where k is the Boltzmann constant, T is the absolute temperature, F (a)I PINA-LNA is the noise figure of the amplifier, and R, is the input impedance. For a 50- input impedance and F=2, n=20 pA/VHz A variety of more complicated receiver designs can reduce the noise current appreciably [Kasper, 1988]. The example shown in Fig. 71. 2(b)uses a high-speed FET. Ri can be increased to maximize the voltage developed by the signal current at the FET input. Input capacitance becomes a limitation by shunting high-frequency com ponents of signal current High-frequency signals are then reduced (b)[PIN-FET] with respect to the noise generated in the FET, resulting in poor high rformance. Various impedance matching technique have been proposed to maximize the CNR for specific frequency Relative Intensity Noise GATE Relative intensity noise(RIN) can originate from the laser or from reflections and Rayleigh backscatter in the fiber. In the laser, RIN FIGURE 71.2 Receivers for broadband caused by spontaneous emission in the active layer. Spontaneous to a low-noise amplifier(a)is simple, but ion drives random fluctuations in the number of photons he laser which appear as a random modulation of the output inten- using designs like the pin FET(b)C,is the ity, with frequency components extending to tens of gigahertz. The undesirable input capacitance noise power spectral density from RiN is 1? RIN, where RIN expressed in decibels per hertz. RIN is also caused by component reflections and double-Rayleigh backscatter in the fiber, by a process called multipath interference. Twice-reflected signals arriving at the detector can interfere coherently with the unre- flected signal. Depending on the modulated optical spectrum of the laser, this interference results in noise that can be significant[Darcie et al, 1991] The CNR, including all noise sources discussed, is given by 21 CNR (71.6) 2BIn2 +2el +RIN All sources of intensity noise are combined into RIN. Increasing m improves the CNR but increases the impairment caused by nonlinearity, as discussed in the following subsection. The optimum operating value for m is then a balance between noise and distortion Figure 71.3 shows the noise contributions from shot noise, receiver noise, and RIN For FM or digital systems, the low CNR values required allow operation with small received optical powers. Receiver noise is then generally the limiting factor. Much larger received powers are required if AM-VSB noise requirements are to be met Although detecting more optical power helps to overcome shot and receiver noise, the ratio of signal to RIN remains constant. RIN can be dominant in high-CNR systems, when the received power is large. AM-VSB systems require special care to minimize all sources of rin. The dominant noise source is then shot noise, with receiver noise and RIN combining to limit CNRs to within a few decibels of the quantum limit. Linearity Requirements Source linearity limits the depth of modulation that can be applied. Linearity, in this case, refers to the linearity of the current-to-light-intensity (I-L) conversion in the laser or voltage-to-light(V-L)transmission for an external modulator. Numerous nonlinear mechanisms must be considered for direct modulation and no existing external modulator has a linear transfer function A Taylor-series expansion of the I-Lor V-L characteristic, centered at the bias point, results in linear, quadratic, cubic, and higher-order terms. The linear term describes the efficiency with which the applied signal is converted e 2000 by CRC Press LLC
© 2000 by CRC Press LLC where k is the Boltzmann constant, T is the absolute temperature, F is the noise figure of the amplifier, and RL is the input impedance. For a 50-W input impedance and F = 2, n = 20 pA/ . A variety of more complicated receiver designs can reduce the noise current appreciably [Kasper, 1988]. The example shown in Fig. 71.2(b) uses a high-speed FET. RL can be increased to maximize the voltage developed by the signal current at the FET input. Input capacitance becomes a limitation by shunting high-frequency components of signal current. High-frequency signals are then reduced with respect to the noise generated in the FET,resulting in poor highfrequency performance. Various impedance matching techniques have been proposed to maximize the CNR for specific frequency ranges. Relative Intensity Noise Relative intensity noise (RIN) can originate from the laser or from reflections and Rayleigh backscatter in the fiber. In the laser, RIN is caused by spontaneous emission in the active layer. Spontaneous emission drives random fluctuations in the number of photons in the laser which appear as a random modulation of the output intensity, with frequency components extending to tens of gigahertz. The noise power spectral density from RIN is I 2 r RIN, where RIN is expressed in decibels per hertz. RIN is also caused by component reflections and double-Rayleigh backscatter in the fiber, by a process called multipath interference. Twice-reflected signals arriving at the detector can interfere coherently with the unre- flected signal. Depending on the modulated optical spectrum of the laser, this interference results in noise that can be significant [Darcie et al., 1991]. The CNR, including all noise sources discussed, is given by (71.6) All sources of intensity noise are combined into RIN. Increasing m improves the CNR but increases the impairment caused by nonlinearity, as discussed in the following subsection. The optimum operating value for m is then a balance between noise and distortion. Figure 71.3 shows the noise contributions from shot noise,receiver noise, and RIN. For FM or digital systems, the low CNR values required allow operation with small received optical powers. Receiver noise is then generally the limiting factor. Much larger received powers are required if AM-VSB noise requirements are to be met. Although detecting more optical power helps to overcome shot and receiver noise, the ratio of signal to RIN remains constant. RIN can be dominant in high-CNR systems, when the received power is large. AM-VSB systems require special care to minimize all sources of RIN. The dominant noise source is then shot noise, with receiver noise and RIN combining to limit CNRs to within a few decibels of the quantum limit. Linearity Requirements Source linearity limits the depth of modulation that can be applied. Linearity, in this case, refers to the linearity of the current-to-light-intensity (I-L) conversion in the laser or voltage-to-light (V-L) transmission for an external modulator. Numerous nonlinear mechanisms must be considered for direct modulation, and no existing external modulator has a linear transfer function. A Taylor-series expansion of the I-L or V-L characteristic, centered at the bias point,results in linear, quadratic, cubic, and higher-order terms. The linear term describes the efficiency with which the applied signal is converted FIGURE 71.2 Receivers for broadband analog lightwave systems. Coupling a pin to a low-noise amplifier (a) is simple, but improved performance can be obtained using designs like the pin FET (b). Ct is the undesirable input capacitance. Hz CNR RIN] = + + m I B n eI I r r r 2 2 2 2 2 [ 2
TOTAL FIGURE 71.3 Current noise densities from receivers, RiN, and not noise as a function of total received photocurrent. Receiver o oise is dominant in FM or some digital systems where the total received power is small. The solid line for receiver noise represents IN(-150 dB/Hz) the noise current for a typical 50-52 low-noise amplifier. More sophisticated receiver designs could reduce the noise to the levels wn approximately by the dotted lines. RIN and shot noise more important in AM-VSB systems 8 ll mmmmmmmn 0.8 0.4 H0bttio 250 FIGURE 71.4 Second-order(a)and third-order(b)distortion products for 42-channel AM-VSB system. The maximum number of second-order products occurs at the lowest frequency channel, where 30 products contribute to the CSO. The maximum number of third-order products occurs near the center channel, where 530 products contribute to the CtB to linear intensity modulation. The quadratic term results in second-order distortion, the cubic produces third order distortion and so on. Requirements on linearity can be derived by considering the number and spectral distribution of the distortion products generated by the nonlinear mixing between carriers in the multichannel signal. Second order nonlinearity results in sum and difference +f) mixing products for every combination of the two channels. This results in as many as 50 second-order products within a single channel, in a 60-channel AM VSB system with the standard U.S. frequency plan. Similarly, for third-order distortion, products result from mixing among all combinations of three channels. However, since the number of combinations of three channels much larger than for two, up to 1130 third-order products can interfere with one channel. The cable industry defines the composite second-order( CSo)distortion as the ratio of the carrier to the largest group of second order products within each channel. For third-order distortion, the composite triple beat( CTB)is the ratio of the carrier to the total accumulation of third-order distortion at the carrier frequency in each channel. The actual impairment from these distortion products depends on the spectrum of each RF channel and on the exact frequency plan used. A typical 42-channel AM-VSB frequency plan, with carrier frequencies shown as the vertical bars on Fig 71.4, results in the distributions of second- and third-order products shown in Fig. 71.4(a)and(b), respectively. Since the remaining carrier is the dominant feature in the spectrum of each annel, the dominated by the video requires that the CSO is -60 dBc(dB relative to the carrier), each sum or difference product must be less than-73 dBc. Likewise, for the CTB to be less than 60 dB, each product must be less than approximately -90dB e 2000 by CRC Press LLC
© 2000 by CRC Press LLC to linear intensity modulation. The quadratic term results in second-order distortion, the cubic produces thirdorder distortion, and so on. Requirements on linearity can be derived by considering the number and spectral distribution of the distortion products generated by the nonlinear mixing between carriers in the multichannel signal. Secondorder nonlinearity results in sum and difference (fi ± fj) mixing products for every combination of the two channels. This results in as many as 50 second-order products within a single channel, in a 60-channel AMVSB system with the standard U.S. frequency plan. Similarly, for third-order distortion, products result from mixing among all combinations of three channels.However, since the number of combinations of three channels is much larger than for two, up to 1130 third-order products can interfere with one channel. The cable industry defines the composite second-order (CSO) distortion as the ratio of the carrier to the largest group of secondorder products within each channel. For third-order distortion, the composite triple beat (CTB) is the ratio of the carrier to the total accumulation of third-order distortion at the carrier frequency in each channel. The actual impairment from these distortion products depends on the spectrum of each RF channel and on the exact frequency plan used. A typical 42-channel AM-VSB frequency plan, with carrier frequencies shown as the vertical bars on Fig. 71.4, results in the distributions of second- and third-order products shown in Fig. 71.4(a) and (b), respectively. Since the remaining carrier is the dominant feature in the spectrum of each channel, the distortion products are dominated by the mixing between these carriers. Because high-quality video requires that the CSO is –60 dBc (dB relative to the carrier), each sum or difference product must be less than –73 dBc. Likewise, for the CTB to be less than 60 dB, each product must be less than approximately –90dB. FIGURE 71.3 Current noise densities from receivers, RIN, and shot noise as a function of total received photocurrent. Receiver noise is dominant in FM or some digital systems where the total received power is small. The solid line for receiver noise represents the noise current for a typical 50-W low-noise amplifier. More sophisticated receiver designs could reduce the noise to the levels shown approximately by the dotted lines. RIN and shot noise are more important in AM-VSB systems. FIGURE 71.4 Second-order (a) and third-order (b) distortion products for 42-channel AM-VSB system. The maximum number of second-order products occurs at the lowest frequency channel, where 30 products contribute to the CSO. The maximum number of third-order products occurs near the center channel, where 530 products contribute to the CTB
FM EXTERNAL FIGURE715 Resonance distortion for directly modulated laser 9-60 with resonance frequency of 7 GHz. Both the second-harmonic 2 and two-tone third-order 2fi f; distortion peak near half the res- m=004 onance frequency and are small at low frequency. Also shown is the _10 same third-order distortion for an external modulator biased at the FREQUENCY(GHz) FM or CDV systems have much less restrictive linearity requirements, because of the reduced sensitivity to impairment. Distortion products must be counted, as with the AM-VSB example described previously, but each product is no longer dominated by the remaining carrier. Because the carrier is suppressed entirely by the modulation, each product is distributed over more than the bandwidth of each channel. The impairment resulting from the superposition of many uncorrelated distortion products resembles gous to the CSO and CtB can be defined for these systems Laser linearity Several factors limit the light-versus-current(L-D linearity of directly modulated lasers. Early work on laser dynamics led to a complete understanding of resonance-enhanced distortion(RD). Rd arises from the same carrier-Photon interaction within the laser that is responsible for the relaxation-oscillation resonance The second-harmonic distortion(2ff) and two-tone third-order distortion(2f: -fi) for a typical 1.3-um wavelength directly modulated semiconductor laser are shown in Fig. 71.5 [ Darcie et al, 1986. Both distortions are small at low frequencies but rise to maxima at half the relaxation resonance frequency. AM-VSB systems are feasible only within the low-frequency window. FM or uncompressed digital systems require enough band- one-octave frequency band(eg-,2-4 GHz), such that all second-order products are out ofbant ating withina e. width per channel that multichannel systems must operate in the region of large RD. Fortunately, the CNR require ments allow for the increased distortion. The large second-order RD can be avoided entirely by op within the frequency range between 50 and 500 MHz, nonlinear gain and loss, intervalence-band absorption, and, more importantly, spatial-hole burning(SHB)and carrier leakage can all be significant. Carrier leakage prevents all of the current injected in the laser bond wire from entering the active layer. This leakage must be ations SHB results from the nonuniform distribution of optical power along the length of the laser In DFB lasers, because of the grating feedback, the longitudinal distribution of optical power can be highly nonuniform. This results in distortion [Takemoto et al., 1990] that can add to or cancel other distortion, making it, in some cases, a desirable effect Even if all nonlinear processes were eliminated, the allowable modulation would be limited by the fact that the minimum output power is zero. Typical operating conditions with, for example, 60 channels, each with an average modulation depth(m)near 4%, result in a peak modulation of 240%. Although improbable, modu- lations of more than 100%result in clipping The effects of clipping were first approximated by Saleh [1989], who calculated the modulation level at which the total power contained in all orders of distortion became appreciable. Even for perfectly linear lasers, the modulation depth is bounded to values beyond which all orders of distortion increase rapidly. Assuming that half the total power in all orders of distortion generated by clipping is distributed evenly over each of N channels, clipping results in a carrier-to-interference ratio(CIR) given by CIR (71.7) e 2000 by CRC Press LLC
© 2000 by CRC Press LLC FM or CDV systems have much less restrictive linearity requirements, because of the reduced sensitivity to impairment. Distortion products must be counted, as with the AM-VSB example described previously, but each product is no longer dominated by the remaining carrier. Because the carrier is suppressed entirely by the modulation, each product is distributed over more than the bandwidth of each channel. The impairment resulting from the superposition of many uncorrelated distortion products resembles noise. Quantities analogous to the CSO and CTB can be defined for these systems. Laser Linearity Several factors limit the light-versus-current (L-I) linearity of directly modulated lasers. Early work on laser dynamics led to a complete understanding of resonance-enhanced distortion (RD). RD arises from the same carrier-photon interaction within the laser that is responsible for the relaxation-oscillation resonance. The second-harmonic distortion (2fi) and two-tone third-order distortion (2f i – fj) for a typical 1.3-mm wavelength directly modulated semiconductor laser are shown in Fig. 71.5 [Darcie et al., 1986]. Both distortions are small at low frequencies but rise to maxima at half the relaxation resonance frequency. AM-VSB systems are feasible only within the low-frequency window. FM or uncompressed digital systems require enough bandwidth per channel that multichannel systems must operate in the region of large RD. Fortunately, the CNR requirements allow for the increased distortion. The large second-order RD can be avoided entirely by operating within a one-octave frequency band (e.g., 2–4 GHz), such that all second-order products are out of band. Within the frequency range between 50 and 500 MHz, nonlinear gain and loss, intervalence-band absorption, and, more importantly, spatial-hole burning (SHB) and carrier leakage can all be significant. Carrier leakage prevents all of the current injected in the laser bond wire from entering the active layer. This leakage must be reduced to immeasurable levels for AM-VSB applications. SHB results from the nonuniform distribution of optical power along the length of the laser. In DFB lasers, because of the grating feedback, the longitudinal distribution of optical power can be highly nonuniform. This results in distortion [Takemoto et al., 1990] that can add to or cancel other distortion, making it, in some cases, a desirable effect. Clipping Even if all nonlinear processes were eliminated, the allowable modulation would be limited by the fact that the minimum output power is zero. Typical operating conditions with, for example, 60 channels, each with an average modulation depth (m) near 4%, result in a peak modulation of 240%. Although improbable, modulations of more than 100% result in clipping. The effects of clipping were first approximated by Saleh [1989], who calculated the modulation level at which the total power contained in all orders of distortion became appreciable. Even for perfectly linear lasers, the modulation depth is bounded to values beyond which all orders of distortion increase rapidly. Assuming that half the total power in all orders of distortion generated by clipping is distributed evenly over each of N channels, clipping results in a carrier-to-interference ratio (CIR) given by (71.7) FIGURE 71.5 Resonance distortion for directly modulated laser with resonance frequency of 7 GHz. Both the second-harmonic 2fi and two-tone third-order 2fi ± fj distortion peak near half the resonance frequency and are small at low frequency. Also shown is the same third-order distortion for an external modulator biased at the point of zero second-order distortion. CIR = + 2 1 6 2 3 1 2 2 p m m ( ) / m e