New closed-form Green's functions for microstrip structures - theory and results
Citations
132 citations
Cites methods from "New closed-form Green's functions f..."
...Extensive research has been done to accelerate this process through methods such as the fast Hankel transform (FHT) approach [12], [13], the window function approach [14], the steepest descent path (SDP) approach [2], and the discrete complex image method (DCIM) [15]–[29]....
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...More recently, Eselle and Ge [29] proposed a new closed-form formulation based on a class of semi-infinite integrals of Bessel functions and applied the generalized pencil of function (GPOF) method to approximate the remaining integrand with another set of complex images (having only dependence), making the method valid for any kind of source-field point combination....
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124 citations
108 citations
Cites background from "New closed-form Green's functions f..."
...The DCIM in the -plane ( is the radial wavenumber) is introduced in [8], but or cannot be extracted from the spectral-domain GF to simplify the computation....
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66 citations
45 citations
Cites background or methods from "New closed-form Green's functions f..."
...The study of DCIM also requires rigorous results from other methods as a verification of the performance....
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...One of these ideas is to avoid the numerical integrations by approximating the integrands or a part of the integrand with some simple functions....
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...Among the many methods of approximating a function by a sum of complex exponentials, we choose the matrix pencil method (MPM) since it is robust to noise and computationally efficient [13]....
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...Finally some conclusions are drawn in Section V....
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References
3,872 citations
"New closed-form Green's functions f..." refers background in this paper
...for a horizontal source have been discussed in [9], [10], and [11], and one may represent it as...
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774 citations
"New closed-form Green's functions f..." refers background in this paper
...for a horizontal source have been discussed in [9], [10], and [ 11 ], and one may represent it as...
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773 citations
"New closed-form Green's functions f..." refers background in this paper
...for a horizontal source have been discussed in [9], [10], and [11], and one may represent it as...
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693 citations
"New closed-form Green's functions f..." refers methods in this paper
...method was improved by Aksun [6], who uses a two-level method and the generalized pencil of function (GPOF) method [7] to approximate the spectral domain without extracting the quasi-static and surface-wave contributions....
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...This method’s accuracy depends on the accuracy of the approximation by the series of exponentials, and the GPOF method [7] was found to be very accurate for this purpose....
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...For the approximation, the GPOF method [7] is a good choice because we do not need to consider the quasi-static images and surface-wave poles (SWPs) when performing the approximation of the spectral-domain Green’s functions....
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684 citations
"New closed-form Green's functions f..." refers methods in this paper
...based on the Sommerfeld identity, called the discrete image method, has been developed [4], [5]....
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...It should be noted that the complex images in our method are distributed on the complex-plane, while the images obtained in the previous method [5], [6] are on the complex -plane....
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...This method first extracts all the quasi-static and surface-wave contributions from the spectral-domain Green’s function, and then approximates the remainder by a series of exponentials using the Prony’s method [5]....
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...Details of this method can be found in [5]....
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...In one of the previous complex image methods, all the quasistatic images [5] and SWPs [2], [5] were extracted from the spectral-domain Green’s function and then the remainder was approximated by a series of complex exponentials using the Prony’s method [5]....
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