JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 21, NO. 12, DECEMBER 2003 3085 Photonic Time-Stretched Analog-to-Digital Converter: Fundamental Concepts and Practical Considerations Yan Han and Bahram Jalali, Fellow, IEEE Invited Paper Abstract—Ultra-wide-band analog-to-digital (A/D) conversion is one of the most critical problems faced in communication, instru- mentation, and radar systems. This paper presents a comprehen- sive analysis of the recently proposed time-stretched A/D converter. By reducing the signal bandwidth prior to digitization, this tech- nique offers revolutionary enhancements in the performance of electronic converters. The paper starts with a fundamental-physics analysis of the time–wavelength transformation and the implica- tion of time dilation on the signal-to-noise ratio. A detailed mathe- matical description of the time-stretch process is then constructed. It elucidates the influence of linear and nonlinear optical disper- sion on the fidelity of the electrical signal. Design issues of a single- sideband time-stretch system, as they relate to broad-band opera- tion, are examined. Problems arising from the nonuniform optical power spectral density are explained, and two methods for over- coming them are described. As proof of the concept, 120 GSa/s real-time digitization of a 20-GHz signal is demonstrated. Finally, design issues and performance features of a continuous-time time- stretch system are discussed. Index Terms—Analog-to-digital (A/D) conversion, microwave photonics, optical signal processing, single-sideband (SSB) mod- ulation, time stretch. I. INTRODUCTION D IGITAL signal processing (DSP) has revolutionized modern communication and radar systems by offering unprecedented performance and adaptivity. For broad-band systems, however, the application of DSP is hindered by difficulty in capturing the wide-band signal [1]. A sampling oscilloscope is not an option because it requires the signal to be repetitive in time. It only provides information about the average signal behavior; hence, it does not operate in real time. The real-time capture of ultrafast electrical signals is a difficult problem that requires wide-band analog-to-digital converters (ADCs). Manuscript received April 15, 2003; revised July 29, 2003. This work was supported by the Defense Advanced Research Project Agency (DARPA) under the Photonic Analog-to-Digital Converter (PACT) program. The authors are with Optoelectronic Circuits and Systems Laboratory, De- partment of Electrical Engineering, University of California at Los Angeles, Los Angeles, CA 90095 USA (e-mail: jalali@ucla.edu). Digital Object Identifier 10.1109/JLT.2003.821731 Fig. 1. Conventional sample-interleaved ADC architecture. The signal is captured by a parallel array of slow digitizer, each clocked at a fraction of the Nyquist rate. The Nyquist criterion is only satisfied when the signal is reconstructed, sample-by-sample, in the digital domain. A detailed discussion on the limits of electronic ADCs is be- yond the scope of this paper [2]. Simply stated, the performance is limited by one or more of the following problems: 1) jitter in the sampling clock; 2) settling time of the sample-and-hold circuit; 3) speed of the comparator (comparator ambiguity); 4) mismatches in the transistor thresholds and passive com- ponent values. The limitations imposed by all these factors become more severe at higher frequencies. The standard approach to deal with this problem is to em- ploy parallelism through the use of the time-interleaved ADC architecture, shown in Fig. 1 [3], [4]. Here, the signal is cap- tured by a parallel array of slow digitizers, each clocked at a fraction of the Nyquist rate. The Nyquist criterion is only satis- fied when the signal is reconstructed, sample-by-sample, in the digital domain. In this paper, we use the term “sample-inter- leaved” to refer to this architecture. It is well known that mis- matches between digitizers limit the dynamic range and, hence, the resolution of sample-interleaved ADC systems [3], [4]. A state-of-the-art electronic ADC, embodied by real-time digi- tizing oscilloscopes (Tektronix TDS7404, or Agilent 54 854A) boasts 20 GSa/s 4-GHz analog bandwidth. Depending on the 0733-8724/03$17.00 © 2003 IEEE