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A response variation (RV) element is introduced to control the consistency of an adaptive wideband beamformer's response over the frequency range of interest. By incorporating the RV element into the linearly constrained minimum variance (LCMV) beamformer, we develop a novel linearly constrained beamformer with an improved output signal-to-interference-plus-noise ratio (SINR), compared to both the traditional formulation and the eigenvector based formulation, due to an increased number of degrees of freedom for interference suppression. In addition, two novel wideband beamformers robust against look direction estimation errors are also proposed as a further application of the RV element. One is designed by imposing a constraint on the RV element and simultaneously limiting the magnitude response of the beamformer within a pre-defined angle range at a reference frequency; the other one is obtained by combining the RV element and the worst-case performance optimization method. Both of them are reformulated in a convex form as the second-order cone (SOC) programming problem and solved efficiently using interior point method. Compared with the original robust methods, a more efficient and effective control over the beamformer's response at the look direction region is achieved with an improved overall performance.