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These problems usually arise from shortcomings in the models that are being used and can, for the most part, be corrected. A common modeling problem arises because of a failure to realize that there are two different basic types of transformers: junction and mesh. Figure 2.1 illustrates these two transformer types, along with the circuit equations that apply to each type. The junction transformer is widely used in power conversion equipment. It is usually the type used by schematic capture programs and is also used to create ideal transformers having multiple windings. The mesh transformer is very common for polyphase power applications and also appears in coupled lter inductors and other magnetic control devices. There are also magnetic devices that are combinations of mesh and junction transformers. In a network, these two types of transformers behave very differently. The substitution of one for the other in a simulation will lead to gross errors, as shown in the example in Fig. 2.2. This is a three-winding, three-leg mesh transformer. If a simple threewinding ideal transformer (Fig. 2.2, upper right) is selected to simulate this transformer, the output voltage phases will be correct only for some excitations. If, for example, the center winding is excited, then the voltages on the other two windings will be correct. However, if one of the

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Stimulated Brillouin Scattering (SBS)

SBS is a power-related phenomenon As long as the power level of a transmitted optical signal remains below a certain threshold, usually on the order of three milliwatts, SBS is not a problem The threshold is directly proportional to the fiber s effective area, and because dispersionshifted fibers typically have smaller effective areas, they have lower thresholds The threshold is also proportional to the width of the originating laser pulse: As the pulse gets wider, the threshold goes up Thus, steps are often taken through a variety of techniques to artificially broaden the laser pulse This can raise the threshold significantly, to as high as 40 milliwatts SBS is caused by the interaction of the optical signal moving down the fiber with the acoustic vibration of the silica matrix that makes up the fiber.

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$34 billion in 2000, and then increasing by 11 percent in 2001 to $37.7 billion. Total revenues were up 5.1 percent in the third quarter of 2002 when compared to the third quarter of 2001. Berkshire s earnings before income taxes grew 228 percent from 1999 to 2000, and then dropped 74 percent between 2000 and 2001. Again, a large portion of the blame was due to 9/11 considerations. During the third quarter of 2002, earnings before income taxes increased 390 percent above the level of the third quarter of 2001. What is Berkshire s growth potential A consensus analyst expectation of earnings-per-share growth over the next five years for Berk-

Modeling of mesh transformers requires caution. The example above shows how errors can be easily made.

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As the silica matrix resonates, it causes some of the signal to be reflected back toward the source of the signal, resulting in noise, signal degradation, and a reduction of overall bit rate in the system As the power of the signal increases beyond the threshold, more of the signal is reflected, resulting in a multiplication of the initial problem It is interesting to note that there are actually two forms of Brillouin Scattering When (sorry, a little more physics) electric fields that oscillate in time within an optical fiber interact with the natural acoustic resonance of the fiber material itself, the result is a tendency to backscatter light as it passes through the material This is called Brillouin Scattering If, however, the electric fields are caused by the optical signal itself, the signal is seen to cause the phenomenon; this is called Stimulated Brillouin Scattering.

To summarize: Because of backscattering, SBS reduces the amount of light that actually reaches the receiver and causes noise impairments The problem increases quickly above the threshold and has a more deleterious impact on longer wavelengths of light One additional fact: In-line optical amplifiers such as erbium-doped fiber amplifiers (EDFAs) add to the problem significantly If there are four optical amplifiers along an optical span, the threshold will drop by a factor of four Solutions to SBS include the use of wider-pulse lasers and larger effective area fibers..

outer leg windings is excited, as shown in the bottom left of Fig. 2.2, then the phase of the simulated voltage (bottom right of Fig. 2.2) will be incorrect. This represents a gross modeling error and illustrates why the modeling must be performed carefully. The selected model will function correctly as a junction transformer, but it will not function correctly as a mesh transformer. Most simulation problems can be avoided by using models that are extensions of the basic SPICE models. The most reliable way to create these models is to base them on the actual physical structure of the magnetic component. This is the principle behind the physical models that are derived using reluctance modeling and are described in the Reluctance and Physical Models section. This approach has many advantages beyond the simple generation of a model. Physical models preserve the relationship between the simulation model and the actual component. This means, for example, if the simulation shows excessive voltage ringing due to a parasitic inductance element, this component can be directly related to the structure of the device. This allows the device to be redesigned in order to reduce the problem. This interchange between the simulation and the device design is a powerful tool. The preservation of the intuitive connections between the device and the simulation model also helps to avoid modeling errors and to interpret the simulation results.

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