Low-Distortion Sinewave Generation Method Using Arbitrary Waveform Generator


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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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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Correspondence to Haruo Kobayashi.

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Responsible Editor: H.-M. Chang



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:

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

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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  • ADC testing
  • Arbitrary waveform generator
  • Digital pre-distortion
  • Sinusoidal signal
  • Distortion shaping