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Asynchronous sigma-delta modulators (ASDMs) are closed-loop nonlinear systems that transform the information in the amplitude of their input signal into time information in the output signal, without suffering from quantization noise such as in synchronous sigma-delta modulators. This is an important advantage with many interesting applications. In contrast with their synchronous counterparts, ASDMs have been underexposed. Both conceptually and analytically, they are quite complex. This paper investigates in detail the analysis, design and circuit-implementation aspects of ASDMs with a binary quantizer. In the ASDM, the amplitude-time transformation is done using an inherent self-oscillation denoted as a limit cycle. The oscillation frequency is addressed as the main design parameter that determines the spectral properties of the ASDMs and the quality of the amplitude-time transformation. Analytical and graphical derivations of the limit cycle frequency are treated. The impact of the filter order and the properties of the nonlinear element are elaborated on. Circuit implementations and the tradeoffs in the design are presented for a first- and a second-order ASDM that target the VDSL front-end specifications. Prototypes are implemented in a digital 0.18-μm 1.8-V CMOS technology. The measured SFDR is 75dB in a frequency band of 8MHz for the first-order ASDM, and 72dB in a band of 12MHz for the second-order ASDM. The dissipated power is 1.5 mW and 2.2 mW, respectively.