Modelling Colored Noise under Large-Signal Conditions
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Date
2006-01-05
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Abstract
A time-domain simulation approach to modelling colored noise in electrical circuits is described. This approach tries to place minimal restrictions on the magnitude and the nature of the noise present in a circuit in an effort to capture the effects of nonlinear interactions between signal and noise. The approach uses the mathematical theory of nonlinear dynamics and chaos to produce stochastic-looking series using simple deterministic iterative rules or maps. The characteristics of these series can be modified easily to produce a large range of spectral characteristics. The advantage of using the chaotic maps approach is that modifying the spectral characteristics usually requires the tweaking of a small number of parameters. This is in contrast to more traditional time-series-based approaches to noise generation which require a large number of parameters to accurately model the characteristics of common sources of noise found in electrical circuits. The validity of this approach to modelling is tested by implementing a unified deterministic and stochastic framework of equations in a high dynamic range simulator. The resulting stochastic system of equations describing a nonlinear noisy network are setup and solved assuming the Stratonovich interpretation. Simulated results are compared with measured results using two representative circuits. The first circuit is a varactor-tuned voltage-controlled oscillator and simulated phase noise at the output of the circuit is compared with measured values. The second circuit is a low-noise X-band MMIC power amplifier and the effect of noise on the amplification of this device is investigated. Gain versus input power curves are generated in simulation when the circuit is fed with large levels of input noise and contrasted with measurement. Both these cases demonstrate that this approach to the modelling of large levels of noise is valid and perhaps even essential in order to accurately predict the effects of having non-negligible levels of noise in an electronic circuit.
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Keywords
colored noise, chaos, noise analysis
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Degree
PhD
Discipline
Electrical Engineering
