tailieunhanh - Ultra Wideband Part 5

Tham khảo tài liệu 'ultra wideband part 5', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 114 Ultra Wideband not significantly decrease if the number of exponentials is above 20. Hence more than 20 exponential functions should be used for approximating a Gaussian doublet pulse with good accuracy. 4. Reflection of UWB Pulses from a Conducting Half Space In this section how to apply the above approach to modeling pulses reflected from a conductive interface is demonstrated and the comparisons between our results and the published ones are made showing a good agreement between them. A pulse which is a linear combination of a finite number of exponential functions is expressed by 11 and is incident from free space onto an interface between free space and a lossy material with conductivity a and relative dielectric constant Er. The reflection coefficients in complex frequency domain for vertical and horizontal polarizations are L .a a . 2 I sr -I--I cos u - sr -I-------sin u _ I sc . I sf R s -----_0 12 I . .a a .2 I sr I---I cos u sr I--------sin u I sS0 V sẼ0 and a2 cos Q - Isr sin Q h 1 I. . a cos Q sr ------sin Q V s 0 respectively where E0 is the permittivity of free space 0 is the incidence angle relative to the normal to the interface and s is the complex frequency. The image function of E t in 11 is E s 14 P 1 s ap The final image functions Fv s Rv s E s and Fh s Rh s E s obviously satisfy conditions 1 - 4 listed in Section 3. A proof is given below that for s p j n - ft l t Fv s and Fh s also obey the above two conditions a and b described in Section 3 under which fl up can be used to approximate fec t p . Here only the proof for Fv s with ap and Cp being real numbers is given since the proofs for Fv s with ap and Cp being complex numbers and for Fh s are similar. If we let sr I cost a jb ss0 15 Transient Modelling of Ultra Wideband UWB Pulse Propagation 115 Er sin20 c1 jd1 sE0 2 Er -----sin 0 c jd N sE0 16 17 a k Er p Jcost b ---B-cost B p- n 2 2 jE0 18 If we denote then . _ 2 p t c E - sin 0 ------------- 1 B 2 2 c1 yj c1 d1 N 2 q C V p P