A novel approach to the exact design of first- and second-order Bode-type variable-amplitude bilinear-LDI switched-capacitor equalizers

This paper presents a novel approach to the exact design of first- and second-order Bode-type variable-amplitude (VA) bilinear-LDI switched-capacitor (SC) equalizers. The proposed design approach is based on the realization of the VA equalizer transfer function as the transfer function of a frequency-independent two-terminal-pair SC network at its input terminal-pair when its output terminal-pair is terminated in a (frequency-dependent) SC one-terminal-pair realization of the dual of the equalizer shaping impedance function. The resulting first-order equalizers produce fan-shaped lowpass or highpass magnitude-frequency responses, while the resulting second-order equalizer produces a bump-shaped (bandpass) magnitude-frequency response. The salient feature of the proposed SC equalizers is that only a single variable capacitor is required to control the fan amplitude in the first-order equalizers and the bump amplitude in the second-order equalizer. Moreover, these equalizers remain BIBO stable for all possible values of the variable capacitor. In addition, they exhibit the important practical feature that a geometrically symmetric change in the value of the variable capacitor causes a corresponding arithmetically symmetric change in the logarithmic magnitude-frequency response of the VA equalizer. An application example is given to illustrate the main results.