Exact design of continuous-time sigma-delta modulators with multiple feedback DACs

A technique for the exact design of the noise transfer function of Continuous-Time (CT) Sigma-Delta modulators with arbitrary and multiple DAC responses and real op-amps is here presented. The approach, that presupposes linear behavior of active blocks, produces a CT modulator with the same noise shaping as its Discrete-Time counterpart. The method operates entirely in the time domain and accounts for non-idealities of real implementations such as finite gain and bandwidth of integrators. The procedure can be effectively implemented with circuit simulators to allow the exact design with transistor level blocks. A design example on a third-order scheme confirms the effectiveness of the method.