1 System analysis of WDM optically-assisted ADC Payam Rabiei and A. F. J. Levi The University of Southern California University Park, DRB 118 Los Angeles, California Presented at UCLA on December 14, 1999.

2 Wavelength division demultiplexing (WDM) optically- assisted ADC in an n-channel system AWGDSP Optical source Modulator DetectorLPFADC DetectorLPFADC DetectorLPFADC RF signal spectrum Reconstructed output signal Time Input sequence of time- interleaved WDM optical pulses Anti-aliasing RF filter RFRF X(  RF ) 1 2 n 1 2 Channel 1 Channel 2 Channel n x(t)x(t) H m  RF  SYNC. CLK.

3 The source and modulator electric field spectrum E m (  nnnn Modulated optical- field spectrum   nnnn Optical-field spectrum E(  Example with N + 1 = 3 optical-modes for each center wavelength, m CC x(t) is the RF signal applied to the modulator, d is optical modulation depth, t C = 2  /  C, a m,k is amplitude of mode k associated with center frequency  m

4 Optical pulse output of multi-wavelength mode-locked laser  Optical pulse using 3 modes spaced by 8 GHz and center wavelength 0  = 1550 nm  Optical pulse using 3 modes and 5 center wavelengths spaced by 40 GHz Wavelength, 0.32 nm (40 GHz) 0 =  nm  = nm (  C = 8 GHz) FWHM = 28 ps FWHM = 4 ps

5 Combined LPF and detector frequency response   00 CC  C  C Ideal low-pass filter

6 Reconstruction of the RF signal using DSP SYNC. CLK.

7 System transfer function for one-pole RC LPF Example with N + 1 = 3 optical-modes for each center wavelength, m and n = 5 channels Set a m,k = 1 and d = 1.

8 System transfer function for 8-pole Butterworth LPF

9 System transfer function for 2-pole Butterworth LPF

10 Transversal filter and integrator system response  Transversal filter and integrator can be used to obtain flat response  The system is more practical   Delay line (t d ) Input (current) Output (voltage)

11 Practical transversal filter response   Delay line (t d ) Input (current) Output (voltage) R R = 50  C = 125 pF t RC = 25.5 MHz t d = 125 ps

12  5-channel system transfer function for large N indicates:  Flatness of frequency response of 1-pole RC LPFs is poor  Flatness of frequency response of 8-pole Butterworth LPFs is good Comparison of 8-pole Butterworth and 1-pole RC LPF for large N

13 Comparison of different filters  Noise  RC one-pole system = . BW  Transversal filter = . BW  8-pole Butterworth ~ 1. BW  Ideal filter = 1. BW  Flatness of system frequency response  RC one-pole systemPoor  Transversal filter Excellent  8-pole Butterworth Good  Ideal filterExcellent  Complexity  RC one-pole systemEasy  Transversal filterEasy  8-pole ButterworthHard  Ideal filterImpossible

14 Jitter in optical source and shot noise in optical detector White noise Jitter noise  = 10 fs, 100 fs, 1 ps N b = Number of bits  RF = Maximum signal frequency  t = Timing jitter (peak-to-peak) For 20 GHz signal, N b = 8  t < 31 fs 4 GHz Detector Shot noise  P = Input power per channel  t = Sampling interval E = Particle energy 0.8 eV for = 1550 nm For N b = 8 and 8 GS/s P = 0.1 mW P = 1 mW gives N b = 9.6  Prob. Jitter

15 Simulation results for the effect of jitter on ENOB and SNR 8-pole Butterworth  -channel system with no shot noise 4 GHz -3 dB bandwidth SNR(dB) = (6.02 ENOB)

16 Simulation results for effect of detector shot-noise on SNR 8-pole Butterworth  -channel system with no jitter 4 GHz -3 dB bandwidth SNR(dB) = (6.02 ENOB)

17 Simulation results for effect of detector shot-noise on SNR 1-pole RC Filter  -channel system 4 GHz -3 dB bandwidth SNR(dB) = (6.02 ENOB)

18 Simulation results for effect of detector shot noise and jitter on ENOB and SNR 8-pole Butterworth  -channel system 4 GHz -3 dB bandwidth SNR(dB) = (6.02 ENOB) b at 40 GS/s possible in 5-channel system using 1 mW received optical power per channel and  = 100 fs jitter

19 Transversal filter shot-noise simulation for 5-channel system R = 50  C = 125 pF t RC = 25.5 MHz t d = 125 ps

20 Effect of frequency response mismatch in LPFs  The effect of single-channel LPF frequency mismatch on the frequency dependence of the ENOB.  Example: 8-pole Butterworth,  -channel system with 4 GHz -3 dB LPF bandwidth and no sources of noise  Difficult to maintain better than 0.25% LPF frequency mismatch over 0 o C < T < 70 o C

21 Time-domain simulation result for noise analysis  Reconstructed time-domain 2 GHz signal in presence of  = 1 ps jitter. The 5-channel system uses 8-pole Butterworth LPFs with 4 GHz –3 dB bandwidth.  Signal-level dependent noise Time, t Signal Jitter

22 Conclusions  In principle, WDM ADC using LPFs and DSP works!  The optical part mixes high-frequency with low-frequency components by aliasing. This is a hybrid opto-electronic RF-mixer.  The main advantages of LPF are lower bandwidth and reduction of noise in the system due to limited bandwidth.  The LPF should be designed for a flat-frequency system response.  LPFs should have matched frequency response.  An anti-aliasing filter is required at the modulator RF input.  To obtain moderate ADC performance (ENOB > 6 and > 40 GS/s):  Relatively long optical pulses (e.g. 28 ps) can be used in the system minimizing optical-pulse amplitude noise.  Optical-pulse jitter must be less than  = 100 fs.  The received optical power per detector must be greater than ~ 1 mW.  ENOB > 10 and > 40 GS/s requires jitter  10 mW per channel

23 Future work  Build on basic model to include  non-linearity in modulator and detector  include physical laser model with RIN and jitter  Need new type of laser to enable optical ADC technology  develop parameters from system model  implement initial laser device  controlled-spectrum mode-locked  low pulse to pulse time-jitter  low amplitude noise  high-power optical output  relatively long optical pulses