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Abstract
We propose a photonic time-stretched analog-to-digital converter (PTS-ADC) based on dispersion-tunable chirped fiber Bragg grating (CFBG), by demonstrating a economical ADC system with seven different stretch factors. The stretch factors are tunable by changing the dispersion of CFBG, in order to obtain different sampling points. Accordingly, the total sampling rate of the system can be improved. Only a single channel is required to increase the sampling rate and achieve the effect of multi-channel sampling. Finally, seven groups of different stretch factors ranging from 1.882 to 2.206 are obtained, which are equivalent to seven groups of different sampling points. We successfully recover the input radio frequency (RF) signals with frequencies from 2 GHz to 10 GHz. In addition, the sampling points are increased by 14.4 times and the equivalent sampling rate is increased to 288 GSa/s. The proposed scheme is suitable for commercial microwave radar systems, which can obtain a much higher sampling rate at a low cost.
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1. Introduction
With the development of wideband signal applications and technologies such as microwave photonic radar and radio frequency (RF) communication systems, the demand for high speed and high sampling rate analog-to-digital converter (ADC) is growing rapidly. However, due to the nature of semiconductor materials, traditional electronic ADC is limited by thermal noise, sampling clock jitter, comparator ambiguity and other factors, which will seriously affect the sampling rate, effective number of bits (ENOB), the input bandwidth and other important indicators to measure the performance of ADC [1]. The photonic ADC is a microwave photonics scheme, which has been used in optical fiber sensors fields [2–5]. Compared with the traditional electronic ADC, the photonic ADC has the advantages of high repetition rate, low time jitter and short pulse width. The photonic ADC can be divided into four types: the photonic assisted ADC, the photonic sampled ADC, the photonic quantized ADC, and the photonic sampled and quantized ADC [6]. Photonic time-stretched ADC (PTS-ADC) is a photonic assisted ADC firstly proposed by Jalali B. in 1999 [7]. The PTS-ADC is able to stretch the broadband RF signal into a low-speed narrowband signal, thereby reducing the requirements on the sampling rate and the input bandwidth of the back-end ADC, enabling the low-speed ADC to sample high-speed broadband signals.
To improve the sampling rate of the PTS-ADC, the methods mainly include adding dispersive media with large dispersion and multi-channel sampling. The phase diversity method and dispersion compensation fibers (DCFs) with dispersion of -1142 ps/nm and -1522 ps/nm were used to realize PTS-ADC with 480 GSa/s sampling rate [8]. A dual channel PTS-ADC system based on dispersion crystal fiber was designed, and the equivalent sampling rate of the ADC system employing dispersion crystal fiber with the same length was five times higher than that of employing normal DCFs [9]. Adopting DCFs with dispersion of -2496 ps/nm and - 2627 ps/nm, a 10 TSa/s PTS-ADC was proposed, but four distributed Raman amplifiers were required [10]. Larger dispersion will bring greater power loss due to dispersion loss, which requires the addition of multistage optical amplifiers that would increase the cost and complexity of the system. To realize multi-channel sampling, wavelength division multiplexer (WDM) and optical delay line were added in the PTS-ADC system [11,12]. Each additional channel would double the equivalent sampling rate while doubling the number of the photoelectric modulators, the dispersion media and other devices. In addition, channel mismatch between different channels would distort the recovered signals [13]. Thus, a PTS-ADC with tunable dispersion and single channel structure to realize the function of low cost and high sampling rate is highly required.
In this paper, we propose a high-speed single channel PTS-ADC system based on tunable dispersion media. Preliminary results have been presented [14]. This paper presents more particular formula derivation and experimental verifications to further illustrate the proposed design. A chirped fiber Bragg grating (CFBG) is glued to a cantilever beam to realize the tunable dispersion, which is firstly adopted. Seven different stretch factors of the RF signals are obtained by adjusting the chirp rate and then the dispersion of the CFBG, resulting in the corresponding seven different groups of sampling points and the improvement of the total sampling rate. Compared to the traditional methods, the proposed design is free of multistage optical amplifiers, and achieves the equivalent effect of multi-channel sampling in a single channel. The equivalent sampling rate is increased to 288 GSa/s. The proposed design has potential application value in microwave radar and other fields.
2. Experimental setup and principle
The experimental setup of PTS-ADC system based on dispersion-tunable CFBG is presented in Fig. 1. The MLL generates an electrical synchronization signal, which is then sent to the reference input (REF IN) port of the vector signal generator (VSG), so that the repetition frequency of the MLL can be used as the clock base of the VSG. The MLL outputs a Gauss type ultrashort optical pulse, whose time domain and frequency domain expression can be written as:
where ${E_0}$ is the amplitude and T is the FWHM (Full Width at Half Maximum) of the optical pulse in the time domain. Then the optical pulse is reflected by the dispersion-tunable CFBG within a specific bandwidth $\Delta \lambda $ and introduces tunable dispersion ${D_0}$, stretching the pulse from femtoseconds to nanoseconds. The width of the reflected optical pulse is expressed as:A DCF with a dispersion ${D_1}$ of -497 ps/nm is set before MZM in order to broaden the time window of reflected the optical signal. After passing through the DCF1, the stretched optical pulse can be expressed as:
Then, the RF signal with frequency ${\omega _{RF}}$ output by the VSG is modulated by the Mach-Zehnder modulator (MZM) onto the stretched optical pulse. The modulated signal, including the information of optical pulse and input RF signal, can be represented as:
After the twice stretched signal is captured by the photodetector (PD), the optical signal is down converted into an electrical signal, which is then sampled by the oscilloscope (OSC). When modulation index m is too small, the photocurrent and envelope current obtained by the photodetector are expressed as follows:
It can be seen that the RF finally signal is stretched M times in the time domain, which is equivalent to reducing the sampling rate requirements of the ADC by M times.
Fig. 1. The experimental setup of the dispersion-tunable PTS-ADC. MLL: mode-locked laser; OC: optical circulator; CFBG: chirped fiber Bragg grating; DCF: dispersion compensation fiber; EDFA: erbium-doped optical fiber amplifier; MZM: Mach-Zehnder modulator;VSG: vector signal generator; OSA: optical spectrum analyzer; PD: photodetector; OSC: oscilloscope.
Figure 2 shows the experimental setup for realizing the tunable dispersion based on the CFBG. A 100 mm long CFBG with an original chirp rate ${\mathrm{{\cal R}}_{\textrm{ch}0}}{\; } = {\; }0.12$ nm/cm is glued to the long side of the right-triangular cantilever beam at a certain angle $\theta = {\; }3.3^\circ $. The length $L{\; }$, the width of the fixed end, and the thickness of the right-triangular cantilever beam is 24 cm, 4 cm and 0.8 cm. In order to fix the central wavelength ${\lambda _0}$ of reflection spectrum, the center of the CFBG is flush with the neutral plane of the cantilever beam [15]. The vertical displacement $\mathrm{\Delta }y$ of the free end is precisely controlled by the strain applying device with a scale knob.
The time delay $\tau $ for the optical wave with wavelength $\lambda $ is expressed as [16]:
Suppose that ${\lambda _a}$, ${\lambda _b}$ and $\Delta \lambda $ are the starting reflection wavelength, the cutoff reflection wavelength and the reflection bandwidth of CFBG, then the width of reflected optical pulse in time domain can be written as:
According to Eq. (3), Eq. (15) and Eq. (17), the dispersion ${D_0}$ of CFBG can be given as:
It is clear that ${D_0}$ will increase in the negative direction when $\mathrm{\Delta }y$ increases. Therefore, the tunable dispersion of CFBG can be obtained by controlling the vertical displacement of the cantilever beam. The stretch factor can be tuned by changing the dispersion of CFBG according to Eq. (10). As shown in Fig. 3, each time a different stretch factor is obtained, one more group of sampling points are added, which is similar to adding one more channel in multi-channel sampling. Thus, the total sampling rate can be improved by obtaining different sampling points corresponding to different stretch factors, and the final effect is equivalent to multi-channel sampling. If N groups of stretched RF signals with different stretch factors ${M_1}$∼ ${M_N}$ are acquired, by compressing and combining the signals together, the total equivalent sampling rate can be increased by ${M_{total}} = \mathop \sum \limits_{n = 1}^N {M_n}$ times. Therefore, a high-speed PTS-ADC with high equivalent sampling rate is achieved by obtaining different stretch factors.
3. Results and discussions
In the experiment, the sampling rate of the oscilloscope is set to 20 GSa/s, and the VSG outputs sinusoidal signals with amplitude of 1.5 V and frequencies of 2 GHz, 3 GHz, 4 GHz, 5 GHz, 6 GHz, 8 GHz and 10 GHz as the input RF signals.
Figure 4 shows the waveform change of optical spectrum versus vertical displacement $\mathrm{\Delta }y$ after propagation through the MZM when modulation index $m = 0$. The 3 dB bandwidth of the optical spectrum increases linearly with increasing vertical displacement $\mathrm{\Delta }y$. According to the dispersive Fourier transform, the dispersive medium will map the wavelength to the time domain, so the non-smooth optical spectrum will lead to the non-smooth electrical envelope of the modulated signal. The causes of spectral unsmoothness will be discussed below. The relationships between $\mathrm{\Delta }y$ and $\mathrm{\Delta }t$, $\Delta \lambda $ and ${D_0}{\; }$ are shown in Fig. 5. It can be seen from Fig. 5(c) that the dispersion can be controlled by tuning vertical displacement. Tunable dispersion ranging from -637.2 ps/nm to -322.2 ps/nm are acquired in the experiment. According to Eq. (10), the calculated stretch factors ${M_1}$∼ ${M_7}$ are 1.882, 1.952, 2.018, 2.064, 2.118, 2.162 and 2.206. The total sampling points ${M_{total}}$ is increased by $\mathop \sum \limits_{n = 1}^7 {M_n} = 14.4$ times, so that the equivalent sampling rate is equal to 288 GSa/s.
Fig. 5. The relationships between the vertical displacement $ \Delta y$ of the cantilever beam and (a) the reflection bandwidth $ \Delta \lambda $, (b) the width of the reflected optical pulse $ \Delta t$, and (c) the dispersion ${D_0}$ of CFBG.
First, set the frequency of input RF signal to 2 GHz. Figure 6(a) and 6(c) represent the waveforms of modulated signals and their envelope signals when the vertical displacement $\mathrm{\Delta }y = 0$ mm and $\mathrm{\Delta }y = 150$ mm respectively. Different vertical displacements $\mathrm{\Delta }y$ values result in modulated signals with different stretch factors M, which is consistent with Eq. (10) and Eq. (18). By using the recovery method in Eq. (13), the 5-point moving average algorithm, the 10-point Gaussian filter algorithm and the Hilbert de-enveloping algorithm, the recovered signals obtained are shown in Fig. 7(c). Due to the unsmoothness of the envelope signal, the signal directly recovered by Eq. (13) has large noise and serious distortion, as shown in Fig. 7(a). Therefore, the 5-point moving average algorithm is applied to denoise, which can generate a signal consisting of the mean values of 5 local data point. Each mean is calculated based on a sliding window of length 5 across neighboring elements of the input signal. To further smooth the directly recovered signal, 10-point Gaussian filter algorithm is adopted, which is essentially similar to the 5-point moving average algorithm. The difference is that a Gaussian weighted average filter is used while the weighted value is Gaussian distribution centered on the element at the current position. The Hilbert de-enveloping algorithm can obtain a signal with all positive frequency components phase-shifted by -90 degrees and all negative frequency components phase-shifted by +90 degrees through Hilbert transform, while the amplitude of the signal remains unchanged. Taking the original signal $\textrm{x}(\textrm{t} )$ as the real part and the signal after Hilbert transformation $\mathrm{\hat{x}}(\textrm{t} )$ as the imaginary part, the analytic signal is $\mathrm{\tilde{x}}(\textrm{t} )= \textrm{x}(\textrm{t} )+ \mathrm{j\hat{x}}(\textrm{t} )$. The absolute value of the analytic signal is the desired envelope value. By dividing the recovered signal by the envelope value, the distortion caused by the unsmooth envelope signal can be reduced.
Fig. 6. (a)Waveforms of modulated signal (red), envelope signal (blue) and (b) the sampling points figure of recovered signal when the vertical displacement $ \Delta y$=0 mm; (c)Waveforms of modulated signal (red), envelope signal (blue) and (d) the sampling points figure of recovered signal when the vertical displacement $ \Delta y$=150 mm. The frequency of input RF signal is 2 GHz.
Fig. 7. (a) Directly recovered signal; (b) The signal after applying 5-point moving average algorithm and 10-point Gaussian filter algorithm; (c) The signal after applying Hilbert de-enveloping algorithm.
The recovered signals are also stretched to different frequencies due to different vertical displacements $\mathrm{\Delta }y$. Besides, seven groups of recovered signals with seven different stretch factors are obtained. The recovered signals are combined together according to the following steps. The seven groups of recovered signals are first compressed to 2 GHz through dividing them by the corresponding stretch factors in the time domain. Then the compressed signals are aligned according to their central points to form the combined signal. Each sampling point of the combined signal is arranged in ascending order according to the time domain value. Finally, the 5-point moving average algorithm and 10-point Gaussian filter algorithm are applied again to reduce the noise of the combined signal. Figure 8 shows the obtained fitting sinusoidal waveform of combined signal. The fitting frequency is 2.005 GHz when R-square is 0.9961. The FFT spectrum of the combined signal is shown in the Fig. 9. The SINAD of the combined signal is 35.16 dB, and the ENOB is calculated by $\textrm{ENOB} = ({\textrm{SINAD} - 1.76} )/6.02 = 5.55$ bits, which means that the resolution will not decrease much while the sampling rate is increased. It can be clearly seen from Fig. 10 that the sampling points of the combined signal by using proposed designed are far more than those directly sampled by the oscilloscope.
Fig. 8. The fitting sinusoidal waveform of combined signal when the frequency of input RF signal is 2 GHz.
Fig. 10. Sampling points comparison of (a) directly sampling and (b) using the proposed design when the frequency of input RF signal is 2 GHz.
Then, respectively set the frequencies of input RF signal to 3 GHz, 4 GHz, 5 GHz, 6 GHz, 8 GHz and 10 GHz. The combined signals recovered by the above method are shown in Fig. 11. The input RF signals are successfully recovered. However, as the frequency of the input RF signal increase, the combined signals will be distorted. There are two main reasons for the signal distortion. One reason is that moving average algorithm and Gaussian filter algorithm will lose effectiveness when the number of sampling points is small in a signal period. For example, if frequency of the input RF signal is 6 GHz and the sampling rate of the oscilloscope is 20 GSa/s, the frequency of the recovered signal will be about 3 GHz, and the oscilloscope will capture about 6 sampling points in a signal period, which is too few for applying the 5-point moving average algorithm. Another reason comes from the non-smooth envelope signals, which causes the difficulties in recovering the correct signal waveform.
Fig. 11. The sampling points figures of combined signal when the frequency of input RF signal are (a) 3 GHz, (b) 4 GHz, (c) 5 GHz, (d) 6 GHz, (e) 8 GHz and (f) 10 GHz.
In order to find out the causes of the non-smooth envelope signal as well as the non-smooth spectrum, the OSA is set after the dispersion-tunable CFBG to observe the optical spectrum of the reflected optical pulse, as shown in Fig. 12. Comparing Fig. 4 and Fig. 12, it can be inferred that the small fluctuations in Fig. 12 are caused by the nonlinearity in the process of MZM modulation, which means that multi-order harmonic components will be introduced when MZM modulates the input RF signal onto the optical pulse. Since the spectrum filtered by CFBG will retain the shape of the input spectrum within the reflection bandwidth, the large fluctuations both in Fig. 4 and Fig. 12 are caused by the spectral clutter of the MLL spectrum, which has a valley bottom at 1549 nm.
In practical applications, the RF signal output from VSG can be multiplexed by means of power splitter and multiple delay lines with different delays, as shown in Fig. 13. The power of RF signal is equally divided for each channel, and the delay caused by the delay line increases by the same multiple as the number of channels increases. For instance, the delay caused by delay line 7 is 7 times that of delay line 1. Finally, the 7 groups of RF signals are multiplexed to one channel. In this way, a new signal containing 7 groups of RF signals with the same power and waveform can be obtained. There is a certain time interval between two adjacent RF signals in the time domain. As a result, the replication of the input RF signal is realized, so that the under-test RF signal can remain unchanged when stretched to different multiples.
Better results are expected if adopting broadband laser with flat spectrum, such as dissipative soliton-based MLL [18] and complementary dual MZM [19], or asymmetrical dual-parallel MZM [20] which can reduce nonlinearity. For further research, the electrical domain method (including electrical predistortion method [21], post compensation method [22]) and optical domain method (including dual polarization control method [23], MZM series/parallel method [24,25], microring-assisted MZM method [26]) could be adopted to suppress the intermodulation distortion generated by the input multi-tone signal in the photoelectric modulation, so that the proposed PTS-ADC can be applied to the multi-tone signal. In order to broaden the frequency range of the input signal and increase the time window of the optical pulse at the MZM input port, other dispersion-tunable media which will not truncate the optical pulse can be considered to replace the CFBG. Besides, applying digital domain pre-compensation method to preprocess the frequency domain information of the modulated signal is also one of the future research directions. In the future research work, the input RF signal could be set as arbitrary waveform signal to verify the effect of increasing the sampling points and improving the accuracy of recovered arbitrary waveform signal.
4. Conclusion
A single channel PTS-ADC system based on dispersion-tunable CFBG is demonstrated. The proposed design has a simple structure being free of large dispersion media. The equivalent high-speed sampling function of multi-channel sampling is achieved in just one single channel. A dispersion-tunable structure based on CFBG is firstly adopted for PTS-ADC. By changing the dispersion of CFBG, seven groups of different stretch factors ranging from 1.882 to 2.206 are obtained. The stretched signals, which is corresponding to the different stretch factors, are compressed and then combined together. As a result, the total sampling rate is increased by 14.4 times, and the equivalent sampling rate is increased to 288 GSa/s. The input RF signals with frequencies from 2 GHz to 10 GHz are recovered successfully. When the frequency of input RF signal is 2 GHz, an ENOB of 5.55 bits is achieved with a R-square of 0.9961. In comparison to traditional methods, the proposed design saves additional channels and multiple sets of devices. While achieving high sampling rate, the proposed design greatly saves the cost of ADC system, and is more suitable for commercial microwave radar systems.
Funding
Department of Natural Resources of Guangdong Province (GDNRC [2022] No. 22); Guangdong Science and Technology Department (2021A0505080002); Intelligent Laser Basic Research Laboratory (No. PCL2021A14-B1); Basic and Applied Basic Research Foundation of Guangdong Province (2021B1515120029); National Natural Science Foundation of China (61871207).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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