A novel approach for approximation of summation to integral with mid-point summation to speed up the spectral domain approach for shielded microstrip lines

This paper presents a new formula involving integral and derivatives of the function, to approximate the summation of a series to an integral with the mid point summation (MPS). The error in approximating the summation with the new formulation, using the same number of terms, converges an order of magnitude faster than the EMF. A general expression has been developed to evaluate the constants involved. Also, a general expression for the special case involving a summation of a product of a sinusoidal function and another function which goes to zero as the argument approaches infinity is developed. A recursive relation to obtain the coefficients of the convergent series is also reported. A practical application of this technique in accelerating the infinite summation of series to obtain very accurate and quick results for the propagation constant, using the spectral domain approach and a few basis functions, for shielded microstrips has been demonstrated in this paper.