A method to minimize output noise in cascade SC filters

Abstract

The output noise in the cascade switch-ed-capacitor (SC) filter depends greatly on the pole-zero combinations as well as the order of cascading the second-order circuits. This paper derives the general condition for the combination/order so that the output noise is minimized. First, the noise transmission from each noise source to the output is analyzed for the second-order circuit. It is shown that the sample-and-hold component in the output noise is sufficiently large compared to the continuous-time component, and the effect of the pole-zero combination is small. Then, the condition for minimizing the noise transmitted from each second-order circuit to the output of the SC filter is investigated. The derived condition is that the amplitude response of the transfer function from the filter input to each second-order circuit should be flat. Translating the condition into the condition for the pole-zero combination/cascading order, the following condition is derived. For the combination, starting from the pole with higher Q, the closest zero is combined; for the order, the circuits are cascaded so that the frequency at which the amplitude response from the filter input to the second-order circuit should be distributed. Finally, simulations are executed for 11th-order low-pass and high-pass filters. It is seen that for approximately 40 percent of 36 ways of combination/order with the foregoing condition, the output noise ranges within 20 percent of the minimum value, which indicates the effectiveness of the presented condition.