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Digital Signal Processing (DSP) has revolutionized modern communication and radar systems. For wideband systems, however, the application of DSP is hindered by the difficulty in performing the Analog-to-Digital Conversion (ADC) of wideband signals. A state-of-the-art electronic ADC, embodied by the real-time Tektronix digitizing oscilloscope (Tektronix TDS7404) boasts 20 Gsample/s, 4 GHz analog bandwidth and an Effective Number of Bits (ENOB) of approximately 4.5 bits, over the full bandwidth. The high sampling rate is achieved by using the time-interleaved architecture. Here the signal is captured by a parallel array of slow digitizer that are sequentially clocked at a sub-Nyquist rate. The Nyquist criterion is satisfied when the signal is reconstructed in the digital domain. It is well known that the mismatches between digitizers in the array limit the dynamic range, so measured by the ENOB.

Figure 1 Wavelength Division Sampling [1]. The Arrayed Waveguide Grating (AWG) in feedback configuration generates a discrete time-wavelength transformation. The system can also function with a continuous chirp where AWG is replaced with a dispersive fiber.

 

The process of ADC can be partitioned into two stages: (i) sampling, and (ii) quantization. Given the lack of an efficient digital optical switch, it has been prudently assumed by researchers that quantization is best done in electronic domain, and optics should be considered as a mean to perform ultrafast sampling. Time-to-wavelength mapping, inherent in chirped optical signals, offers a natural mechanism for sampling a wideband RF signal and to demultiplex the samples into a parallel array of digitizer [1,2]. The discrete-time implementation of this approach is shown in Figure 1 [1]. The spectrum of pulses from an actively mode locked laser are broadened via a nonlinear pulse compression stage (SuperContinuum generation) and sliced to attain discrete wavelength-to-time mapping. The multi-wavelength pulse stream samples the analog signal in an electrooptic modulator. A passive wavelength demultiplexer is then used to perform serial to parallel conversion. An array of slow electronic digitizers quantize each channel. For an N channel system, the aggregate sampling rate would be N.fs, where fs is the sampling rate of individual electronic digitizers. This approach uses photonics for sampling and serial-to-parallel conversion, otherwise, the ADC architecture is identical to that of time-interleaved system. It offers an ultra-high sampling rate, with an accuracy (ENOB) which will fundamentally be limited by the mismatch between different channels.

Figure 2 Time-stretch Analog-to-Digital Conversion [3]. (a) with a time-limited input signal, and (b) with a continuous-time input signal.

 

An entirely new A/D architecture is the so-called time-stretch ADC, shown in Figure 2 [3]. Here the analog signal is slowed down prior to sampling and digitization by an electronic digitizer. For a time-limited input, a single channel, shown in Figure 2a, suffices. A continuous-time input can be captured with a multi-channel system shown in Figure 2b, where the partitioning of the continuous signal into parallel segments can be performed in the wavelength domain through time-to-wavelength mapping. Slowing down the signal prior to digitization has several advantages. For a stretch factor of M, the effective sampling rate is increased to M.fs. The input bandwidth of the electronic digitizer is also increased by M. The error associated with the jitter in the sampling clock of the digitizer is reduced due to a reduction in the signal slew rate. For a time-limited input, only a single digitizer is needed (Figure 1a) hence eliminating the inter-channel mismatch problem. For the continuous-time system (Figure 2b) it has recently been shown that mismatch errors can be corrected using the information available in the signal [4]. This is an important advantage of the time-stretch ADC over the time-interleaved ADC. It exploits a fundamental difference between the two systems: in the former, the signal at each channel is sampled at or above the Nyquist rate whereas in the latter, it is sampled at a fraction of the Nyquist rate.

Figure 3 Physical implementation of the time-stretch preprocessing. Single SideBand (SSB) modulation removes the electrical bandwidth limitation imposed by dispersion. The differential Mach-Zehnder (MZ) modulation is used to remove common-mode distortion.

 

Figure 3 shows the physical implementation for a single channel time-stretch ADC. The input electrical signal is modulated onto a chirped optical carrier. This is followed by dispersion, leading to temporal stretching of the modulation envelope. A single sideband modulation format eliminates the dispersion penalty that would otherwise place a limit on the electrical bandwidth. While a phase distortion remains, the effect is static and can be filtered in the digital domain. The differential scheme, using dual-output Mach-Zehnder modulator, is used to remove temporal distortions caused by the non-uniform power spectral density of the supercontinuum source and the RIN noise. It is important to note that this system is different than the time-lens, both in theory and in physical implementation. In the time-lens, the input signal must be dispersed. For ADC applications, the input signal is electrical. The lack of any wideband and low-loss electrical dispersive technology makes it difficult to use the time-lens in ADC applications.

Figure 4 Experimental demonstration of the time-stretch ADC. Real-time capture of a 20GHz input at 120 Gsample/s is demonstrated. The system has an effective bandwidth of 24 GHz.

 

Figure 4 shows 120 Gsample/s real-time digitization of a 20GHz signal [5]. This was achieved by cascading a 6x photonic time-stretch preprocessor with the 20Gsample/s Tektronix TDS7404 digitizer which has a 4GHz bandwidth. The time-stretch increases the bandwidth to 24GHz making it possible to capture a 20GHz signal with the 4GHz digitizer. Presently, the Signal-to-Noise Ratio (SNR) is 3.5bits over the full 24GHz effective bandwidth. This is one-bit lower than the 4.5 bit resolution of the electronic digitizer. The detailed discussion of this phenomenon is beyond the length-limit of this paper, but simply stated, it originates from partial loading of the digitizer in our experiment. With a modified O-E stage, we expect to recover this reduction in the SNR to the point that it will be limited purely by the electronic digitizer.
Time-frequency techniques can also be used to generate ultra wideband electrical waveforms with arbitrary modulation [7-8]. In this approach the spectrum of a broadband optical pulse is shaped according to the waveform of interest. Following dispersion, this spectral waveform is directly transformed into an identical time waveform, which is subsequently converted to electronic domain using a photodetector. In a recent demonstration, intelligent digital control of the spectrum has been used to render the system insensitive to the nonuniform power spectral density of the optical source [8]. The system directly converts digital data to ultra wideband analog waveforms.
In summary, this paper has outlined novel applications of time-to-wavelength mapping techniques in data conversion. For analog-to-digital conversion, the general approach is to increase the performance of an electronic digitizer by optical signal pre-processing. Presently, the time-stretch technique appears to be the most promising in enabling ultra wideband analog-to-digital conversion with moderate resolutions. Optical spectrum shaping plus dispersion has important applications in ultra wideband digital-to-analog conversion.


[1] A.S. Bhushan, F. Coppinger, B. Jalali, S. Wang, H.F. Fetterman, Electron Lett, 34, p. 474, 1998.
[2] T.R. Clark, J.U. Kang, R.D. Esman, Photonics Tech. Lett, 11, p. 1168, 1999.
[3] Bahram Jalali, Fred Coppinger, “Data Conversion Using Time Manipulation” US Patent 6,288,659, September, 2001.
[4] Y. Han, B. Razaei, B. Jalali, V. Roychoudhuri, Proceedings of the 2003 Instrumentation and Measurement Technology Conference (IMTC/03) 20-22 May 2003 in Vail, Colorado USA.
[5] Yan Han, Bahram Jalali, “Differential Photonic Time-Stretch Analog-to-Digital Converter”, CLEO 2003.
[6] B.H Kolner and M. Nazarathy, “Temporal imaging with a time lens”, Optics Letters, 1989, vol. 14, pp. 630-632.
[7] B. Jalali, P. Kelkar, and V. Saxena,. 14th Annual Meeting of the IEEE Lasers and Electro-Optics Society (Cat. No.01CH37242), Piscataway, NJ, USA., vol.1, pp.253-4, 2001.
[8] J. Chou, Y. Han, and B. Jalali, Technical Digest of the 2002 Microwave Photonics Conference, MWP 2002, November 5-8, 2002, Awaji, Japan, Paper T2-1, pp. 93-96.

 

 



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