Abstract: Differential microphone arrays （DMAs） are designed to leverage compact microphone arrangements to measure the gradient of the sound pressure field. They offer advantages such as high spatial gain， frequency-invariant spatial response， and a small array aperture. Consequently， DMAs have found wide application in areas such as spatial audio， teleconferencing， smart home systems， hearing aids， and security systems. Among various DMA configurations， the circular DMA （CDMA） is noteworthy for its beam-steering capability and ease of deployment， making it suitable for a broad range of applications. The majority of existing CDMA designs rely on methods that approximate the desired spatial response using the Jacobi-Anger expansion. However， CDMAs designed using this approach often lack the flexibility needed to effectively suppress interference in practical scenarios， which can degrade the quality of the captured acoustic signals. To address this limitation， this paper proposes a design methodology for CDMAs with controllable interference suppression constraints. The approach formulates the array design as a constrained optimization problem， wherein the degree of interference suppression can be flexibly adjusted via the constraint parameters. Through a series of transformations， the problem is ultimately reduced to a quadratic eigenvalue problem， allowing for explicit analytical solutions. Simulation results demonstrate that the proposed method achieves beamforming designs that satisfy predefined interference suppression requirements while closely approximating the target spatial response under a specified signal-to-interference ratio （SIR）. Furthermore， compared to approaches that impose direct post-null constraints， the arrays designed using this method exhibit greater robustness， effectively mitigating sensitivity to array imperfections and self-noise.