Closed-form solution of the quantization error in quadruple-loop Σ-Δ A/D converters

Recently, a mathematical technique was developed for the determination of the quantization error for a triple-loop Σ-Δ A/D converter. The technique is based on representing the internal quantization error by a corresponding Fourier series expansion. The proposed paper is concerned with the determination of the closed-form solution of the internal quantization error for a conventional quadruple-loop Σ-Δ A/D converter configuration operating under overload-free quantization and with an arbitrary input signal excitation. The internal quantization error is then determined for the important case of an arbitrary sinusoidal input signal. A computational investigation of the result confirms the validity of the closed-form solution of the internal quantization error