Improvement of Dynamic Range Upper Limit for Phase Generated Carrier Algorithm Based on Linear Interpolation

Bingtao Cai; Limin Xiao; Xiaobao Chen

doi:10.3788/LOP232687

Laser & Optoelectronics Progress, Volume. 61, Issue 17, 1706011(2024)

Improvement of Dynamic Range Upper Limit for Phase Generated Carrier Algorithm Based on Linear Interpolation

Bingtao Cai¹, Limin Xiao^1、*, and Xiaobao Chen^2、**

¹Department of Optical Science and Engineering, School of Information Science and Technology, Fudan University, Shanghai 200433, China

²The 23rd Research Institute, China Electronics Technology Group Corporation, Shanghai 201900, China

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Figures & Tables(15)

Fig. 1. Schematic diagram of Classic-PGC modulation and demodulation algorithm

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Fig. 2. Variation of $\bar{A}$ value when increasing signal strength $D$ and frequency $F$ . (a) Signal strength D increases by 10‒50 rad; (b) signal frequency F increases by 1000‒5000 Hz

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Fig. 3. $\bar{A}$ value changes with different times of moving average

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Fig. 4. Variation of $\bar{A}$ value with moving average filtering when increasing signal strength D and frequency F. (a) Signal strength D increases by 10‒50 rad; (b) Signal frequency F increases by 1000‒5000 Hz

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Fig. 5. Simulation test of demodulation function of Interpolation PGC algorithm. (a) Two signals formed by three sine term sample symbols without flipped; (b) Lissajous formed by two signals of the Fig.5(a); (c) two signals formed by three sine term sample symbols with flipped; (d) Lissajous formed by two signals of the Fig.5(c); (e) comparison between demodulation results of Interpolation-PGC algorithm and theoretical design values

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Fig. 6. Related coefficient between simulated excitation signal and algorithm demodulation output

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Fig. 7. Simulation results of dynamic range Classic-PGC algorithm with the same sampling rate and different carrier frequencies

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Fig. 8. Result of digital mixing and low-pass filtering at a sampling rate of 300 kHz and a carrier frequency of 50 kHz. (a) Results of first harmonic mixing and second harmonic mixing after low-pass filtering; (b) Lissajous formed by two orthogonal signals after low-pass filtering

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Fig. 9. Comparison of dynamic range between Interpolation-PGC and Classic-PGC with the same 50 kHz carrier frequency

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Fig. 10. Schematic diagram of experimental verification

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Fig. 11. Comparison of dynamic range measurements between Interpolated-PGC and Classic-PGC at 2 kHz

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Table 1. Difference of two consecutive samples of tested signal at different amplitudes and frequencies
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Table 1. Difference of two consecutive samples of tested signal at different amplitudes and frequencies
Simulation Different amplitude @1 kHz Different frequency @6.8 rad
Amplitude /rad 1 2 4 6.8 8 Frequency /Hz 100 200 400 800 1000
Difference /% 0.002 0.09 0.35 1.0 1.4 Difference /% 0.01 0.04 0.16 0.65 1.0

Table 2. Distribution of cosine and sine terms after dividing 6 sampling points within a carrier cycle
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Table 2. Distribution of cosine and sine terms after dividing 6 sampling points within a carrier cycle
Sample period N-1 N N+1
Sample point $I_{N - 1}^{5}$ $I_{N}^{0}$ $I_{N}^{1}$ $I_{N}^{2}$ $I_{N}^{3}$ $I_{N}^{4}$ $I_{N}^{5}$ $I_{N + 1}^{0}$
Cosine term — $I_{N (c o s)}^{0}$ — — $I_{N (c o s)}^{3}$ — — $I_{N + 1 (c o s)}^{0}$
Sine term $I_{N - 1 (s i n)}^{5}$ — $I_{N (s i n)}^{1}$ $I_{N (s i n)}^{2}$ — $I_{N (s i n)}^{4}$ $I_{N (s i n)}^{5}$ —

Table 3. Interpolation scheme for missing sine and cosine terms
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Table 3. Interpolation scheme for missing sine and cosine terms
$\begin{matrix} {I_{N}^{1}}_{(c o s)} = {I_{N}^{0}}_{(c o s)} + \\ [{I_{N}^{3}}_{(c o s)} - {I_{N}^{0}}_{(c o s)}] / 3 \end{matrix}$ $\begin{matrix} {I_{N}^{2}}_{(c o s)} = {I_{N}^{3}}_{(c o s)} - \\ [{I_{N}^{3}}_{(c o s)} - {I_{N}^{0}}_{(c o s)}] / 3 \end{matrix}$
$\begin{matrix} {I_{N}^{4}}_{(c o s)} = {I_{N}^{3}}_{(c o s)} + \\ [{I_{N + 1}^{0}}_{(c o s)} - {I_{N}^{3}}_{(c o s)}] / 3 \end{matrix}$ ${I_{N}^{5}}_{(c o s)} = {I_{N + 1}^{0}}_{(c o s)} - [{I_{N + 1}^{0}}_{(c o s)} - {I_{N}^{3}}_{(c o s)}] / 3$
${I_{N}^{0}}_{(s i n)} = [{I_{N - 1}^{5}}_{(s i n)} + {I_{N}^{1}}_{(s i n)}] / 2$ ${I_{N}^{3}}_{(s i n)} = [{I_{N}^{2}}_{(s i n)} + {I_{N}^{4}}_{(s i n)}] / 2$

Table 4. Maximum output amplitude at different frequency with different carrier frequencies
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Table 4. Maximum output amplitude at different frequency with different carrier frequencies
F_c /kHz Frequency /Hz
100 125 160 200 250 320 400 500 800 1000
20 103 83 63 52 42 33 26 19 12 9
30 148 118 91 77 62 44 34 28 17 14
50 246 196 153 122 98 76 60 47 29 23

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Bingtao Cai, Limin Xiao, Xiaobao Chen. Improvement of Dynamic Range Upper Limit for Phase Generated Carrier Algorithm Based on Linear Interpolation[J]. Laser & Optoelectronics Progress, 2024, 61(17): 1706011

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Paper Information

Category: Fiber Optics and Optical Communications

Received: Dec. 18, 2023

Accepted: Feb. 5, 2024

Published Online: Sep. 14, 2024

The Author Email: Limin Xiao (liminxiao@fudan.edu.cn), Xiaobao Chen (stlcxb@foxmail.com)

DOI:10.3788/LOP232687

CSTR:32186.14.LOP232687

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology

Table 1. Difference of two consecutive samples of tested signal at different amplitudes and frequencies

Table 1. Difference of two consecutive samples of tested signal at different amplitudes and frequencies

Table 2. Distribution of cosine and sine terms after dividing 6 sampling points within a carrier cycle

Table 2. Distribution of cosine and sine terms after dividing 6 sampling points within a carrier cycle

Table 3. Interpolation scheme for missing sine and cosine terms

Table 3. Interpolation scheme for missing sine and cosine terms

Table 4. Maximum output amplitude at different frequency with different carrier frequencies

Table 4. Maximum output amplitude at different frequency with different carrier frequencies