Explain the operation and design considerations of sigma-delta modulators for ADCs.

Sigma-delta modulators use oversampling and noise shaping to achieve high resolution with simple comparators. The integrator accumulates the difference between input and quantizer output, pushing quantization noise to higher frequencies where it is filtered. Design considerations include: Oversampling ratio (higher gives more resolution but requires faster clock), Loop order (higher order provides more aggressive noise shaping but stability becomes critical), Quantizer levels (multi-bit improves SNR but requires DAC linearity), Integrator topology (affects stability and SNR), and Digital decimation filter design. A second-order modulator achieves approximately 15-bit resolution at 64x oversampling.