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Low-Distortion Sinewave Generation Method Using Arbitrary Waveform Generator

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Abstract

This paper describes algorithms for generating a low-distortion single-tone signal, for testing ADCs, using an arbitrary waveform generator (AWG). The AWG consists of DSP (or waveform memory) and DAC, and the nonlinearity of the DAC generates distortion components. We propose here to use DSP algorithms to precompensate for the distortion. The DSP part of the AWG can interleave multiple signals with the same frequency but different phases at the input to the DAC, in order to precompensate for distortion caused by DAC nonlinearity. Theoretical analysis, simulation, and experimental results all demonstrate the effectiveness of this approach.

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Acknowledgments

We would like to thank T. Matsuura, N. Takai, Y. Yano, T. Gake, T. J. Yamaguchi, H. Miyashita, S. Kishigami, K. Rikino, S. Uemori and K. Wilkinson for valuable discussions.

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Authors and Affiliations

  1. Electronic Engineering Department, Gunma University, 1-5-1 Tenjin-cho, Kiryu Gunma, 376-8515, Japan

    Kazuyuki Wakabayashi, Keisuke Kato, Takafumi Yamada, Haruo Kobayashi, Fumitaka Abe & Kiichi Niitsu

  2. Semiconductor Technology Academic Research Center (STARC), Yokohama, 222-0033, Japan

    Osamu Kobayashi

Authors
  1. Kazuyuki Wakabayashi
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  2. Keisuke Kato
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  3. Takafumi Yamada
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  4. Osamu Kobayashi
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  5. Haruo Kobayashi
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  6. Fumitaka Abe
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  7. Kiichi Niitsu
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Corresponding author

Correspondence to Haruo Kobayashi.

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Responsible Editor: H.-M. Chang

Appendix

Appendix

This appendix describes the explicit power spectrum of the DAC output Y(nT s ) for the simultaneous cancellation algorithm of HD3 and HD2 in Section 4.1. Equation 14 can be written as follows:

$$\begin{array}{rll} D_{in}(n) &=& \frac{1}{4}\left[(1 + W^n + W^{2n} + W^{3n})X_0(n)\right. \\ &&{\kern12pt} +(1 + W^{n-1} + W^{2(n-1)} + W^{3(n-1)})X_1(n) \\[6pt] &&{\kern12pt} +(1 + W^{n-2} + W^{2(n-2)} + W^{3(n-2)})X_2(n) \\[6pt] &&{\kern12pt} +\left.(1 + W^{n-3} + W^{2(n-3)} + W^{3(n-3)})X_3(n)\right].\\ \end{array} $$
(21)

Here \(W = \exp (j \pi/2)\). Then explicit Y(nT s ) can be obtained from Eqs. 16, 17 and 21 as follows:

$$\begin{array}{rll} Y(nT_s)&=& \frac{1}{2}cA^2+\frac{\sqrt{\mathstrut 6}}{4}\left(aA + \frac{3}{4}bA^3\right)\sin (2 \pi f_{in} n T_s) \\[6pt] &&- \frac{\sqrt{\mathstrut 6}+\sqrt{\mathstrut 2}}{8}\left(aA + \frac{3}{4}bA^3\right) \\[6pt] &&\times\left[\sin \left(2 \pi \left(\frac{1}{4}f_s+f_{in}\right)nT_s\right)\right.\\[6pt] &&{\kern15pt} +\left. \cos \left(2 \pi \left(\frac{1}{4}f_s+f_{in}\right)nT_s\right)\right] \\[6pt] &&- \frac{\sqrt{\mathstrut 6}-\sqrt{\mathstrut 2}}{8}\left(aA+\frac{3}{4}bA^3\right) \\[6pt] &&\times\left[\sin \left(2 \pi \left(\frac{1}{4}f_s-f_{in}\right)nT_s\right)\right. \\[6pt] &&\left.\cos \left(\pi \left(\frac{1}{4}f_sf_{in}\right)nT_{s}\right)\right] \frac{1\sqrt{\mathstrut 3}}{8}cA^2 \end{array}$$
$$\begin{array}{rll} \phantom{Y(nT_s),.}&&\times\left[\sin \left(2\pi \left(\frac{1}{4}f_s+2f_{in}\right)nT_s\right)\right. \\ &&\left. \cos \left(\pi \left(\frac{1}{4}f_sf_{in}\right)nT_{s}\right)\right] \frac{1\sqrt{\mathstrut 3}}{8}cA^2 \\ &&\times\left[\sin \left(2\pi \left(\frac{1}{4}f_s-2f_{in}\right)nT_s\right)\right. \\ &&\left. \cos \left(2\pi \left(\frac{1}{4}f_s-2f_{in}\right)nT_s\right) \right] \frac{\sqrt{\mathstrut 2}}{16}bA^3\\ &&\times\left[\sin \left(2\pi \left(\frac{1}{4}f_s+3f_{in}\right)n T_s\right)\right. \\ &&\left. \cos \left(2\pi \left(\frac{1}{4}f_s+3f_{in}\right)nT_s\right) \right] \frac{\sqrt{\mathstrut 2}}{16}bA^3\\ &&\times\left[\sin \left(2\pi \left(\frac{1}{4}f_s-3f_{in}\right)n T_s\right)\right. \\ &&\left. \cos \left(2\pi \left(\frac{1}{4}f_s-3f_{in}\right)nT_s\right)\right] \\ &&-\, \frac{\sqrt{\mathstrut 2}}{4} \left(aA\frac{3}{4}bA^3\right)\cos \left(\pi \left(\frac{1}{2}f_sf_{in}\right)nT_s \right) \\ &&-\, \frac{\sqrt{\mathstrut 2}}{8}bA^3 \cos \left(2\pi \left(\frac{1}{2}f_s-3f_{in}\right)nT_s\right). \end{array}$$

We see that 2 f in, 3 f in components are cancelled in Y(nT s ).

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Wakabayashi, K., Kato, K., Yamada, T. et al. Low-Distortion Sinewave Generation Method Using Arbitrary Waveform Generator. J Electron Test 28, 641–651 (2012). https://doi.org/10.1007/s10836-012-5293-4

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