Browsing by Author "Freeborn, Todd"

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    Approximated Fractional Order Chebyshev Lowpass Filters
    (2015-03-26) Freeborn, Todd; Maundy, Brent; Elwakil, Ahmed S.
    We propose the use of nonlinear least squares optimization to approximate the passband ripple characteristics of traditional Chebyshev lowpass filters with fractional order steps in the stopband. MATLAB simulations of , , and order lowpass filters with fractional steps from  = 0.1 to  = 0.9 are given as examples. SPICE simulations of 1.2, 1.5, and 1.8 order lowpass filters using approximated fractional order capacitors in a Tow-Thomas biquad circuit validate the implementation of these filter circuits.
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    Design and Implementation of Fractional Step Filters
    (2010) Freeborn, Todd; Maundy, Brent J.
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    Indirect Measurement of Fractional Impedances
    (2013-12-13) Freeborn, Todd; Maundy, Brent
    This thesis investigates the measurement of fractional-order parameters that describe the electrical impedance of tissues and devices without requiring direct impedance measurements. Concepts from fractional calculus are imported to develop fractional circuit theory and derive the voltage and current excited step responses and magnitude responses of the single-dispersion Cole impedance model which is widely used in biomedicine and biology. Using these responses a numerical graph-fitting and non-linear least squares fitting routine have been applied to MATLAB simulations to assess the accuracy of this approach to extract the fractional impedance parameters that describe this model. Experimentally collected data from fruit tissues and ideal Cole models validate these methods. These fractional calculus concepts are further applied to develop the circuit theory to describe the current excited step response and magnitude response of the double-dispersion Cole impedance model. MATLAB and PSPICE simulations of assess the accuracy of this approach to extract the fractional impedance parameters that describe this model. Experimentally collected data from the current-excited step response and voltage excited magnitude response of apples validates these methods. Finally, the fractional circuit theory is applied to develop the expression for the voltage-excited step-response of a fractional model for a supercapacitor which is then used with non-linear least squares method extract the impedance parameters that characterize the model. This method is validated experimentally using results collected from low capacity supercapacitors with manufacturer ratings of 0.33 F, 1 F, and 1.5 F and high capacity supercapacitors with 1500 F and 3000 F manufacturer ratings.