This thesis describes the design of a front-end application-specific integrated circuit (ASIC), which will be put into the tip of a miniature ultrasound probe for 3D Trans-Esophageal Echocardiography (TEE). To enable 3D TEE, a matrix piezoelectric ultrasound transducer with more than 2000 elements will be used. Since a gastroscopic tube cannot accommodate the cables needed to connect all the transducer elements directly to an imaging system, local channel-count reduction is necessary. The main task of the ASIC is to provide appropriate signal conditioning in the tip of the probe to achieve channel-count reduction. The main goal of this thesis work is to design such an ASIC using simple, low-power circuits, while still maintaining good image quality. In addition to the electronics design, the interconnection between the matrix transducer and the ASIC is another important parallel research topic.