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1、CHAPTER 9 ANALOG SYSTEMS,9.1 OVERVIEW OF ANALOG LINKS 9.2 CARRIERTO-NO1SE RAT1O 9.2.1 Carrier Power 9.2.2 Photodetertor and Preamplifier Noises 9.2.3 Relative Intensity Noise(RIN)9.2.4 Reflection Effects on RIN 9.2.5 Limiting Conditions,9.3 MULTICHANNEL TRANSMISSION TECHNIQUES 9.3.1 Multichannel Amp
2、litude Modulation 9.3.2 Multichannel Frequency Modulation 9.3.3 Subcarrier Multiplexing,In telecommunication networks the trend has been to link telephone exchanges with digital circuits.A major reason for this was the introduction of digital integrated-circuit technology which offered a reliable an
3、d economic method of transmitting both voice and data signals.Since the initial applications of fiber optics were to telecommunication networks,its first widespread usage has involved digital links.However,in many instances,it is more advantageous to transmit information in analog form instead of fi
4、rst converting it to a digital format.Some examples of this are microwave-multiplexed signals,subscriber services using hybrid fiber/coax(HFC),video distribution antenna remoting,and radar signal processing.For most analog applications,one uses laser diode transmitters,so we shall concentrate on thi
5、s optical source here.When implementing an analog fiber optic system,the main parameters one needs to consider are the carrier-to-noise ratio,bandwidth,and signal distortion resulting from nonlinear ties in the transmission system.Section 9.1describes the general operational aspects and components o
6、f an analog fiber optic link.Traditiona1ly,in an analog system,a carrier-to-noise ratio ana1ysis is used instead of a signal-to-noise ratio analysis,since the information signal is normally superimposed on a radio-frequency(RF)carrier.Thus,in Sec.9.2 we examine carrier-to-noise ratio requirements.Th
7、is is first done for a single channel under the assumption that the information signal is directly modulated onto an optical carrier.,For transmitting multiple signals over the same channel,one can use a sub carrier modulation technique.In this method,which is described in Sec.9.3,the information si
8、gnals are first superimposed on ancillary RF sub carriers.These carriers are then combined and the resulting electrical signal is used to modulate the optical carrier.A limiting factor in these systems is the signal impairment arising from harmonic and intermodulation distortions.,9.l OVERVIEW OF AN
9、ALOG LINKS,Figure 9-l shows the basic elements of an analog link.The transmitter contains either an LED or a laser diode optical source.As noted in Sec.4-4 and shown in Fig.4-35,in analog applications,one first sets a bias point on the source approximately at the midpoint of the linear output region
10、.The analog signal can then be sent using one of several modulation techniques.The simplest form for optical fiber links is direct intensity modulation,wherein simply varying the current around the bias point in proportion to the message signal level modulates the optical output from the source.Thus
11、,the information signal is transmitted directly in the baseband.A somewhat more complex but often more efficient method is to translate the baseband signal onto an electrical sub carrier prior to intensity modulation of the source.This is done using standard amplitude-modulation(AM),frequency-modula
12、tion(FM),or phase-modulation(PM)techniques.No matter which method is implemented,one must pay careful attention to signal impairments in the optical source.These include harmonic distortions,intermodulation products,relative intensity noise(RIM)in the laser,and laser clipping.In relation to the fibe
13、r-optic element shown in Fig.9-l,one must take into account the frequency dependence of the amplitude,phase,and group delay in the fiber.Thus,the fiber should have a flat amplitude and group-delay response within the passband required to send the signal free of linear distortion.In addition,since mo
14、dal-distortion-limited bandwidth is difficult to equalize,it is best to choose a single-mode.,9.l OVERVIEW OF ANALOG LINKS,fiber.The fiber attenuation is also important,since the carrier-to-noise performance of the system will change as a function of the received optical powerThe use of an optical a
15、mplifier in the link leads to additional noise,known as amplified spontaneous emission(ASE),as is described in Chap.11:In the optical receiver,the principal impairments are quantum or shot noise,APD gain noise,and thermal noise.,In analyzing the Performance of analog systems,one usually calculates t
16、he ratio of rms carrier power to rms noise power at the input of the RF receiver following the photodetection process.This is known as the carrier-noise ratio(CNR).Let us look at some typical CNR values for digital and analog data.For digital data,consider the use of frequency-shift keying(FSK).In t
17、his modulation scheme,the amplitude of a sinusoidal carrier remains constant,but the phase shifts from one frequency to another to represent binary signals.For FSK,BERs of10-9 and10-15 translate into CNR values of 36(l5.6 dB)and 64(l8.0 dB),respectively.The analysis for analog signals is more comple
18、x,since it sometimes depends on user perception of the signal quality,such as in viewing a television picture.A widely used analog signal is a 525-line studio-quality television signal.Using amplitude modulation(AM)for such a signal requires a CNR of 56 dB,since the need for bandwidth efficiency lea
19、ds to a high signal-to-noise ratio.Frequency modulation(FM),on the other hand,only needs CNR values of l5-l8 dB.If CNRi represents the carrier-to-noise ratio related to a particular signal contaminant(e.g.,shot noise),then for N signal-impairment factors the total CNR is given by,9.2 CARRIERTO-NO1SE
20、 RAT1O,9.2 CARRIERTO-NO1SE RAT1O,For links in which only a single information channel is transmitted,the important signal impairments include laser intensity noise fluctuations,laser dipping,photoreceptor noise,and optical-amplifier noise.When multiple message channels operating at different carrier
21、 frequencies are sent simultaneously over the same fiber,then harmonic and intermodulation distortions arise.Furthermore,the inclusion of an optical amplifier gives rise to ASE noise.In principle,the three dominant factors that cause signal impairments in a fiber link are sh0t noise,optical-amplifie
22、r noise,and laser clipping.Most other degradation effects can be sufficiently reduced or eliminated.In this section,we shall first examine a simple single-channel amplitude modulated signal sent at baseband frequencies.Section 9.3 addresses multichannel systems in which intermodulation noise becomes
23、 important.Problem 9-l0 gives expressions for the effects of laser clipping and ASE noise.,9.2.l Carrier Power,To find the carrier power,let us first look at the signal generated at the transmitter.As shown in Fig.9-2,the drive current through the optical source is the sum of the fixed bias current
24、and a time-varying sinusoid.The source acts as a square-law device,so that the envelope of the output optical power P(t)has the same form as the input drive cornet.If the time-varying analog drive signal is s(t),then,where Pt is the optical output power at the bias current level and the modulation i
25、ndex m is defined by Eq.(4-54).In terms of optical power,the modulation index is given by,where Ppeak and Pt are defined in Fig.9-2.Typical values of m for analog applications range from 0.25 to 0.50.For a sinusoidal received signal,the carrier power C at the output of the receiver(in units of A2)is
26、,where is the unity gain resp0nsivity of the photodetector,M is the photodetector gain(M=l for pin photodiodes),and P is the average received optical power.,9.2.l Carrier Power,9.2.2 Photodetertor and Preamplifier Noises,The expressions for the photodiode and preamplifier noises are given by Eqs.(6-
27、l6)and(6-l7),respectively.That is,for the photodiode noise we have,Here,as defined in Chap.6,is the primary photocurrent,ID is the detector bulk dark current,M is the photodiode gain with F(M)being its associated noise figure,and B is the receiver bandwidth.Then,the CNR for the photodetector only is
28、 CNRdet=C/2N,Generalizing Eq.(6-l7)for the preamplifier noise,we have,Here,Rqe is the equivalent resistance of the photo detector load and the preamplifier,and Ft is the noise factor of the preamplifier.Then,the CNR for the preamplifier only is CNRdet=C/2N,9.2.3 Relative Intensity Noise(RIN),Within
29、a semiconductor laser,fluctuations in the amplitude or intensity of the output produce optical intensity noise.These fluctuations could arise from temperature variations or from spontaneous emission contained in the laser output.The noise resulting from the random intensity fluctuations is called re
30、lative intensity noise(RIN),which may be defined in terms of the mean-square intensity variations.The resultant mean-square noise current is given by,Then,the CNR due to laser amplitude fluctuations only is CNRRIN=C/2RIN Here,the RIN,which is measured in dB/Hz,is defined by the noise-to-signal Power
31、 ratio.,where is the mean-square intensity fluctuation of the laser output and PL is the average laser light intensity.This noise decreases as the injection-current level increases according to the relationship,9.2.3 Relative Intensity Noise(RIN),Substituting the CNRs resulting from Eqs.(9-4)through
32、(9-7)into Eq.(9-l)yields the following carrier-to-noise ratio for a single-channel AM system:,In implementing a high-speed analog link,one must take special precautions to m1nlmlze optical reflections back into the laser.2 Back-reflected signals can increase the RIN by l0-20 dB as shown in Fig.9-5.T
33、hese curves show the increase in relative intensity noise for bias p0ints ranging from l.24 to l.62times the threshold-curent level.The feedback power ratio in Fig.9-5 is the amount of optical power reflected back into the laser relative to the light output from the source.As an example,the dashed l
34、ine shows that at.l.33Ith the feedback ratio must be less than-60 dB in order to maintain an RIN of less than-l40 dB/Hz.,9.2.4 Reflection Effects on RIN,Let us now look at some limiting conditions.When the optical power level at the receiver is low,the preamplifier circuit noise d0ndnateS the system
35、 noise.For these,we have,9.2.5 Limiting Conditions,In this case,the carrier-to-noise ratio is directly proportional to the square of the received optica1 power,so that for each l-dB variation in received optical power,C/N will change by 2 dB.For well-designed photodiodes,the bulk and surface dark cu
36、rrents are small compared with the shot(quantum)noise for intermediate optical signal levels at the receiver.Thus,at intermediate power levels the quantum-noise term of the photodiode will dominate the system noise.In this case,we have,so that the carrier-to-noise ratio will vary by l dB for every l
37、-dB change in the received optical power.If the laser has a high RIN value so that the reflection noise dominates over other noise terms,then the carrier-to-noise ratio becomes,9.2.6 Limiting Conditions,which is a constant.In this case,the Performance cannot be improved unless the modulation index i
38、s increased.,So far,we have examined only the case of a single signal being transmitted over a channel.In broadband analog applications,such as cable television(CATV)super trunks,one needs to send multiple analog signals over the same fiber.To do this,one can employ a multiplexing technique where a
39、number of baseband signals are superimposed on a set of N sub carriers that have different frequencies f1,f2.f N.These modulated subcarriers are then combined electrically through frequency-division multiplexing(FDM)to form a composite signal that directly modulates a single optical source.Methods f
40、or achieving this include vestigial sideband amplitude modulation(VSB-AM),frequency modulation(FM),and subcarrier multiplexing(SCM).0f these,AM is simple and cost-effective in that it is compatible with the equipment interfaces of a large number of CATV customers,but its signal is very sensitive to
41、noise and nonlinear distorti0n.Although FM requires a larger bandwidth than AM,it provides a higher signal-to-noise ratio and is less sensitive to source nonlinearities.Microwave SCM operates at higher frequencies than AM or FM and is an interesting approach for broadband distribution of both analog
42、 and digital signals.To simplify the interface with existing coaxial cable systems,current fiber links in CATV netw0rks primarily use the AM-VSB Scheme described in Sec.9.3.1,9.3 MULTICHANNEL TRANSMISSION TECHNIQUES,The initial widespread application of analog fiber optic links,which started in the
43、late l980s,was to CATV networks.These coax-based television networks operate in a frequency range from 50 to 88 MHz and from l20 to 550 MHz.The band from 88 to l20 MHz is not used,since it is reserved for FM radio broadcast.The CATV networks can deliver over 80 amplitude-modulated vestigial-sideband
44、(AM-VSB)video channels,each having a noise bandwidth of 4MHz within a channel bandwidth of 6 MHz,with signal-to-noise ratios exceeding 47 dB.To remain compatible with existing coax-based networks,a multichannel AM-VSB format was also chosen for the fiber optic system.Figure 9-7 depicts the technique
45、 for combining N independent messages.An information bearing signal on channel i amplitude-modulates a carrier wave that has a frequency fi,where i=l,2.,N.An RF power combiner then sums these N amplitude-modulated carriers to yield a composite frequency-division-multi-plexed(FDM)signal which intensi
46、ty-modulates a laser diode.Following the optical receiver,a bank of parallel bandpass filters separates the combined carriers back into individual channels.The individual message signals are recovered from the carriers by standard RF techniques.For a large number of FDM carriers with random phases,t
47、he carriers add on a power basis.Thus,for N channels the optical modulation index m is related to the per-channel modulation index mi by,9.3.1 Multichannel Amplitude Modulation,9.3.1 Multichannel Amplitude Modulation,9.3.1 Multichannel Amplitude Modulation,If each channel modulation indexes mi has t
48、he same value mc,then,As a result,when N signals are frequency-multiplexed and used to modulate a single optical source,the carrier-to-noise ratio of a single channel is degraded by l0logN.If only a few channels are combined,the signals will add in voltage rather than power,so that the degradation w
49、ill have a 20log N characteristic.When multiple carrier frequencies pass through a nonlinear device such as a laser diode,signal products other than the original frequencies can be produced.As noted in Sec.4.4,these undesirable signals are called intermodulation products and they can cause serious i
50、nterference in both in-band and out-of band channels.The result is a degradation of the transmitted signal.Among the intermodulation products,generally only the second-order and third-order terms are considered,since higher-order products tend to be significantly smaller.Third-order intermediation(I
