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Switched-capacitor filters with digitally programmable capacitor arrays (DPCAs) offer a solution to the diverse needs to the market for audio-frequency high-order low-pass filters. Cascading switched-capacitor biquads which contain binary or geometrically weighted DPCAs are not a viable way to produce precision high-order responses, because of the errors introduced by capacitance quantization. To overcome this problem, a ladder-based structure is proposed. It uses DPCAs tailored to provide exactly the capacitances required to realize a restricted but useful set of responses. A simple procedure for synthesizing such filters is presented and illustrated with a detailed example. A CMOS prototype chip which provides eight seventh-order responses was fabricated. A 3-bit word programs its response: elliptic (with four different selectivities), Chebyshev, inverse Chebyshev, Butterworth, or modified Bessel (modified to have stopband notches). Experimental results are included which show that with this design philosophy, performance is not sacrificed for programmability.