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This paper shows applied sensitivity analysis for easier design and practical application of a planar half-wavelength low-pass filter (LPF) using defected ground structure (DGS). Typically, it is difficult to deploy planar half-wavelength low-pass filters when high power durability is required because of the very narrow line-widths of high impedance transmission line. Here, we propose a new configuration for the high impedance microstrip line using DGS structure to allow broader line width and high power handling capability. The sensitivity of the scattering parameters was calculated using the self-adjoint sensitivity formula in order to determine the proposed filter's dimension. The paper also highlights the validity of the proposed LPF optimization with its measured performance.