Not yet reviewed by Pith; the record is open.

Microresonator-based Kerr frequency combs ("Kerr microcombs") constitute chip-scale frequency combs of broad spectral bandwidth and repetition rate ranging from gigahertz to terahertz. An appealing application exploiting microcombs' coherence and large repetition rate is microwave and millimeter-wave generation. Latest endeavor applying two-point optical frequency division (OFD) on photonic-chip-based microcombs has created microwaves with exceptionally low phase noise. Nevertheless, microcomb-based OFD still requires extensive active locking, additional lasers, and external RF or microwave sources, as well as sophisticated initiation. Here we demonstrate a simple and entirely passive (no active locking) architecture, which incorporates an optoelectronic oscillator (OEO) and symphonizes a coherent microcomb and a low-noise microwave spontaneously. Our OEO microcomb leverages state-of-the-art integrated chip devices including a high-power DFB laser, a broadband silicon Mach-Zehnder modulator, an ultralow-loss silicon nitride microresonator, and a high-speed photodetector. Each can be manufactured in large volume with low cost and high yield using established CMOS and III-V foundries. Our system synergizes a microcomb of 10.7 GHz repetition rate and an X-band microwave with phase noise of $-$97/$-$126/$-$130 dBc/Hz at 1/10/100 kHz Fourier frequency offset, yet does not demand active locking, additional lasers, and external RF or microwave sources. With potential to be fully integrated, our OEO microcomb can become an invaluable technology and building block for microwave photonics, radio-over-fiber, and optical communication.