EE541 - EE 541, Fall 2009: Course Notes #9 Characterization...

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EE 541, Fall 2009: Course Notes #9 Characterization of the Dynamic Range of Active Networks Dr. John Choma Professor of Electrical Engineering University of Southern California Ming Hsieh Department of Electrical Engineering University Park: Mail Code: 0271 Los Angeles, California 90089–0271 213–740–4692 [USC Office] 213–740–8677 [USC Fax] ABSTRACT: This report is a documentation of analytical techniques for characterizing the de- gree of nonlinearity implicit to active networks designed to achieve nominally lin- ear performance input -to- output performance characteristics. It addresses such metrics as total harmonic distortion, intermodulation levels, intercept points, and spurious free dynamic range. Aside from addressing the theoretic nature of these nonlinear performance metrics, the report attempts to instill design-oriented in- sights by discussing measurement, simulation, and other engineering issues rele- vant to the meaningful disclosure of nonlinear performance profiles. Original: July 2006
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Course Notes #9 USC Viterbi School of Engineering J. Choma Nonlinear Analyses - 271 - August 2006 1.0. INTRODUCTION All electronic circuits are nonlinear networks because the active devices embedded within them have inherently nonlinear static volt-ampere characteristics and nonlinear intrinsic energy storage parasitics. When these inherently nonlinear circuits are earmarked for linear sig- nal processing applications, design care must be exercised to bias relevant active devices well within their nominally linear volt-ampere domains. Moreover, additional care must be taken to ensure that the perturbations in quiescent operating points incurred in active elements by all input signals applied to these networks are sufficiently small to sustain device operation in their approximately linear regimes. With suitable biasing implemented and applied signals constrained to sufficiently small amplitudes, the response, y(t) , to a signal excitation, x(t) , applied to an electronic circuit can be described to first order by the linear time domain relationship, 01 y(t) a a x(t). ≈+ (1) In this expression, the constant, a 0 , is determined by network biasing considerations, which ac- count for targeted power dissipation constraints. Parameter a 1 , along with such other linear performance metrics as impedance levels, bandwidth, phase and delay responses, phase and gain margins, rise, fall, and settling times, and the like derive from analyses executed on a small sig- nal model of the network undergoing study. Indeed, a 1 is identically the small signal input -to- output (I/O) gain of the considered circuit. Since (1) pertains to time domain analytical investigations, the constants, a 0 and a 1 , are necessarily real numbers. However, these numbers can be positive or negative.
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EE541 - EE 541, Fall 2009: Course Notes #9 Characterization...

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