Fully digitized 2D ultrasound transducer arrays require one ADC per channel with a beamforming architecture consuming low power. We give design considerations for per-channel digitization and beamforming, and present the design and measurements of a continuous time delta-sigma modulator (CTDSM) for cardiac ultrasound applications. By integrating a mixer into the modulator frontend, the phase and frequency of the input signal can be shifted, thereby enabling both improved conversion efficiency and narrowband beamforming. To minimize the power consumption, we propose an optimization methodology using a simulated annealing framework combined with a C++ simulator solving linear electrical networks. The 3rd order single-bit feedback type modulator, implemented in a 65 nm CMOS process, achieves an SNR/SNDR of 67.8/67.4 dB across 1 MHz bandwidth consuming 131 [Formula: see text] of power. The achieved figure of merit of 34.2 fJ/step is comparable with state-of-the-art feedforward type multi-bit designs. We further demonstrate the influence to the dynamic range when performing dynamic receive beamforming on recorded delta-sigma modulated bit-stream sequences.