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Development of a laser diode clipping model

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Title:
Development of a laser diode clipping model
Creator:
Chamberlain, Craig M
Publication Date:
Language:
English
Physical Description:
vii, 74 leaves : illustrations ; 29 cm

Subjects

Subjects / Keywords:
Diodes, Semiconductor ( lcsh )
Fiber optics ( lcsh )
Diodes, Semiconductor ( fast )
Fiber optics ( fast )
Genre:
bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

Notes

Bibliography:
Includes bibliographical references (leaf 75).
General Note:
Submitted in partial fulfillment of the requirements for the degree, Master of Science, Electrical Engineering.
Statement of Responsibility:
by Craig M. Chamberlain.

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Source Institution:
University of Colorado Denver
Holding Location:
Auraria Library
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
37366672 ( OCLC )
ocm37366672
Classification:
LD1190.E54 1996m .C43 ( lcc )

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DEVELOPMENT OF A LASER DIODE CLIPPING MODEL by Craig M Chamberlain BSEE, University of South Florida, 1988 A thesis submitted to the University of Colorado at Denver in partial fulfillment of the requirements for the degree of Master of Science Electrical Engineering 1996

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This thesis for the Master of Science degree by Craig M. Chamberlain has been approved by Do las Ross Tamal Bose Mike Radenkovic

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Chamberlain, Craig M. (M.S., Electrical Engineering) Development of a Laser Diode Clipping Model Thesis directed by Associate Professor Douglas Ross Fundamental limits in a fiber optic network can dictate the number of video and data channels that can be multiplexed into a cable television network. The most prominent distortions are relative intensity noise (RIN) in the laser diode, nonlinear distortions (NLD) such as those characteristic of the laser diode, and photo diode shot noise. There is a basic limit to the number of cable video channels and the optical depth of modulation that can be put on a laser diode before impairments distort the video to such an extent as render quality unacceptable. The distortion is seen in the form of composite second order (CSO) and composite tnple beat (CTB) impairments, as well as clipping noise. This research will show the development of a laser diode clipping model used to detennine and simulate the clipping effect in a laser diode. This model will allow a clearer understanding of the effects of clipping in a cable television network and the limitations that it imposes on the network. This abstract accurately represents the content of the candidate's thesis. I recommend its publication. Signed ouglas Ross

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............................................................................................................. ....................................................................... ...................................................................... ................................................................................ 3 .............................................................................................. 3 ....................................................... .......................................................................................... 8 ............................................................................................ 8 ................................................................................ 9 ........................................................... ................................................................................ ..................................................................................... 13 ......................................................................................... 13 ....................................................................................... ...................................................... ................................................................... .................................................................................................... ........................................................................ ...................... : ................................... ...................................................... ................................................................................ ....................................................... .......................................................................................... 25 ...................................................... ...................................................... ........................................................................... ........................................................................................................ ...................................................... ........................................................

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3.2 Measuring the Minimum DOM for No Clipping ................................................ 34 3.3 Depth of Modulation vs. CINLD Ratio ............................................................... 36 3.4 CINLD Ratio vs. Channel ................................................................................... 36 3.5 Graphical Data .................................................................................................... 37 3.6 Summary of Results ............................................................................................ 40 4. Laboratory Results ................................................................................................ 41 4.1 Test Set-up .......................................................................................................... 41 4.2 Procedure for Measuring Clipping ...................................................................... 44 4.3 Data Taken .......................................................................................................... 45 4.3.1 Continuous Wave Carriers ............................................................................... 45 4.3.2 Modulated Carriers .......................................................................................... 47 4.3.3 Examples of DOM Calculations ...................................................................... 50 4.4 Data Results ........................................................................................................ 52 4.5 Distortion Data .................................................................................................... 54 4.6 Notes on the Measurements ................................................................................ 58 4.7 Summary of Data ................................................................................................ 59 5. Comparison of Laboratory and Model Results ..................................................... 60 5.1 Graphical Comparisons of Laboratory and Model Data ..................................... 60 5.2 Comparison of Channel vs. CINLD .................................................................... 63 5.3 Summary ............................................................................................................. 65 6. Conclusions/ Future Work .................................................................................... 66 6.1 Future Work ........................................................................................................ 66 Appendices A l'ypical Channel Line Up ....................................................................................... 68 B Model of Cable Television Headend ...................................................................... 72 C Depth Of Modulation and Carrier-to-Nonlinear Distortion Data ........................... 73 References .................................................................................................................. 75 v

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FIGURES Figure 1.1 Cable System Frequency Plan ................................................................... 4 Figure 1.2 Traditional and Future Cable Frequency Plans ........................................ 4 Figure 1.3 Cable System Components ........................................................................ 5 Figure 1.4 VSB Signal Transformation ...................................................................... 6 Figure 1.5 Upconverted Channel Signal ..................................................................... 7 Figure 1.6 Headend Block Diagram ........................................................................... 8 Figure 1.7 Tree and Branch Topology ........................................................................ 9 Figure 1.8 lIFC Network .......................................................................................... 11 Figure 1.9 Branch of lIFC Network ......................................................................... 11 Figure 1.10 Reflections in a System......................................................................... 14 Figure 1.11 Transfer Characteristics .... .................... ..... ..... ....................................... 15 Figure 1.12 CSO/CTB. ................................................. ..... ..... .................................. 16 Figure 2.1 Laser Bias ................................................................................................ 19 Figure 2.2 High-Level System Block Diagram ........................................................ 22 Figure 2.3a Headend Block Diagram ........................................................................ 23 Figure 2.3b Individual Channel in Headend Block .................................................. 23 Figure 2.4a Representation of Headend Output Signal (Time Domain) Channel 2............................................................................................... 24 Figure 2.4b Representation of Headend Output Signal (Frequency Domain) Channel 2............................................................................................... 24 Figure 2.5 High-Level Laser Block Diagram ........................................................... 25 Figure 2.6 Detailed Laser Block Diagram ................................................................ 26 Figure 2.7 Plot of the LII Characteristics of the Test Diode ..................................... 27 Figure 2.8 Filter Design System (Channel 13) ......................................................... 29 Figure 2.9 Signal Calculator Front Panel.. ................................................................ 31 Figure 2.10 Example of Headend Output ......................................................... 32 Figure 3.1 Sample Depth of Modulation Calculation ............................................... 33 Figure 3.2 Depth of Modulation Calculation / Calibration ....................................... 34 vi

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Figure 3.3 Theoretical Limit Of DOM with No Clipping ........................................ 35 Figure 3.4 Clipping Starts to Occur .......................................................................... 35 Figure 3.5 Depth of Modulation vs. CarrierlNLD Ratio .......................................... 36 Figure 3.6 CINLD vs. Channel ................................................................................. 37 Figure 3.7 Time Domain Representation of Clipped Signal ..................................... 38 Figure 3.8 Frequency Domain Representation of Clipped Signal ............................ 38 Figure 3.9 CW Carrier with Distortions ................................................................... 39 Figure 3.10 Headend Output (No Clipping) Frequency Domain ............................. 39 Figure 3.11 Headend Output (Severe clipping) Frequency Domain ........................ 40 Figure 4.1 Test Set-Up of Clipping System .............................................................. 41 Figure 4.2 Pre-distortion Block Diagram .................................................................. 42 Figure 4.3 Photodiode Small Signal Model.. ............................................................ 43 Figure 4.4 CW Carriers at Nominal Levels (no clipping) ......................................... 46 Figure 4.5 CW Carriers at Severe Clipping Levels .................................................. 47 Figure 4.6 Modulated NTSC Headend (no clipping) ................................................ 48 Figure 4.7 Modulated NTSC Headend (severe clipping) ......................................... 49 Figure 4.8 Channel vs. Depth Of Modulation ........................................................... 53 Figure 4.9 Channel vs. CINLD ................................................................................. 53 Figure 4.10 Channel 13 Distortions .......................................................................... 54 Figure 4.11 Channel 13 Distortions with Modulated Carrier ................................... 55 Figure 4.12 Channel 13 Distortions with CW Carrier .............................................. 56 Figure 13 Channel 46 Distortions ............................................................................. 57 Figure 4.14 Channel 70 Distortions .......................................................................... 58 Figure 5.1a Channel 13 Model. ................................................................................. 60 Figure 5.1b Channel 13 Laboratory (Comparison of Distortions) ............................. 61 Figure 5.2a Channel 13 Model. ................................................................................. 62 Figure 5.2b Channel 13 Laboratory (Comparisons of Distortions with CW Carriers in Band) .................................................................... 63 Figure 5.3 Comparison of Laboratory and Model Data Channel vs. CINLD ........... 64 vii

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1. Introduction Cable television has enjoyed enonnous growth because of its widespread popularity, and has grown from being a video provider to a telecommunications services provider. These services include High-Definition Television (HDTV), High Speed Data Services, and telephony. As cable services have expanded, new technologies have been used, and it has become increasingly important that the highest quality of service be maintained. This research is intended to explore one of the areas of cable industry growth, use of fiber optic technology, and the challenges that this technology has brought to the industry. This work is intended to provide a basic design tool for cable television operators, as they design and upgrade the cable television infrastructure. In a typical fiber optic network design, laser relative intensity noise (RIN) and photodiode shot noise are device-specific and should be considered in the network noise budget. Nonlinear distortions (NLD) in a laser diode, such as laser clipping, can limit system perfonnance. In order to get the best carrier to noise (CNR) and carrier to interference (CII) out of a laser diode, it is common practice in the cable industry to run the diode into a limited amount of clipping. Based on past research, there is a basic limit to the number of cable video channels and the depth of modulation that can be put on a laser diode before impainnents distort the video to such an extent as to render it unacceptable. This project developed a laser diode clipping model that is used to detennine and to simulate the clipping effect in a laser diode. The model will demonstrate the effects of clipping on cable networks. This report gives a brief overview of the cable television industry and its natural progression towards a hybrid analog and digital network, background infonnation on the clipping problem, and a description of the simulation development and simulation results. 1.1 Goals and Objectives of this Study There are several goals associated with developing this model. The laser diode clipping model will allow cable network designers to understand the limitations that nonlinear distortions (NLD) have on a fiber optic communications system. The basic model blocks developed here are "stepping stones" to developing a larger, more complicated model of the HFC network that is now common in the cable industry. Using the custom blocks of the headend and the laser diode model, the user can add digital services and see the effects of NLD on these data services. Any laser diode can now be easily modeled given a few defined parameters.

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Nonlinear distortions are the limiting factor in a cable network with multiple carriers. With this model, a network designer can now predict some of the possible limitations in a new network, without the cost and time associated with testing and reconfiguring the network after it is built. According to A.C. Nielsen, cable television service is enjoyed by more than 59 million US households. Cable service passes about 95 percent of the households in the US, which equates to a market penetration of about 63percent.[1] Cable television uses a physical transmission plant to distribute many television signals throughout a community or an area. The acronym CATV stands for Community Antenna Television Services, but it is recognized today as cable television. The original purpose for cable television was to deliver broadcast signals in areas where over-the-air reception was very poor. Poor-quality reception is usually due to long distances between transmitters or to mountainous terrain. In 1948, Ed Parson of Astoria, Oregon, built the first CATV system, consisting of twin-lead transmission wire strung from housetop to housetop. 1950, Bob Tarlton built a system in Lansford, Pennsylvania, using coaxial cable on utility poles, under a franchise from the city. These first few systems usually served small communities and had just a few televisions channels. Picture quality was somewhat poor, but the cable systems allowed subscribers to view broadcast television, which they couldn't receive over the air. Another area where cable television was welcomed in its early development was in large cities such as New York, where many large buildings produce extensive reflections of the over-the-air broadcast signals, making the television picture unwatchable. By the late 1960's all areas that could benefit from a direct coaxial connection to a cable television provider had been connected to a cable system, and growth in the industry slowed to a crawl. The advent of satellite delivery of signals to the headend in the 1970's brought a new explosive growth in the cable industry; in existing cable systems and in areas that previously had not required cable because of their good terrestrial transmission. With signals delivered by satellite, many additional television channels could be delivered to the home. This sparked several new categories of service: "Super Stations" -local stations that are distributed over satellite, such as Turner Broadcast System (TBS) which pioneered this concept. 2

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Specialized channels for news, weather, sports, education, and shopping. Exam ples are CNN, The Weather Channel, ESPN, Home Shopping Network, and Mind Extension University. Movie channels such as Home Box Office (HBO) and Showtime. The cable industry was not intended to be a general-purpose communications system, but in the last few years new technologies have led the industry to expand into different areas of communications and to become involved in many different applications. The late 1980's and early 1990's have brought an increased interest in the "Infonnation Superhighway," also called the National Infonnation Infrastructure (NIl). A national infonnation infrastructure will provide all types of services to the consumer, including entertainment video, telephony, multimedia, access to data services, etc. Because of cable's high-bandwidth capabilities and its depth of penetration, these services are likely to be delivered via the cable infrastructure, in both analog and digital fonnat. Thus, cable is becoming more that just the "community antenna" for areas of poor reception. Cable television is becoming a means of delivering nationally transmitted high-quality video. 1.3 Basic System Layout 1.3.1 The Cable System The cable industry primarily has been used to provide high-quality signals originating from a central location called a headend and send the signal "downstream" to the subscriber. Only recently has the need for "upstream" transmission been required for new services. These services have included Near Video on Demand, Video on Demand, Telephony and high-speed data services all which will require two-way transmission. Recently operators of most large cable systems have begun extensive upgrades of existing cable plats, which has included extensive use of fiber in both the upstream and downstream directions. The typical upgraded cable system is a closed system with spectrum use from 50 to 550 MHz in the "downstream" direction (to the consumer) and from 5 to 42 MHz in the "upstream" or return path. Figure 1.1 shows a typical frequency plan for a 400-MHz system. While more advanced systems will go up to 750 MHz, or even 1 GHz, most systems are currently limited to 550 MHz. A typical system is made up of modulated analog signals frequency spaced at 6-MHz intervals, as shown in Figure 1.1. Appendix A shows a typical channel line-up for a local cable system. In the near future, cable systems will also carry digital signals for a variety of different applications. It is this combination of analog and digital signals that future cable systems will carry. Figure 3

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1.2 shows a high-level diagram of a traditional cable frequency plan and one possible future frequency plan (as digital services are integrated into the networks). 3 3 eo 70 5 5 eo 1>.2 AI ... C IIID /'.... Figure 1.1 Cable System Frequency Plan 22 7 7 170 leo 5 42 sse 5 42 ko 50 9 Figure 1.2 Traditional and Future Cable Frequency Plans 4 .....

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Prior to the 1980's when fiber optic communication technology became economically feasible, cable networks were constructed exclusively with coaxial cable. There are five major segments to a cable system: 1) the headend, 2) the trunk cable, 3) the distribution cable, 4) the drop cable to the home, and 5) consumer electronics and associated wiring in the home (television set and VCR). Segments 2, 3, and 4 are the main focus of this study, and are shown in Figure 1.3 : ..... ; : ......... ; : _J : ____ __ Figure 1.3 Cable System Components Currently, cable television channels occupy 6 MHz of bandwidth according to NTSC (National Television Standards Committee) standard. Each television channel consumes 6 MHz, using vestigial sideband amplitude modulation (VSB-AM). VSB AM contains about the same bandwidth advantage as single sideband modulation but does not have the disadvantages of stringent roll-off filters and a difficult modulation process. we begin with a double sideband amplitude modulation CDSB-AM) signal and filter out one of the sidebands, using a filter that does not closely approach an ideal filter, Figure 1.4 depicts the resultant VSB transformation. 5

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t -w 112 .. ... .. 0 Recona1ruted SiQnal Figure 1.4 VSB Signal Transfonnation 6 lPF

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Compared with the 8.4 MHz needed for DSB-AM, VSB-AM transmits one complete sideband and only a vestige of the other. At the time the NTSC standard was created, electronics consisted of vacuum tubes: it was important to avoid the complexities of single sideband transmission. VSB-AM was an effective compromise for the constraints of the times. Once the signal is modulated, it is then unconverted to the appropriate RF frequency to be placed onto the cable system. Figure 1.5 shows the frequency layout of a single, upconverted channel of a local cable system. While VSB is an older technology, created in the 1940's, the cost of a change-over would be an enonnous economic impact. There are approximately 200 million television sets and 100 million VCRs in use; the change-over to any new technology would take an estimated 20 years. 4 ilMII------4.5 11 ... .-----3.58 1 1Figure 1.5 Upconverted Channel Signal 7

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1.3.3 Headend Description While the headend at each cable system can be distinctly different, there are several components that are similar. The headend can be thought of as the main signal reception, origination, and modulation point for the cable system. It performs some or all of the following functions: Receives satellite programming Receives over-the-air broadcast of television and radio signals Receives return-band signals from subscribers Modulates received signals onto channel assignments Inserts local advertising. Figure 1.6 shows a basic block diagram of a headend. Figure 1.6 Headend Block Diagram The trunk cable, the distribution cable, and the drop section will be discussed in detail in Section 1.4, System Architectures. 1.4 System Architectures There are two distinct type of architectures in cable networks today: the tree-and branch topology and the Hybrid Fiber/Coax (HFC) system. 8

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The cable architecture used until the 1980's was called the "tree-and-branch topology," shown in Figure 1.7. The cable system is divided into three major parts: the trunk, the distribution, and the drop. The trunk is intended to cover large distances up to several miles. Amplifiers in the trunk portion of the system are spaced at 2000-foot intervals to maintain signal quality. At certain points, the signal is tapped off using a bridger amplifier. This tapped portion of the system is then fed into the feeder portion of the network The trunk portion of the cable network makes up approximately 12 percent of the cable system [2]. Figure 1.7 Tree and Branch Topology The next section of the system can be considered the feeder, or the distribution, portion of the system. This is a second level of cable design, and is entirely different from the trunk portion. The distribution portion of the system feeds the passive taps to the subscribers and has a maximum length of a few miles; limited by the number of taps to subscribers Approximately 38 percent of the total footage of a cable system is comprised of the distribution, or feeder, network [2] High power levels are required to supply all the taps, and thus amplifiers used in this portion of the network are operated closer to the nonlinear region. Therefore, only a few amplifiers can be used in this 9

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portion of the network, and intennodulation distortion becomes one of the limiting factors. (System limiting factors will be discussed in the next section.) The last section of the cable system is the drop cable that goes from the tap to the subscriber's home. This portion of the trunk is the hardest to maintain, because the operator has little control over what the subscriber decides to do to the signal when it reaches the home. Consumer components with poor perfonnance are readily available from local distributors, with the ability to greatly reduce signal quality in the home. (HFC) As fiber optic technology became more mature, it seemed to be the natural progression to upgrade cable systems with fiber optics. A hybrid fiber/coax (HFC) architecture has evolved to replace the tree-and-branch topology. Figure 1.8 shows a basic HFC network. this architecture, fiber optic cabling feeds a node. A node can consist of anywhere from 200 to 1 ()()() subscribers. As fiber optic technology becomes more cost-effective, the node size will become smaller, and this will allow more effective bandwidth usage and allow more services to be delivered to the subscriber. Optical-to-electronic (OlE) conversion takes place at each node, and the subscriber is then fed the signal through a minimum length of coaxial cable and active devices, thus maintaining high signal quality. This architecture allows the cable operator to deliver high quality with minimum maintenance (most trunk amplifiers are eliminated). In an HFC network, both fiber optics and coaxial cable complement each other very well. The advantages of fiber are well known. They include very low attenuation, high bandwidth, relatively low cost of the fiber, and immunity to electromagnetic interference. Some disadvantages include the high cost of optical transmitters, receivers, and components. Also, service and maintenance of optical equipment takes very specialized training which is becoming required in all HFC networks. These limitations make it too costly to put fiber optics into the home at this time. On the other hand, coaxial cable and RF electronics are relatively inexpensive and the service required is minimum. This is why coaxial cable is used in the distribution portion of the network. Fiber/coax networks take advantage of the best features of each technology. Optical fiber is used to transmit high-quality signals from a cable headend out into the neighborhoods. An optical receiver then converts the optical signal to an electrical signal. The signal is distributed within the neighborhood using short, coax tree-and branch topology (Figure 1.9). 10

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Figure 1.8 HFC Network r---=-..., ____ @ o Figure 1.9 Branch of HFC Network

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The HFC network is the architecture of choice among major cable system operators as they upgrade their networks, but there are many different ways to implement a fiber archtecture. Some examples of different HFC architectures used by multiple system operators (MSOs) follow. [3] 1. TCl's Dual Ring Starlbus 2. CableLabs' Active Coaxial Network Architecture 3. Antec's Cable Integrated Services Network 4. Cox's Ring-In-Ring 5. ADC Video Systems' Flexible Distribution Architecture 6. Texscan's Cell Network OPTPIRF Architecture 7. Scientific-Atlanta's FSA Mini-Star 8. Scientific-Atlanta's FITf 9. Time Warner Cable's Residential Network Architecture 10. General Instruments' Broadband Telecommunications Architecture 11. Adelphia's Cable's Passive Coaxial Network 12. Philips Broadband Networks' Diamond Net Telco Network 13. Philips Broadband Networks' Diamond Net Fiber Backbone Each architecture depends on several key items, the the most important of which is the topology of the area (i.e., rural, suburban, or urban). This is more commonly known as the population density or homes passed per mile. Other key items are the components to use and the wavelength to use. There is presently an ongoing debate within the industry whether to use 1310 nm or 1550 nm. Both have distinct advantages in terms of loss and dispersion qualities, and optical amplifiers operating at 1550 nm are readily available now. Several other issues that are worth mentioning are the type of plant (aerial or underground), node size, and powering requirements. Crucial to deploying the an HFC network that is flexible and robust enough to adapt to future service requirements is the installation of an optical fiber distribution system that offers optimized optical transport of both analog and digital signals. Many of these architectures are becoming very well defined and deployment is widespread within the industry.

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1.5 Signal QualitylImpairments When designing a cable system, there are certain levels of signal quality that must be maintained. There are guidelines set by the Federal Communications Commission (FCC) and the National Cable Television Association (NCTA) on how to measure signal quality and what signal qualities to maintain in a system. Signal quality is affected by certain impairments common to most cable systems. This section gives a brief overview of the major impairments and then discusses in some detail nonlinear impairments which are directly related to the clipping problem. 1.5.1 Carrier-to-Noise Ratio Two major causes of signal degradation occur at a receiver: thermal noise and shot noise. Thermal noise is an unavoidable consequence of random motion of electrons in electronic circuits, and is capable of degrading system performance. The dominant factor at the photodiode receiver is shot noise. Shot noise is caused by the discrete nature of electrons in a semiconductor device. The objective is to maintain the signal at a sufficient level above the noise floor to prevent the noise from creating visible interference in the television picture. The relationship between the RF signal and the noise floor of the transmission system is called the carrier-to-noise ratio. This carrier to-noise ratio is generally defined as the ratio of the signal power to the noise power within a specified bandwidth. From the NCTA Recommended Practices for Measurements on Cable Television Systems [4], the definition of carrier-to-noise ratio is: the power in a sinusoidal signal, whose peak is equal to the peak of a visual carrier during the transmission of a synchronizing pulse, divided by the associated system noise power in a 4-MHz bandwidth. This ratio is expressed in dB. The carrier is the desired power level to which undesired random Gaussian noise is compared, when the random noise has a bandwidth equal to or greater than the desired signal. This noise is called white noise, which by definition is independent of frequency within the band of interest. It is the energy inherent in all matter and varies with the thermal agitation of the material. According to FCC 76.605(a)(7) as of June 3D, 1995, the signal-to-noise ratio shall be no less than 43 dB [5]. 1.5.2 Multipath or Ghosts Multipath is a condition whereby two or more propagation paths exist between the transmitting and receiving sites. Signals arrive at the receiving point at different times 13

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along different path lengths. Different path lengths result from reflections of the transmitted signal by impedance mismatches along the path line. These mismatches can occur in a number of different locations in the network, including connectors and splices, and can be due to damage to the cable itself (tight bending, or rodents chewing on the cable). While care is taken to mitigate reflections at the trunk and the distribution levels, there is little control at the drop level and a majority of reflections happen at this point [6]. Reflections cause ghosts, which can be seen as a shifted image in the picture. Figure 1.10 shows a representation of reflections in a system. 'A A A( V .. ---"1 Figure 1.10 Reflections in a System 1.5.3 Nonlinear Distortions wideband coaxial and fiber optic systems, many RF signals are passed through a single active device such as an amplifier or a distributed feedback (DFB) laser. The output of each of these active devices is susceptible to nonlinear distortion and will produce various undesirable effects called intermodulation distortion. These effects take several forms, but all are the result of several or many individual signals interacting with or on each other. The most common of these are Composite Second Order (CSO), Composite Triple Beat (CTB), and laser diode clipping. This section discusses these nonlinear distortions as they relate to a cable network, and in particular, an HFC system. Figure 1.11 shows the typical transfer function of a device, which is characterized by Equation 1.1 where A is the transfer characteristic of the device.

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Figure 1.11 Transfer Characteristics Equation 1.1 When the transfer characteristic (A) is nonlinear, the equation can be rewritten as a power series. Equation 1.2 The higher-order products are responsible for the nonlinear distortions known as CSO and CTB, shown in Figure 1.12 (these nonlinear distortions will be described further in the following two sections). By the time the system gets to the forth-order products, they are not a factor the system design, but the secondand third-order products are, and they can combine with the clipping components to limit system performance. It will be shown in the model simulations that clipping will have these higher-order products.

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CTe Figure 1.12 CSO/CTB Composite Second Order CSO can be thought of in the following manner. In a multiple-carrier network, take two frequencies, and f2, that pass though a nonlinear device such as an amplifier or a laser diode. At the output of the device are the original signals and f2, and two new signals, fl f2 and fl-f2 (sum and difference of the original signals). As an example, take two cable television frequencies, f2. Ch 12 Ch 13 205.25 MHz 211.25 MHz = 416.50 MHz This frequency falls into Channel 56. Notice that this beat falls 1.25 MHz above the NTSC carrier frequency. Therefore, CSO can be thought of as a clustering of second order beats 1.25 MHz above and below the visual carrier of a system. Composite Triple Beat Composite triple beat distortions are spurious carriers that are generated by the sum and differences of any three carriers as a signal is passed through a nonlinear device. A clustering of third-order beats occurs around the visual carriers in cable systems. With 77 carriers in a standard 50-550 MHz system, there can be thousands of CTB beats

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within a channel. While these beats are random, their phases can add up, and thus one can visually see the impainnent's amplitude vary more than 20 dB. One can have any combination of three frequencies within the system. A good reference can be found in [7]. With the development of the laser diode clipping model, CSO and CTB are generated by the nonlinear characteristics of the diode model and the diode goes into clipping. 1.5.4 Other Distortions found in Cable Systems There are other distortions found in cable systems that can limit the perfonnance of the network. While the impainnents by themselves are not limiting factors, when multiple impainnents are introduced into the network the additive effects limit the network. Other impainnents found in networks are phase noise, residual FM (low-level FM in the local oscillator), hum modulation (power-supply noise getting into the network), and adjacent channel interference (adjacent channels leaking into one another). 17

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2. Most broadband fiber optic cable systems have a transmission capacity of around 80 channels in the 50 550 MHz range. The most common operating condition for the transmitters is to modulate the laser so that the largest negative peaks in the modulating current drive the laser down to near zero power. This is referred to as the clipping limit. For 80 channels, this corresponds to a modulation depth per channel of a few percent, where the modulation depth is the ratio of the peak amplitude of the modulated light signal per channel to the DC optical power. all of the carriers were ever exactly in phase, the peak current would drive the laser well below zero power and the laser would exhibit severe distortion. Fortunately, the probability of all the carries aligning in phase is small. The fundamental trade-off's related to modulation depth are carrier-to-noise ratio and distortion. The higher the modulation depth, the better the but the worse the distortions. The goal for broadband laser transmitters is to meet linearity requirements for optical modulation depths up to the clipping limit. In an amplitude-modulated fiber optic system, the laser signal is biased at a point approximately between the lasing point and the saturation region, as shown in Figure 2.1. The laser is then biased so that the output is in the linear region. The maximum depth of modulation of the laser occurs when the maximum excursion of the modulation carrier just reaches the lasing threshold. In a cable network, there are N carriers; the maximum depth of modulation that can be expected without clipping distortion is )Xl00%. Equation 2.1 The modulated waveform is the sum of all the individual carriers on the system, as seen in the following equation. 18

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Poll m; cos( <1 J m; 114 Figure 2.1 Laser Bias Equation 2.2 The distortions in multichannel video systems are due to a large number of distortion beats that fall at particular frequencies within the operation band. These take the fonn of CSO and CTB (as discussed in the previous section) and, with the laser diode, the clipping components take on the fonn of impulsive components.

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2.1 Previous Work Some of the first work on clipping was done by Saleh [8]. Most of the following work done by other researchers was based entirely on agreement or disagreement with Saleh. One of the basic assumptions that Saleh makes is that the nonlinear distortion products are uniformly distributed over all the channels. Testing of the laser diode clipping model should show if this is accurate or not. A basic common parameter used by most of the researchers as a baseline measurement is CINLD. However, some care must be taken in comparing results, because some of the authors measured the power in a 4-MHz bandwidth while others used a 6-MHz channel bandwidth. The 4-MHz channel bandwidth comes from old testing methodology in the cable industry. A more accurate measurement bandwidth is 6 MHz, the total bandwidth in a cable channel. Saleh [8] used 6 MHz, as did Philips and Darcie [9], while Chung and Jacobs [10] used a 4-MHz bandwidth. Another difference is that the most previous work was done with 42 channels, with a cable system based on 50 400 MHz, while this new model uses 50 550 MHz which will generate more distortion products. 2.2 Model Development This section describes how the laser diode clipping model was developed. 2.2.1 Software Package Used for Model Development This simulation was developed using Signal Processing Workstation (SPW) by Alta Group of Cadence Design Systems. SPW is a communications simulations package with built-in blocks of standard communications systems. These blocks have variable parameters for inputs. The blocks were developed in the Block Diagram Editor (BDE) portion of the software; the basic design environment of SPW. The BDE allows one to create and edit digital signal processing and communications systems in block diagram form, then wire the systems together to reflect the signal flow. From the BDE, the Signal Flow Simulator is invoked to generate and execute simulation programs. Once the simulation runs successfully, the Signal Calculator can be run so that complete analysis of the signal can be completed. Using the Signal Calculator, one can perform operations such as add, subtract, multiply, and divide signal; edit any part of the signal; and apply various math functions such as sine, cosine, tangent, etc. The most powerful function of the signal calculator is its signal processing and signal analysis features such as fast Fourier transforms (FFTs), histograms, and eye diagrams. The software was used on a Sun Sparc20 workstation. The laser diode clipping model 20

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was developed as a unique system; therefore. some of the blocks had to be custom designed (the headend block and the laser diode). The simulation of laser diode clipping is very simple conceptually. The time domain modulated signal is generated by the model blocks. The composite signal is inputted in the laser diode block and then the output is placed in a filter to get a specific frequency band. A FFf is then done on the clipped signal. and the results put into a spectrum analyzer or a signal calculator. The execution of the computation is quite extensive. An ample number of sample points must be taken to ensure that the required resolution is obtained for accurate results. Undersampling can result in distortion levels that do not accurately represent the true distortion. The model has the advantage of allowing the user to change several parameters so that a variety of tests can be simulated. 2.3 A high-level block diagram of the clipping model is shown in Figure 2.2. This diagram shows the highest level of the simulation. SPW is a multilayer program in which the details are in sublayers of the blocks. Several other layers of the simulation exist and will be described in detail in the following sections.

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lSI IQ] Laser Diode clipping Model FLtlJOH EQ f--*_. dB FlA-lCT ION I!] HOISE GBIIATOR -. .... GEHERMOR .... T I T I T S ,...dB 'p' FILTER T T UllLl.SIM FILTER .... __ I T Figure 2.2 High-Level System Block Diagram SIGIIAL SINK ::::j ..... ,'1_-SIGNAL SIHK .... 11-1;11 _' .. '.,C ....., S 1111( --:l ."-.... --PI

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2.3.1 Headend Block The frequency plan shown in Figure 1.1 was used as an outline to develop the headend block. The headend block contains carriers capable of both modulated and unmodulated carriers. The headend block was set up such that all frequencies were used in the 50 550 MHz band; the carriers were placed at the NTSC carrier frequencies at 6-MHz intervals. This allows approximately 77 channels of video. From Figure 1.1 you can see that carriers were not placed in the FM radio band, as is the common configuration in a system. Some operators use this frequency band to place FM signals in the headend so that customers in poor-reception areas can enjoy FM radio. Figure 2.3 (a and b) shows the main headend block and one individual channel within the block (Appendix B shows the complete headend configuration). Figure 2.3a Headend Block Diagram GENERATOR FUHCT ICIi Figure 2.3b Individual Channel in Headend Block The main waveform signal generator sets up the main NTSC frequency carrier of each channel. On the frequency input of each main carrier, there is another function 23

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generator. This second function generator allows the user to modulate the carrier with several types of wavefonns. CW carriers were used for these simulations. There is a noise generator on the input of the phase of the carriers. A unifonn distribution was used on the phase inputs of the carrier frequency to simulate a random phase on each carrier. The delay block on each distribution was used to ensure that the phase was random on each carrier. It was found that, during initial simulations, if no delay was placed on the unifonn distribution, each phase came out the same and the model did not yield believable results. The delay ensures that each carrier has a different phase when running simulations. Figure 2.4(a and b) shows the output of Channel 2 (54 60 MHz) in both the time domain and the frequency domain. This example shows how all the carriers in the headend are set up. WI 6.24 5.76 VillW_Sia iteratiCIII 0 99999. iDsUmce 620: Channel 2 1 11es/V111W Sii620.S1g Double SIIIIp. freq. Pts 100000 Pointe. 0 YUle 0 sec Value -5.93 Figure 2.4a Representation of Headend Output Signal (Time Domain) Channel 2 -30 -45 -60 Mag -75 -90 -105 -120 Example Output Channel 2 (54 KHz 60KHz) "'."",.T ...... Point. Bini Pts 58+07 5.5&+07 68+07 6.5&+07 2 650]9 2895 524289 5. 52171e+01 -]4.2946 -1. 11144 Figure 2.4b Representation of Headend Output Signal (Frequency Domain) Channel 2 24

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2.3.2 Test Channel Block This block allows the user to select and to change the channel being tested. It is made up in the same as any other channel in the headend, but it is easily accessible and the user doesn't have to go into sublevels of the model to change certain parameters. This test channel allows the user to measure the depth of modulation of the channel and to tum the channel off so that in-frequency band distortion products can be analyzed. The test channel block allows the user a great deal of versatility in the simulation. 2.3.3 Gain Block The next stage of the model is a gain block. This amplifier block is a linear amplifier; it exhibits no nonlinearities such as saturation point. This ensures that the diode itself is the only device that exhibits nonlinearities. The main reason for this block is to allow the user to easily to change the power of the entire headend signal into the laser diode. This block can be input as either a gain or a loss, allowing convenient depth-of-modulation and distortion measurements. Therefore, it was only necessary to ensure that the levels were equal coming out of each headend signal. 2.3.4 Laser Diode Model The upper level block diagram of the laser diode is shown in Figure 2.5. Figure 2.5 High-Level Laser Block Diagram This block is not a block from the SPW library, but a custom block designed for this project. A detailed laser diode block is shown in Figure 2.6 25

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IS) :; IS) 0 1Si----'l// ,n ou gn a TABULAR ONLINEA Figure 2.6 Detailed Laser Block Diagram The laser diode consists of an input from the headend module and the test channel. The constant block allows a laser bias to be set for the diode and gives the user the freedom to change the bias point as needed. The laser diode module itself has parameters taken from a standard, off-the-shelf diode used in the cable industry (Table 2.1). It is manufactured by a major cable television vendor who has placed thousands of these systems in the field. 26

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Table 2.1 Typical Laser Diode Specifications Optical Power Output 8mW Channel Loading 80 NTSC channels Slope Efficiency 0.25 mW/ma Bias Point 60 rna Threshold 40 rna The diode data are put into tabular form and called up as part of the SPW program. Figure 2.7 shows the UI characteristics curve of the diode. The SPW program uses linear interpolation between the data points. This tabular form allows the user to change parameters to accommodate different slope efficiencies and lasing thresholds. Table 2.2 shows the input file used for the model. There are no nonlinearities, such as dark current or saturation point, built into the model at this time. 20.0 18.0 16.0 i' 14.0 12.0 10.0 o 8.0 ... ; 6.0 o 4.0 2.0 Figure 2.7 Plot of the LII Characteristics of the Test Diode 27 .0

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2.3.5 Table 2.2 Laser Diode Model Input File data $ signal type = double vector type = interlaced vector length = 12 number of vectors = 2 number of signal points = 59 sampling frequency = 1 starting time = 0 $ 0.0 0.0 10.0 0.0 11.0 0.0 12.0 0.0 13.0 0.0 14.0 0.0 15.0 0.0 16.0 0.0 17.0 0.0 1B.0 0.0 19.0 0.0 20.0 0.0 21.0 0.0 22.0 0.0 23.0 0.0 24.0 0.0 25.0 0.0 26.0 0.0 27.0 0.0 2B.0 0.0 29.0 0.0 30.0 0.0 31.0 0.0 33.0 0.0 35.0 0.0 37.0 0.0 39.0 0.0 40.0 0.0 41.0 .30 43.0 .90 45.0 1.50 47.0 2.1 49.0 2.70 51.0 3.30 53.0 3.90 55.0 4.50 57.0 5.10 59.0 5.70 60.0 6.00 61.0 6.30 63.0 6.90 65.0 7.50 67.0 B.10 69.0 8.70 71.0 9.30 73.0 9.90 75.0 10.5 77.0 11.1 79.0 11.7 The filter block of the model allows the user to pick the frequency band at which to view the clipping effects. The filter block is designed using a filter design program 28

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(FDS) built into the Comdisco software. The filters are easily designed so that any channel can be picked within the frequency range used. Figure 2.8 shows the typical design characteristic of a filter. This is a Channel 13 filter simulation. A Butterworth filter characteristic was used. This filter is being used only as a roofing filter so that one specific channel can be looked at. The filter has a fast roll-off so that no power outside the channel is in the data. = Frequency Response = ,--II -.May -UI (em I.b ... --1..08 2 .. 08 2..08 Impulse Response a 0a /\ \ -l.2Se-S! 50s = -a-= -0 Pole Zero = = "= = = = .... 01 _. .. 01 -. \ -I 1 = ..... 1.0 : ------_/ Figure 2.8 Filter Design System (Channel 13) 29

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2.3.6 Simulation Signal Sinks The final blocks in the model are the signal sinks. The signal sinks allow the user to analyze various portions of the model. They show the output of the headend, the clipped headend, and the filtered channel. There are several view simulations (that are hidden from the main top-level diagram) in the model. They are placed as verification viewers when one is evaluating the simulation. 2.4 Signal Analysis Block The Signal Calculator is a versatile tool that allows the user to perform all types of analysis on the signals generated by the simulations. One of the more powerful aspects of the tool is that it allows the user to perform a very large FFf. Figure 2.9 shows the signal calculator front panel. This figure is representative of the output of the signal calculator. The three signals are from the signal sinks. A close look at the panel shows the different tools available in the simulation. As an example, Figure 2.10 shows a 524,288-point FFf on the headend signal. 30

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0.2 -0.2 50 -50 ImJ 0.5 -0.5 /cru!J!1!J!lfiher ''1 Type Double s-p. freq le.10 Pt lOOOOO Point 0 Ti.e 0 MC val.... 1.3le-106 s-p. freq 1e_10 pt. lOOOOO PoiDti 0 Ti.e 0 !lee Value 1.9 r&1!J!1!J!/cl.pped. "'1 Type Double s-p. Freq le_1o Pt. Pointl 0 Ti.e 0 sec Tal.... 4.22e-107 Figure 2.9 Signal Calculator Front Panel

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(dB) (rad.J. ... ) -15 -30 Headend output (lasQr Input) Frequency Re&pon&e PoinU 292120 Bin' 299H ,Pt& 524289 Freq 5.11141e+08 -1).4409 2. 1410' Figure 2.10 Example of Headend Output 2.5 Notes The way that the model was developed allows the user to quickly change all types of parameters in order to run a variety of different tests. 32

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3. Model Results 3.1 Determination of the Depth of Modulation The first part of the simulation calibrated the output levels for a certain depth of modulation (DOM). This will allow future users to easily change the value. The range of DOM measured was from 1.25 to 8%. It was measured in the following manner. The definition of DOM is the ratio of the peak amplitude of the modulated light signal per channel to the DC optical power. The measurement is made by looking at the output of the laser diode with one carrier turned on. So, by changing the values of the amplifier and running the simulation, the DOM was measured for a number of different amplifier values. Figure 3.1 shows a sample of the DOM calculation. This figure shows the test channel with the output amplifier set to 0 dB. It was previously calculated that the laser bias measurement is 6 mW of output power (this is the measured output for the 60-ma laser bias). From Figure 3.1, it can be seen that the peak excursion is 6.24 mW. This measurement was simplified by the test channel section of the model. The test channel allowed the value of the amplifier to be easily changed, and allowed the simulation to be run with the rest of the headend turned off. 6.24 5.76 View_Sill iteratian 0 "",. installce 620: Channel 2 iles/view silll620.sig Type Double Jreq. z Pts 100000 inti z 0 Tillie 0 sec Value -5.'3 Figure 3.1 Sample Depth of Modulation Calculation The DOM is calculated as: 33

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Therefore, for this data point, the DOM is = [6.24 -= 4.00% 6.0 Equation 3.1 The rest of the DOM calculations are shown in Figure 3.2. A user can use this plot to choose a DOM for a certain simulation for this specific laser. A network designer can easily change the simulation to run whatever DOM is desired. ." C 1 5 = 5 UJ ... 0 Q. E -15 -+-Series1 Figure 3.2 Depth of Modulation Calculation / Calibration It is clear from Equation 2.2 that the maximum depth of modulation that a system can have if no clipping is to OCCl m; S While this constraint is too conservative for a real system, it is a good check of the model. The calculated DOM for 34

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this 75-channel system is = 1.33%, setting the amplifier to -9.0 dB which equates to a DOM of 1.41 % (from Figure 3.2). A simulation was run with 300,000 sample points; it did not clip. Figure 3.3 shows the time domain output of the laser with the 300,000 samples. The absence of clipping was to be expected; the probability of all the carriers aligning in negative phase is very small. ite .. aooooo a,"". DstaDce ,aD: laser ... 1 .... 10. .. --s""":iJn-'fiftl20.--Sl'-'Ii Type .. Double Sap. freq. .. 1 Ph .. 100000 Pointe 0 200000 sec Value fi. 47 Figure 3.3 Theoretical Limit Of DOM with No Clipping The point at which the model started to clip is 1.78%, which equates to an amplifier setting of -7 dB. Figure 3.4 shows the time domain figure of the output just as the diode starts to clip. Notice that the level goes below zero output level. 12.135 Figure 3.4 Clipping Starts to Occur 35

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3.3 Depth of Modulation vs. CINLD Ratio Previous work Chung and Jacobs [10] was done with a 42-channel cable system. This allowed much more DOM per channel. The model presented here is much more representative of the updated cable systems with 75 channels. One of the important parameters that most researchers calculated was DOM vs. CINLD. This is the next set of data taken in this project. From the previous graph. several points along the DOM were chosen and the CINLD ratio was measured. The results are shown in Figure 3.5. From an interpolation of this graph. it can be seen that. in order to get a CINLD of greater than 40 dB ( in which the picture quality would be acceptable). the DOM can be only 1 %. There are techniques. such as pre-distortion (discussed in Section 4.11), that can give a 10to 15-dB improvement in the CINLD numbers. 50 45 40 35 30 Cl 25 ...J E: 20 15 10 5 0 0 10 Figure 3.5 Depth of Modulation vs. CarrierlNLD Ratio 3.4 CINLD Ratio vs. Channel Another important parameter to measure is the distortion ratio in a number of different channels with the DOM kept constant. Results should show that the distortion 36

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products are relatively equal in the band for a given DOM. Figure 3.6 shows the results of testing 10 different channels. 'a -c Z (.) 3.5 M Figure 3.6 CINLD vs. Channel To better illustrate the effects of the distortions on the signal, Figures 3.7 through 3.11 show different parts of the simulation for a DOM of 4.0% (amplifier setting of 0). The figures were plotted at Channel 13.

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1m 0.2 -0.2 (r.-l> ... ) output of filter /craigsigs/fiber.sig Type = Double Salp. Freq. I Pts 300000 Pointe 0 Tue 0 sec Value 1.33e-I06 Figure 3.7 Time Domain Representation of Clipped Signal t!elp DisLorion Products Channel 13 -45 -60 -75 Frequency Response -90 ___ Point. 273219 -105 Bin. 11075 Pts 524289 -120 Freq 2. 1123ge+08 Kag. -43.3623 Phase -2.76457 2. 05e+08 2.1e+08 2.15e+08 2.2e+08 Figure 3.8 Frequency Domain Representation of Clipped Signal 38

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Mag (dB) Pha.e Mag (dB) Pha.e -30 -45 -60 -75 -90 -105 I. -I. -I. Ch.me1 13 CI/ carin vitb Di.torti .... (_ 4\;) Frequency Response Point, 213375 ll231 524289 Pts Freq Hag. 2.D8e.06 2.1e.06 2.12e+06 2.Ue.06 2.18e+06 2.2&+06 Phase 2. 14214e+06 -80.743 3.1019 Figure 3.9 CW Carrier with Distortions Headand Output (laser Input) Frequency Response PoinU 292120 Bin. 29916 Pta 524289 Freq 5.11141e+08 Hag. -13.4409 Phase 2.14106 Figure 3.10 Headend Output (No Clipping) Frequency Domain 39

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(dB) -I. Cx"'ple Hea
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4. Laboratory Results In order to test the model, a clipping experiment was set up with a laser diode transmitter and a receiver pair that was available. This chapter describes the set-up and the data taken. 4.1 Test Set-up Figure 4.1 shows the test set-up for a clipping experiment used to help modify and refine the clipping model. The set-up allows the user to select either a matrix generator that has continuous wave (CW) carriers from 50 MHz to 1 GHz or a test headend that has modulated carriers from 50 to 550 MHz. The biggest difference between using the modulated or unmodulated carriers is that the average power of the modulated carriers is less than the average power of the CW carriers. Both systems are set up with peak power measurements using a spectrum analyzer. The modulated carrier's power is set up using maximum hold on the analyzer. Peak powers will be the equal for both carriers. Therefore, average and peak powers for the CW carriers are the same, but the average and peak powers of the modulated carriers are different. The amplifier and attenuator allow the user to control the power into the laser diode. With this control, one can drive the laser into clipping as much as needed. is important to ensure that all carrier levels have equal power levels. Figure 4.1 Test Set-Up of Clipping System

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The laser transmitter is an off-the-shelf product that has been manufactured for several years. It contains a DFB laser with an output of about 8 m W. One of the limitations of this set-up is that the laser has an RF detector that limits the amount of RF into the laser to make sure that the device is not damaged. A more optimum test would be to have a laser with no control circuitry, but care must be taken to ensure that the laser is protected from damage. For the purposes here, even with power-limit circuitry in the transmitter, there is more than enough headroom in the test set-up to ensure enough clipping of the video signals. The transmitter was loaded with 77 channels of video and the limit of depth of modulation (DOM) before the laser cut off at about 6 percent. The laser has a built-in pre-distortion circuitry. This design helps linearize the distortion products in the device. Pre-distortion techniques are well known in RF and microwave electronics. pre-distortion, the RF/microwave signal is passed through a device which is designed to generate distortion that is equal in amplitude and opposite in sign (phase) to the system-created distortions. The signal is then applied to the RF device, or the laser in this case. The distortions created by the primary device are then canceled by the injected distortion. The test set-up is a complex design, in that the CSO and CTB as described in Section 1 are very dynamic in both amplitude and phase, so the pre-distortion must have very fast loops to compensate for these dynamic conditions. Figure 4.2 show a block diagram of the pre-distortion concept. Figure 4.2 Pre-distortion Block Diagram This pre-distortion technique can improve distortion products in the range of 10-15 dB. This improvement will become evident when comparing model test data to actual transmitter clipping data. 42

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It would be more optimum to use a laser with no pre-distortion to check the model; however, most laser transmitters in use in the cable industry today use pre-distortion. A future, optimized version of the model may use a laser with pre-distortion modeled. The test used 20 km of single mode fiber, to simulate a typical cable television fiber run and to ensure that there was enough loss to not saturate the detector. The loss of the fiber was approximately 0.5 dBIkm. The fiber coupler and the photo diode detector are used as a test point in the system. This allowed access to a test point and testing of the link at the same time. Finally, a fiber optic receiver was used to complete the link. There are several ways to test the amount of clipping that occurred in the system. Saleh showed that there was a limit to the amount of optical modulation that could be done before the distortions became too great [8]. An example DOM calculation is presented in Section 4.2. Figure 4.3 shows the small signal model of the detector. v r -1 1 c J 7 -Figure 4.3 Photodiode Small Signal Model 43

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4.2 1. Set up the test system as shown in Figure 4.1 2. Feed the system with approximately 77 analog channels (50 550 MHz) of a matrix generator (CW carriers). It should be noted that this test set-up can be used with digital carriers and/or modulated carriers. At least one of the carriers should have modulation so that the picture can be viewed on a monitor. Color bars work well, or even a local channel will show the effects of clipping very well. 3. Increase the DOM of the laser. This is accomplished by changing the RF drive level to the input of the laser, by disabling the AGC on the laser diode. The amount of clipping that will be measured will be an objective measurement. That is, the distortion in the picture on the monitor is observed at the point where the picture becomes too disturbing to look at. This is the point at which clipping should be measured. 4. To measure the DOM, the following steps should be taken. l-Jx Equation 4.1 With no carriers modulating the system, the test detector current should be mea sured across the resistor. This is the bias current of the detector (!bias). This test set-up assumes the total fiber optic system is run in the linear region and that no nonlinearities are introduced by the optic cable; the laser power is a direct reflection of the diode current. Now force the system into clipping by increasing the pow-er levels of the carriers. Whenthe system goes into clipping, tum off all the carriers except one and mea sure the power in that one carrier on the spectrum analyzer. This carrier measures the rms power of one carrier in the system. Convert this power to a current (this is the current across the two 50-.Q resistors; therefore, a parallel resistance of 25 .Q). Then convert this to a peak current by multiplying by 1.414. (Section 4.3.3.1 shows the details of two DOM calculations.) It should be noted that the reason for using the optical directional coupler and another photodiode is that it was an easier task to measure from this test point rather than disassemble the cable optical receiver. Because the DOM measurement is relative to Ipeak and !bias, it is not necessary to be precise in the calibration of the system (one doesn't have to be concerned with the loss of fiber or the photo-44

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diode responsivity). It is just a scale factor, but the measurement is still relative, so the DOM can be measured accurately. 5. DOM measurements give a good qualitative measurement of how a system will perfonn, and the limitations of the system. However, it is also useful to look at the distortions themselves on the spectrum analyzer and to measure the power associ ated with the distortions. To do this, force the system into clipping and tum off one carrier in the system. The distortions can be measured within this 6-MHz spec trum. Now the carrier-to-interference ratio (CII) can be measured. (The carrier power was previously measured.) 4.3 Data Taken 4.3.1 Continuous Wave Carriers This set of data was taken on continuous wave carriers. The carriers were from a fully loaded matrix generator, with the carriers from 50 to 550 MHz. Sixteen (16) randomly picked test channels were measured. These channels were picked randomly but covered various parts of the band. The DOM of each channel was measured. Laser diode clipping was very severe in the channel (the picture was unwatchable). A typical channel level for good carrier-to distortion levels should be greater that 40 dB. The measurements were taken at a level of around 25 dB. Spectrum analyzer plots and vector signal analyzer plots were taken of the interference of several channels. The ClIlevel of each impainnent was measured. Figure 4.4 shows the CW carriers as they are input into the laser transmitter at nominal carrier levels. This is the composite signal that was inputted into the laser. Figure 4.5 shows the headend levels as they go into clipping. It took approximately 10 dB of attenuator change send the system into complete clipping this amount of power in to the laser completely made the video unwatchable. 45

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04:53 PM 0.0 10 dBI Cklerator Name Crajg Chamberl!in AmN 10dB 1111 CormIent, 11 MWf t> 3 Figure 4.4 CW Carriers at Nominal Levels (no clipping) 46

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et N-," 1m VB"" 1 T he Eo Figure 4.5 CW Carriers at Severe Clipping Levels 4.3.2 Modulated Carriers Figures 4.6 and 4.7 show a modulated headend with and without clipping, respectively. There are two things to notice in these figures: the noise outside the band is up approximately 10 dB, and more nonlinear distortions are evident in the clipping figure. Even though the amplitudes of the carriers vary due to the modulations in the clipped signal, one can see more carrier amplitude variations due to the clipping distortions. 47

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10:4:3 AM HZ 1 HZ VB"" HZ HZ sec Figure 4.6 Modulated NTSC Headend (no clipping) 48

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10:51 AM HZ 1 HZ HZ HZ Figure 4.7 Modulated NTSC Headend (severe clipping) 49

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This section shows the calculations used to measure the depth of modulation (DOM) of two channels. The first channel is Channel 13 and the second is Channel 46. Using Figure 4.3, small signal model, as a reference Ibias= a. Measured voltage across the I-ill resistor: 0.460 volts b. Total current (lbias): 462 JUlIllps c. Measured power in the channel: -51.20 dBm. Converting this power to a current -51.20 dBm 10 = 7.58E-9 W (this is rms power). From the small signal model, one can see that the total equivalent power is across two 50-Q resisters in parallel; equivalent resistance is 25 II Therefore the current can be calculated (P = 12R) 12 = [7.58 E-] 1 = 17.41E-6 amps (rms value). To convert to peak value, mUltiply by 1.414: 50

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I peak = 17.41E-6 amps x 1.414 = 24.63E-6 amps DOM:: [Ipeak ]X1oo = [24.63E-6 100 = bias 460E-6 amps J Depth of Modulation = 5.34% a. Measure the carrier power in a 6-MHz band: -51.20 dBm b. Measure the interference level: -77.0 dBm c. ClIlevel: -51.20 dbm (-77.0 dbm) = 25.8 dB Using Figure 4.3, small signal model, as a reference Ibias a. Measured voltage across the 1-Q resistor: 0.461 volts b. Total current (Ibias): 462 J.lamps c. Measured power in the channel: -51.80 dbm Converting this power to a current -51.8 dBm = 10 log [Pout] 1mW Pout 6.60E-9 W (this is rrns power).

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From the small signal model, one can see that the total equivalent power is across two 50-0 resisters in parallel; equivalent resistance is 25 .u Therefore, the current can be calculated (P =I2R) I = 16.25E-6 amps nns value. Convert to peak value by multiplying by 1.414: I peak = 16.25E-6 amps x 1.414 = 22.98E-6 amps DOM= [Ipeak ]Xl00 [2298E-6amps] xl00 4.98% I bias 461E-6 amps Depth of Modulation = 4.98 a. Measure the carrier power in a 6-MHz band: -51.8 dBm b. Measure the interference level: -76.47 dBm c. CII: -51.8 dBm (-76.47 dBm) = 24.67 dB The following figures show the tabulated data of all the channel tests. Figure 4.8 shows the tabulated data on the channel versus DOM and Figure 4.9 shows the carrier to-interference ratios (carrier-to-nonlinear distortions). Appendix C shows the actual data collected. 52

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7 6 5 -4 :::IE o 3 2 o a:I o ... ... ... U 5 o Figure 4.8 Channel vs. Depth Of Modulation Figure 4.9 Channel VS. CINLD 53

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Note: This channel line-up is different than that of the headend presented in Appendix A. This is a matrix generator channel line-up. The Channel 82 power level was somewhat low due to the limits of the matrix generator, thus the CII level was lower. 4.5 Distortion Data Figures 4.10 through 4.14 show the clipping distortions observed in some of the test channels. Figure 4.10 shows the distortions in Channel 13, with clipping. Notice that CSO and CTB are also in the band. The carrier has been turned off so just the impairments are shown. ":09 AM 1011 11 "l.t .J VIII"' 11''1 ,r, Hz J ,.,J.. 1',..1' Figure 4.10 Channel 13 Distortions 54

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Figures 4.11 and 4.12 show the same channel, but with a test CW carrier and an NTSC modulated carrier (color bars) input to give some reference value of where the carriers' amplitudes were in relation to the impairments. It is important to keep in mind that the impainnents are not stationary; but for measurement purposes, the average value was taken. Taking an average value is a typical measurement practice in the cable industry. The peak values of the impainnents can be as high as 20 dB larger in certain cases. Date: 01-07-96 Time: 17 PM TRACE A: Chi Spectrum -10 dBm LDgMeg 10 dB /d1v -110 dBm A Merker PDwer Center: 213 MHz 218 000 000 Hz '\ '-152 658 d8m ,1\ Span: 6 MHz Figure 4.11 Channel 13 Distortions with Modulated Carrier 55

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Date: 01-07-96 Time: 04: 20 TRACE A: Ch1 Spectrum -20 dBm LagMeg 10 dB /d1v -120 dBm A Merker \A..J \.AI lrJ Power -23 d Center: 213 MHz 216 000 000 Hz An n t\.J 1 -55 dBm ct> r0\J lAJ 'V\ Spen: 6 MHz Figure 4.12 Channel 13 Distortions with CW Carrier Figures 4.13 and 4.14 show the impainnent in Channels 46 and 70. A comparison of all impainnents in the channels will show that all the impairments have the same basic shape in the channel. 56

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Date: 01-07-96 Time: 04: 12 PM TRACE A: Ch1 Spectrum -20 dBm LDgMeg A Merker 10 dB Id1y 354 000 000 Hz l/\J lAJu \J V' VL -120 dBm PDwer -80 108 d Center: 387 MHz Figure 4.13 Channel 46 Distortions 57 -57 09B dBm 11 11 r0\J V\J Spen: e MHz

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Data: 01-07-96 Time: 04: 31 PM TRACE A: Chi Spectrum -20 dBm LogMeg 10 dB A M k er er 49B 000 000 Hz n 11\ \J\J VV V' -12 dB 0 Power 071 Center: !S01 MHz Figure 4.14 Channel 70 Distortions 4.6 Notes on the Measurements -61 516 dBm \jU Spen: 6 MHz The power measurements were made on an HP 89440A Vector signal analyzer. This piece of test equipment is capable of power measurements with a specified power band. The power measurements were made in a 6-MHz bandwidth for all tests. To ensure that the instrument's limitations were not involved in the distortion measurement, the noise floor of the vector analyzer was measured. It measured -81.0 dBm, which is 7 dB below the distortion measurement. A good rule of thumb is that the instrument should be at least 6 to 10 dB lower than the measurement being made. 58

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Figures 4.8 and 4.9 give a good summary of the test data. The DOM measured in each channel was basically the same. The small discrepancy that was measured was probably due to a minimal error in setting up the matrix generator (each power setting has to be individually set, and the channels drift a little over time). The CINLD ratio in all the test channels measured equally. This agrees with Saleh[8] in that the distortions are distributed equally in the channels. This equal distribution allows the system designer to know that they don't have to worry about certain frequency portions of the band when designing a network. Looking at the graphs of the distortions, one can see that the distribution of the distortions in the channel is the same. 59

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5. Comparison of Laboratory and Model Results 5.1 Graphical Comparisons of Laboratory and Model Data A good comparison of the model and laboratory data is to consider the spectrum analyzer graphs of the data and the model. Figure 5.1 shows data taken at Channel 13. A close comparison of the graph shows that the model closely resembles the actual laboratory data. In the development of the model, it was predicted that secondand third-order products would be created. The model shows both of these nonlinear distortions are developed as the carriers are put through the laser, a nonlinear device. This follows the power series Equation 1.2. The model predicts the distortions in the band very well. Figures 5.2a and 5.2b show the carrier in the band with the distortion products. Again, both model and laboratory data are shown. Mag (dB) -45 -60 -75 -90 -105 -120 -I_loU 0.5\'01 ion Products Channel 13 rrequency Response -___ PoinU 273219 Bin. 11075 Pts 524289 rreq = 2. 1123ge+08 '-T-----r-...I...----r----r----Hag. -43.3623 2. 05e+08 2.1e+08 2.15e+08 2. 2e+08 Phase -2.76457 Figure 5.la Channel 13 Model 60

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11 :09 AM JIIlt HZ HZ Craig Chamberlain '1 '111'11 J\.ut III P" I" ,ec Comment, 1'7:(;'" Figure 5.1b Channel 13 Laboratory (Comparison of Distortions)

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-30 -45 -60 -75 -90 -105 I. -I. 13 CV urrier Diatorti .... 4\) Point, Pts ______ r____ __ ______ ____ ___ Nag. Phase 2.D8e.oc; 2.1 06 2.12"-2.lSe+OIi 2.1Be+06 2.2..06 Figure 5.2a Channel 13 Model 62 273315 11231 524289 2. 14214e+06 -80.743 3.1079

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w r'\ V'\J z "n lI\. U lI' V t> 'V\J Figure 5.2b Channel 13 Laboratory (Comparisons of Distortions with CW Carriers in Band) 5.2 vs. This section discusses comparisons of model and laboratory tests on a different set of data. The comparisons are made on Channel vs. CINLD. It was previously stated that the distortions in each channel should be equal for a given depth of modulation level. From Figure 3.6 and Figure 4.9, it is shown that the power distribution within the channels is equal. A comparison of the results is shown in Figure 5.3. The comparison shows that the distortions are equal throughout the frequency band. The difference in the comparison is the laser tested in the laboratory had pre-distortion built-in (as previously discussed in Section 4). This predistorter gives about 10 to15 dB of gain, as 63

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seen in the comparisons of the two graphs. The model and laboratory results differ by about 13 dB, as seen in Figure 5.3. m 'C Z o ... ... ... (J 5 o 'C C z ... ... (J N N M Figure 5.3 Comparison of Laboratory and Model Data Channel VS. CINLD 64

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5.3 Section 5 shows the comparisons of the laboratory and clipping model data. These comparisons show that the model is well-developed and tracks the laboratory data very consistently. However, to further refine the model, a more comprehensive set of laboratory data could be taken, and exact specifications of a laser diode could be obtained. For the laser diode used in this study, some of the laser properties had to be inferred because the manufacturer would only provide nominal details. Eventually, some of the nonlinear characteristics of the diode, such as dark current, could be modeled, but for the purpose of making an initial design of a system, this model works very well. 65

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6. Conclusions! Future Work The goal of this project was to develop a model for a laser diode that could simulate the effects of clipping in a multiple carrier network. The analog version of the model is now well-developed and has been evaluated on a variety of different channels. Some of the advantages of using the software and of the way that the simulation was developed are: 1. The model is easy to use and allows system designers to conduct a good preliminary evaluation of an HFC network. 2. Different laser diodes can be easily modeled for different parameters such as bias point, lasing threshold and slope efficiencies. The modeler can now vary the bias point and look at the trade-off of carrier-to-noise ratio (CNR) to carrier to non linear distortions (CINLD). This allows a system designer to put in the laser diode data and look at the results of loading down the network. 3. This basic analog model can be used as a building block for developing and modeling a complete HFC network. As cable systems begin to be upgraded, this tool can be used to provide some design guidelines. The model characterized the NLD as predicted. The distortion products that were of most concern were Composite Second Order and Composite Tripe Beat, and the clipping components. The laboratory test and the model data correlated very well. 6.1 Future Work While this basic design is validated and is useful for designing analog networks, it can easily be modified for a variety of different applications. Some these applications are: 1. As cable operators begin to deploy digital services such as high-speed data and high-definition television (HDTV), new blocks can be added to the model. The HDTV standard is capable of transmitting nearly 40 Mbits per 6-MHz channel, but requires a minimum carrier-to-noise ratio of around 30 dB for good quality. SPW has a variety of built-in blocks that can simulate digital signals. Then the 66

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Bit Error Rate of the signals can be measured and the EtlNo (ratio of bit energy to noise power) can be calculated. From this, performance parameters for digital systems can be inferred. 2. The model can be modified to run on the return path or "upstream" (5 to 42 MHz). While this section of spectrum does not have many carriers for video transport, it allows the user to have two-way capability. Unfortunately, this band of frequencies has a lot of outside interference, such as from Ham radios. These radios transmit at high energy levels and can ingress into the cable system. While these pulses are not long in duration, they can send the system into severe clipping, and video and data can be destroyed. The model can simulate these impulsive type of distortions. 3. A total HFC network can be modeled, including the coaxial portion of the network. This would include amplifiers and their effects on the system. The tool is easy to use, and can be easily expanded for a variety of different applications. 67

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Appendix A Typical Channel Line Up Channel No. Frequency Call No.'s Channel line -up Band (MHz) 2 54 60 KWGN Denver Ch. 2 Indep 3 66 DBS Split field Prime-Hughes 4 66 KCNC Denver Ch. 4 NBC 5 76 82 Open 6 82 88 Denver Ch. 6 PBS 7 174 180 KMGH Denver Ch. 7 CBS 8 180 186 Open PPV guide 9 186 192 Denver Ch. 9 ABC 10 192 198 KDVR Denver Ch. 31 Fox 11 198 204 KBDI Broomfield Ch 12 PBS 12 204 210 Open 13 210 -216 KDVR Denver Ch. 31 Fox 14 120 126 HBOWest Home Box Office 15 126 132 TMC West The Movie Channel 16 132-138 Max West Cinemax 17 138 144 SHO West Showtime 18 144 150 ENC Encore 19 150 156 Open 20 156 162 Open 21 162 168 DIS West Disney Channel 22 168-174 MEV Mind Extension Vni. 23 216 222 IDC Discovery Channel 68

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Channel No. Frequency Call No.'s Channel line -up Band (MHz) 24 222 228 BET Black Entenainment 25 228 234 FAM Family Channel 26 234 240 C-SPAN C-SPAN 27 240 246 C_SPAN II C_SPANII 28 246 252 NICK Nickelodeon 29 252 258 MTY Music Television 30 258 264 VH-I Video Hits I 31 264 270 C.C. Comedy Channel 32 270 276 Open 33 276 282 USA USA Network 34 282 288 ESPN Entenainment & Spons 35 288 294 CNBC Cable News & Broadcast 36 294 300 Bravo Bravo 37 300 306 lll..N Headline News 38 306 312 CNN Cable News Network 39 312 318 AMC American Movie Classics 40 318 324 Turner Network News 41 324 330 A&E and Entenainment 42 330 336 C-TY CounTY 43 336 342 LIFE Lifetime 324 348 TNN Nashville Network 45 348 354 TWC Weather Channel 46 354 360 ESPN II Entenainment & Spons 47 360 366 QVC Quality Value Conven. 48 366 372 STARZ! STARZ! 49 372 378 TBS Turner Broadcast 69

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Channel No. Frequency Call No.'s Channel line -up (MHz) 50 378 384 UNI Univision 51 384 390 WGN Chicago Ch. 9 Ind. 52 390 396 Value Vision 53 396 402 HSN Home Shopping Network 54 402 408 TV Food Network 55 408 414 CHC Cable Health Channel 56 414 420 EWTN Eternal Television Network 57 420 426 E! Entertainment TV 58 426 432 NT Nostalgia TV 59 432 438 TVC Travel Channel 438 444 TB The Box 61 444 450 DW Deutsche Welle 62 450 456 KWGN Denver Ch. 2 indep 63 456 462 TLC Learning Channe 64 462 468 KCNC DenverCh.4 65 468 474 TBN Trinity Broadcast Net. 66 474 480 KRMA Denver Ch. 6 PBS 67 480 486 KMGH Denver Ch. 7 CBS 68 486 492 CMT Country Music Tele. 69 492 498 KUSA Denver Ch. 9 ABC 70 498 504 MOR MORMusic 71 504 510 TVC Travel Channel 72 510 516 SHO digital Showtime Digital 73 516 522 TMC digital The Movie Channel Digital 74 522 528 HBO digital HBO Digital 75 528 534 Open 70

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Channel line (MHz) 76 534 540 Open 77 540 546 Open 78 546 552 Open 71

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Co; J/l r:: ." >1 72

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Appendix C This appendix contains the data tables collected from the depth of modulation (DOM) and carrier-to-nonlinear distortion (CINLD) data taken from the laboratory laser diode clipping tests Depth of Modulation Data Depth of Channel Freq. Range Channel V(bias) Modulation (MHz) Power (dBm) (DOM) 4 66 -72 -50.35 .461 5.89 5 76 -82 -50.02 .460 6.13 11 198 204 -50.0 .460 6.14 12 204 210 -50.63 .461 5.70 13 210 216 -51.2 .460 5.35 20 156 -162 -50.8 .462 5.58 21 162 -168 -50.95 .458 5.53 46 354 360 -51.8 .461 4.98 47 360 366 -51.60 .459 5.12 48 366 372 -51.50 .459 5.17 49 372 378 -51.36 .459 5.26 65 423 429 -51.15 .460 5.38 66 429 435 -51.08 .460 5.42 67 435 -441 -52.36 .461 4.67 82 522 528 -52.20 .460 4.77 73

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CII 4 66 -72 -50.35 -76.20 25.85 5 76 82 -50.02 -75.73 25.71 11 198 204 -50.0 -75.60 25.60 12 204 210 -50.63 -75.67 25.04 13 210 216 -51.2 -77.0 25.85 20 156 162 -50.8 -77.46 26.66 21 162 168 -50.95 -77.30 26.35 46 354 360 -51.8 -76.47 24.67 47 360 366 -51.60 -76.70 25.10 48 366 372 -51.50 -76.45 24.95 49 372 378 -51.36 -76.10 24.74 65 423 429 -51.15 -76.58 25.43 66 429 435 -51.08 -76.60 25.52 67 435 441 -52.36 -76.51 24.15 82 522 528 -52.20 -76.05 23.85 74

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[1] National Cable Television Association Cable Television Developments, Fall 1995. [2] W.S. Cicora, "Cable Television in the United State---An Overview," Cable Television Laboratories, Inc., 1995. [3] CED Magazine, 1995-1996 CED Cable TV Fiber Topologies Comparison Wall Chart. [4] National Cable Television Association, NCTA Recommended Practices for Measurements on Cable Television Systems, Washington D.C., 1993. [5] FCC Code of Federal Regulations #47 parts 70 to 79. [6] CableLabs, "Digital Transmission Characterization of Cable Television Systems," Cable Television Laboratories, Inc., 1995. [7] J.L. Thomas, Cable Television: Proof of Perfonnance. New Jersey: Prentice Hill, 1995. [8] A.A.M. Saleh, "Fundamental Limit on the Number of Channels in Subcarrier Multiplexed, Lightwave CATV system," Electron. Lett., Vol. 25., No. 12, pp. 776-777. [9] M.R. Phillips and T.E. Darcie, "Numerical Simulation of Clipping-Induced Distortion in Analog Lightwave System," IEEE Trans. Photo. Tech. Lett., Vol. 3, No. 12, pp. 1153-1155, December 1991. [10] C.J. Chung and Ira Jacobs, "Simulation of the Effects of Laser Clipping on the Perfonnance of AM SCM Lightwave Systems," IEEE Trans. Photo. Tech. Lett., Vol. 3, No. 11, November 1991. 75