A pre-delay reconstruction sigma-delta beamformer (SDBF) was recently proposed to achieve a higher level of integration in ultrasound imaging systems. Nevertheless, the high-order reconstruction filter used in each channel of SDBF makes the beamformer highly complex. The beamformer can be simplified by reconstructing the signal after the delay-and-sum process with only one filter. However, this post-delay reconstruction-based design degrades image quality when dynamic focusing is performed. This paper shows that employing a simple pre-delay filter is sufficient to achieve similar performance as conventional pre-delay reconstruction SDBF, as long as the pre-delay filter provides the required pre-delay signal to-quantization noise ratio (SQNR). Based on this finding, we proposed a cascaded reconstruction beamformer that uses a boxcar filter as the pre-delay filter in each channel. Simulations using real phantom data demonstrate that the proposed beamforming method can achieve a contrast resolution comparable to that of the pre-delay reconstruction beamforming method. In addition, the hardware can be greatly simplified compared with the pre-delay reconstruction beamformers.