1. Obtaining a wideband response from a resonant antenna using traditional electromagnetic numerical methods is often very computationally demanding. A technique is presented which accurately extrapolates the complete response using only early-time and low- frequency data, which can be obtained relatively easily. The response is represented as a summation of N orthogonal polynomials and M damped sinusoids. Damped sinusoids are utilized to efficiently represent the effects of resonances in the response. A genetic algorithm (GA) is used to select all required parameters for stable and accurate results. Abstract Response Representation  Time and freq. response represented by two summations:  N weighted orthogonal polynomials:  Represent “transient” behavior of response  Associate Hermite polynomials used  M damped sinusoids:  Represent “resonant” behavior of response  Amplitude, decay factor, and resonant freq. define each pair  are the extrapolated versions of  Single set of N polynomial weighting coefficients:  Determined from matrix eq. using only early-time/low-freq. data  Damped sinusoid parameters found from response data  Accurately characterize resonances of response Numerical Results Extrapolation of Wideband Responses from Resonant Antennas using Early-Time and Low-Frequency Data J. Michael Frye and Dr. Anthony Q. Martin  Early-time and low-freq. data used to extrapolate complete time & freq. response (late-time, high-freq.)  Early-time data contains high-freq. information  Low-freq. data contains late-time information  Computationally intensive data (late-time, high –freq.) is extrapolated rather than directly computed.  Partition into early/late-time and low/high-freq data: Extrapolation Approach E-Shaped Patch Antenna  Dual-band (1.9 GHz & 2.4 GHz)  Designed for wireless communications applications  Differentiated Gaussian pulse voltage excitation up to 4 GHz  Extrapolated response: driving-point current due to pulse Cavity-Backed Slot Antenna with Monopole GA-Based Parameter Selection  Highly resonant: cavity modes, slot and wire resonances  Differentiated Gaussian pulse voltage excitation up to 15 GHz  Extrapolated response: driving-point current due to pulse  Data to left of vertical dashed line is known (early-time/low-freq.)  Data to right is extrapolated (late-time/high-freq.)  Accurate extrapolation with 6% of time data and 25% of freq. data  N=32 (orthogonal polynomials), M=9 (damped sinusoids) Extrapolation of Driving-Point Current Response  Vertical dash line indicates point of extrapolation  Accurate extrapolation with 2.5% of time data and 25% of freq. data  N=484 (orthogonal polynomials), M=44 (damped sinusoids)  Parameters must be carefully selected for stable/accurate results  Genetic algorithm (GA) optimization is utilized  Global search technique inspired by evolutionary biology concepts  Represents possible parameter combinations as chromosomes  Finds optimal solution by evaluating ‘fitness’ of potential solutions  Minimize difference between actual and extrapolated responses:  E cannot be directly minimized in practice because it requires complete knowledge of the response (which must be extrapolated)  Approximate E using only early-time/low-freq data:  By minimizing, all necessary extrapolation parameters can be reliably selected to yield an accurate extrapolation Applications  Rapid numerical analysis of resonant antennas over an ultra-wide frequency band  Tool for the design and analysis of wideband, multi- band, or switched antennas  Aid in optimization of antenna designs which meet performance goals for multiple applications