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An elliptical patch antenna is simulated to illustrate how FEKO can be applied to investigate time domain characteristics of UWB antennas including the fidelity, a measure of how similar the radiated waveform is to the excitation signal.
Ultra-wideband (UWB) antennas are often used for short range, indoor transmission due to low FCC emission requirements and where short pulse lengths enable transmission of high data rate signals. Typical applications include high precision through-wall radar imaging and PC-peripherals like wireless printers. In such cases, additional time domain analysis is necessary to characterize the antenna’s overall performance for pulsed signal transmission. Parameters (e.g. pulse distortion, antenna fidelity) need to be analysed together with standard antenna performance parameters for reliable design. In this white-paper, a printed elliptical UWB monopole antenna is used to illustrate these concepts.
Synthesis with Antenna Magus
The initial antenna synthesis was performed with Antenna Magus using the microstrip fed planar elliptical monopole antenna model with a design goal of fmin = 2 GHz. The initial design was tweaked to improve the operational bandwidth (BW) by optimizing the feed gap spacing. The final design is exported for fullwave simulation in FEKO.
Antenna geometry and Antenna Magus synthesis results
Fullwave Simulation with FEKO
The antenna is simulated with a finite substrate and the S11(f), far field radiation pattern, peak gain and beam widths are compared with the results estimated by Antenna Magus. The fullwave simulation results are in good agreement with the synthesized results.
E- and H-plane gasn, peak gain and beamwidths
FEKO Time Analysis and Fidelity Calculation
A modulated Gaussian pulse is defined mathematically in FEKO for the excitation signal that will be used for the Time Analysis:
where fmod is the modulation frequency of the pulse; t0 is the time shift; and T is proportional to the pulse width. Choosing fmod = 6.5 GHz, t0 = 500 ps and T = 140 ps generates a typical UWB pulse with a center frequency of 6.5 GHz. A second pulse with fmod = 10 GHz is also used for the analysis to compare the performance for different pulses. The 2 pulses are used to excite the antenna and the radiation of the pulses in the far field are calculated using the Time Analysis functionality in POSTFEKO.
When using Time Analysis the time domain results are obtained by applying an Inverse Fast Fourier Transformation (IFFT) on the frequency domain simulation results. It is important to remember this when choosing the simulation start and stop frequencies and the spectrum of excitation pulse: if part of the pulse spectrum does not fall within the same frequency range as the simulation it is possible that windowing effects will introduce numerical artifacts into the time domain results.
Pulse signal waveform and frequency spectrum of the 2 excitations
The voltage signal (fmod = 10 GHz) used to excite the antenna and the normalized radiated pulses at theta, phi = (0, 90) and (90, 0) respectively are shown in the figure below. It is clear that the radiated pulses are neither identical to the excitation signal nor to one another. This implies that the distortion of the signal is a function of the radiation direction, which is essentially the motivation to investigate the fidelity for the antenna.
The antenna fidelity can be defined as 
where a(t) is the excitation signal and the response r(t) is the radiated pulse for a given theta and phi. The fidelity is in essence a measure of how similarly a pulse is radiated compared to the excitation signal. When the 2 signals are identical the fidelity reaches its maximum value 1. The equation uses the normalized signals to factor out any scaling effects and a time delay which allows for phase shifts that may occur. A Python script was written to calculate the convolution operation in the fidelity equation. The results are plotted in POSTFEKO and the data is exported as a text file, which is used as an input for the script.
Comparison of the calculated fidelity values for the 2 pulses with published results
|theta, phi||modulated 6.5 GHz||published ||modulated 10 GHz|
The table shows the calculated fidelity values which agree well with the results published in . The dependency of the fidelity value on the radiation direction is highlighted again in the table and can also be visualized in the previous figure: the distortions for the (0, 90) signal (fidelity = 0.975) are smaller than the (90, 0) signal (fidelity = 0.871). In general the fidelity values for the antenna are high which means that it is suitable for UWB applications where pulse radiation characteristics are important.
The FEKO workflow was shown for characterizing both time and frequency domain performance of an UWB monopole antenna. This included an analysis of the antennas fidelity characteristics for 2 different UWB pulses, which agreed well with published results.
This white-paper illustrated how the Time Analysis functionality in FEKO can be incorporated into design procedure to evaluate time domain characteristics for more comprehensive design of UWB antennas.
 D. Lamensdorfr and L. Susmad; “Baseband-Pulse-Antenna Techniques,” IEEE Trans. on Antennas and Propagation, vol. 36, no. 1, February 1994.
 Li Bao-ping and Wang Yan; “Characteristic Investigation Impulse Radiation of Two UWB Antennas,” Proceedings of the Third International Symposium on Computer Science and Computational Technology, 14-15th August 2010.
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