Analysis and optimization of noise in continuous-time OTA-C filters

A general procedure is presented for noise analysis and optimization in continuous-time operational transconductance amplifier (OTA)-C filters of arbitrary order and topology. Based on a matrix description of a general OTA-C filter structure, universal expressions are derived that permit computing the filter noise and optimizing the noise performance in any OTA-C filter. The results are not only useful for classical (discrete or integrated) OTA-C designs at medium to high frequencies but also in modern radio-frequency integrated circuits (RFICs) by carefully replacing transistors or electronic subcircuits by OTA (macro) models. The formulas are easy to implement and are readily included in computer-aided analysis and optimization algorithms. The accuracy of the proposed algebraic method is confirmed by a comparison with SPICE-simulation results. Two application examples are given: Finding the minimum-noise a multiple-loop-feedback filter configuration to implement fifth-order Butterworth and Bessel transfer functions, and determining the optimal biquad sequencing and gain distribution in a cascade realization of an eighth-order Butterworth filter.