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which components must be varied, and in which direction, in order to generate the worst-case result. A Monte Carlo analysis provides the statistical weighting, but per se does not provide the worst-case result. Monte Carlo analysis is generally used to calculate the mean and standard deviation of a particular performance characteristic. This analysis takes signi cantly longer to run than the worst-case analysis, because it requires many simulations.

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7 billion That market value is 34 times earnings of $2085 per share, but only 174 times book value of $40,926 per share Berkshire pays no annual dividend The events of September 11th significantly affected the expenses and earnings of the insurance group and negatively affected Berkshire s stock.

a shift toward the longer wavelength, blue end of the spectrum. The trailing edge, on the other hand, decreases the refractive index of the core, causing a shift toward the shorter wavelength, red end of the spectrum. This causes an overall spreading or smearing of the transmitted signal a phenomenon known as chirp. It occurs in fiber systems that transmit a single pulse down the fiber and is proportional to the amount of chromatic dispersion in the fiber: the more chromatic dispersion, the more SPM. It is counteracted with the use of large effective area fibers.

The optimizer analysis is a powerful PSpice feature that allows a series of simulations and measurements to be automatically performed over a range of component values, based on a design objective speci ed by the user. Circuit variables may be swept through a speci ed range of values. This feature is useful for determining, for example, the damping components of an EMI lter as a design objective.

Cross-Phase Modulation (XPM)

When multiple optical signals travel down the same fiber core, they both change the refractive index in direct proportion to their individual power levels. If the signals happen to cross, they will distort each other. While XPM is similar to SPM, there is one significant difference: While selfphase modulation is directly affected by chromatic dispersion, crossphase modulation is only minimally affected by it. Large effective area fibers can reduce the impact of XPM.

EXHIBIT 8-16

Introduction Magnetic components are a vital part of most power electronic equipment, and the models used in a simulation must faithfully reproduce or predict the behavior of the circuit. Most of the other electronic components in these circuits have predetermined models that have been derived from standardized components. Magnetic components, however, are rarely standardized and are generally designed for speci c applications. In most cases the model, or at least the component values within the model, must be altered for each new circuit simulation. PSpice has four basic magnetic component models built into it: A linear inductor An ideal transformer A coupled inductor model A nonlinear core model All of these are very useful for simulation but must be used with some care if the correct model is to be obtained. In some cases, the model may fail dramatically, thereby giving grossly erroneous results, as we shall see later. Most of the time, however, the errors are more subtle. For example, the details of the noise and ringing due to parasitics in the transformer may not be reproduced correctly. Cross-regulation between windings with varying loads, high-frequency winding losses, and the proper distribution of ripple currents in coupled lter inductors are also quantities that are often not modeled accurately.

Four-Wave Mixing (FWM)

FWM mixing is the most serious of the power/refractive index-induced nonlinearities today because it has a catastrophic effect on DWDMenhanced systems. Because the refractive index of fiber is nonlinear and because multiple optical signals travel down the fiber in DWDM systems, a phenomenon known as third-order distortion can occur that seriously affects multichannel transmission systems. Third-order distortion causes harmonics to be created in large numbers that have the annoying habit of occurring where the actual signals are, resulting in their obliteration. Four-wave mixing is directly related to DWDM. In DWDM fiber systems, multiple simultaneous optical signals are transmitted across an optical span. They are separated on an ITU-blessed standard transmission grid by as much as 100 GHz (although most manufacturers today have reduced that to 50 GHz or less). This separation ensures that they do not interfere with each other. Consider now the effect of dispersion-shifted fiber on DWDM systems. In DSF, signal transmission is moved to the 1,550 nm band to ensure that dispersion and loss are both minimized within the same window. However, minimal dispersion has a rather severe, unintended

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