation 29, 

LOPT, dB = (fiber length) . (fiber attenuation) + 
(# connectors) . (connector loss) 

0.4 dB (OPT) 
, --


LOPT dB = (5 km )..
. ------------------------------..
+ ()2 .(0.5 dB max )

km 
LOPT, dB = 3 dB. 

Substituting these values into equation 4 on page 6 
gives for the gain of the optical transmitter, receiver, 
and fiber: 

equation 30, 

GOPTICAL LINK = 20 log(ηTx, RF(ηRx, RF) – 2 LOPT, dB + 
10 log(ROUT/RIN) 

GOPTICAL LINK = 20 log [(0.06 mW/mA) 

(0.375 mA/mW)] – 2 x 3 dB + 0