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Homework #1 of Advanced Analog Integrated Circuit Design 1. Please derive the Quantization Noise in Ideal ADCs (10%) 2. (a) What is the Aperture Error? (10%) (b) Find the maximum sampling error for a S/H circuit that is sampling a sinusoidal signal that could be described as Vin=A．sin2π．fin．t, Where A is 1V and fin=46.8MHz. Assume that the aperture uncertainty is equal to 10ps. (10%) (c) Find the maximum resolution of an ADC which can use the S/H `described in (b) while maintaining a sampling error less than 0.5LSB(10%) 3. Please explain the operation principle for R-2R based DAC, and show an example for 5-bit R-2R based DAC (draw its schematic) (20%) 4. For algorithmic (or cyclic) ADCs, if Vin=0.68V, and Vref=2V (-1V to 1V), based on its flow graph, please show the digital output for 6-bit output. (20%) 5. For Flash (or parallel) ADC, please show its schematic for a 4-bit case. If Vin=0.68V, and Vref=2V (Vrefn=-1V to Vrefp=1V), please show the digital output code ( in thermometer code format) for the 4-bit example. (20%)