High-Frequency Low-Distortion Signal Generation Algorithm with AWG

Transcription

1 High-Frequency Low-Distortion Signal Generation Algorithm with AWG Shohei Shibuya, Yutaro Kobayashi Haruo Kobayashi Gunma University 1/31

2 Research Objective 2/31 Objective Low-distortion sine wave generation for ADC test Our Approach DSP algorithm using AWG AWG : Arbitrary Waveform Generator

3 OUTLINE 3/31 Research background Phase-switching algorithm Proposed solution Theoretical analysis Conclusion

4 OUTLINE 4/31 Research background Phase-switching algorithm Proposed solution Theoretical analysis Conclusion

5 Research background 5/31 Semiconductor industry Silicon cost decreasing Test cost increasing Silicon cost Test cost Low cost test Low cost LSI production

6 Arbitrary Waveform Generator 6/31 AWG : Arbitrary Waveform Generator AWG DSP Digital wave DAC analog output Ideal AWG output spectrum fundamental Real AWG output spectrum (DAC has 3 rd nonlinearity ) fundamental HD3 fin fin 3fin DAC nonlinearity Harmonic distortion of AWG

7 ADC Test Cost Using AWG 7/31 AWG AWG : Expensive Long testing time Mass production Test cost high Low cost test Low cost AWG Test performance

8 Conventional ADC Test 8/31 Test signal AWG Z = b 1 Y + b 3 Y 3 ADC ADC output spectrum conventional HD3 3 Y = a 1 D in + a 3 D in AWG: Arbitrary Waveform Generator fin 3fin Freq. AWG HD3+ADC HD3 Inexpensive AWG output includes HD3 HD3 : 3 rd order Harmonic Distortion Conventional ADC nonlinearity test Over estimate of HD3

9 Low-Cost, Accurate Test of ADC with AWG 9/31 Conventional method Proposed method fundamental HD3 fundamental HD3 fin 3fin Freq. AWG HD3+ADC HD3 fin 3fin Only ADC HD3 Freq. Accurate ADC linearity test with inexpensive AWG Only DSP program change No hardware change No requirement for AWG nonlinearity identification

10 OUTLINE 10/31 Research background Phase-switching algorithm Proposed solution Theoretical Analysis Conclusion

11 Low Distortion Sine Wave Generation 11/31 Phase switching signal algorithm Our previous proposal Interleave sampling X 0, X 1 every one clock AWG φ = φ 0 φ 1 DSP Din DAC CLK X 0 Din X0 X1 X0 X1 X 1 X 0 = A cos 2πf in nt s + φ 0 n: even X 1 = A cos 2πf in nt s + φ 1 n: odd φ = φ 0 φ 1 = π/n HDN is cancelled.

12 Power[dB] Power[dB] Simulation Result of Phase Switching Signal 12/31 DSP D in DAC 3 Y = a 1 D in + a 3 D in Y (AWG output) 0 fin 0 fin fin fin distortion shaping Normalized frequency f/fs Normalized frequency f/fs

13 Phase Switching Conventional 3 rd order non-linear system Phase rotation by x3 Principle of 3rd Harmonics Cancellation 13/31 fundamental: fin 3 rd harmonics: 3 fin Θ = π/3 3Θ = π Two waves with phase difference π are cancelled

14 OUTLINE 14/31 Research background Phase-switching algorithm Proposed solution Theoretical Analysis Conclusion

15 Problem of Phase Switching Algorithm 15/31 Distortion shaping cancels HD3, but spurious around fs/2 appears. Phase switching signal is applicable only for low frequency signal generation. distortion shaping We propose phase switching method for high frequency

16 Proposed Solution 16/31 High frequency low distortion signal generation Interleave sampling X 0, X 1 every one clock AWG φ = φ 0 φ 1 DSP Din DAC CLK X 0 Din X0 X1 X0 X1 X 1 X 0 = A cos 2πf in nt s + φ 0 n: even X 1 = A cos 2πf in nt s + φ 1 n: odd φ = φ 0 φ 1 = 2π/N N-th order image is cancelled

17 Unified Principle of Low-Distortion Signal Generation 17/31 3 rd order nonlinearity φ Two sinusoidal signals (frequency : fin) 3φ Two 3 rd order harmonics (frequency : 3fin) Interleave sampling every one clock (Sampling frequency : fs) Image signal : fs/2-fin 3 rd order image signal : fs/2-3fin

18 HD3 Component Cancellation 18/31 Two 3 rd order harmonics 3φ Reverse phase Same phase 3φ = π,3π, Cancelled HD3 3φ = 2π,4π, Cancelled fs/2-3fin

19 AWG Output with Conventional Method 19/31 DSP D in DAC Y = a 1 D in + a 3 D in 3 Y (AWG output) D in = sin 2πf in_conv nt s HD3 component (3fin) is folded back as aliasing

20 Simulation Result of Proposed Method 20/31 DSP D in DAC Y = a 1 D in + a 3 D in 3 Y ( AWG output) X 0 = A cos 2πf in nt s + π/3 n: even X 1 = A cos 2πf in nt s π/3 n: odd 3f out component is cancelled

21 Low-Distortion High-Frequency Signal 21/31 fin fs/2-fin =fout f in, 3f in components reduction by HPF Low distortion sinusoidal signal f out = f s 2 f in 3fin Attenuated HPF fs/2-3fin = 3fout

22 ADC Output with HPF 22/31 No attenuation of fin component Attenuation of fin component with HPF ADC HD3 appears If fin component is NOT reduced If fin component is reduced by HPF ADC HD3 component is cancelled (ADC 3 rd distortion cannot be measured) Accurate ADC HD3 measurement

23 OUTLINE 23/31 Research background Phase-switching algorithm Proposed solution Theoretical Analysis Conclusion

24 Model for Theoretical Analysis 24/31 AWG Y(n) Z(n) DSP DAC HPF ADC D in Y = a 1 D in + a 3 D in 3 Z = b 1 Y + b 3 Y 3 AWG Input with Phase Switching D in nt s = A sin 2πf in nt s π 3 A sin 2πf in nt s + π 3 n: odd n: even AWG Nonlinearity Model Y nts = a 1 D in n + a 3 D in n 3 ADC Nonlinearity Model For Simplicity f s(awg) = f s(adc) Z n = b 1 Y nt s + b 3 Y nt s 3

25 AWG Output Theoretical Analysis 25/31 AWG Y(n) Z(n) DSP D in DAC Y = a 1 D in + a 3 D in 3 HPF Spurious Cut by α,β ADC Z = b 1 Y + b 3 Y 3 Y = a 1 D in + a 3 D in = α 1 2 a 1A a 3A 3 sin 2πf in nt s filter 0 α, β 1 f in : input frecuency f s sampling frecuency β 1 4 a 3A 3 sin 2π 3f in nt s a 1A a 3A 3 cos 2π f s 2 f in nt s Proposed method uses this component

26 ADC Output Without HPF 26/31 ADC output Z nt s = b 1 Y + b 3 Y 3 = {b 1 R b 3R(R 2 + 2αβPQ + 2β 2 Q)} cos(2π f s 2 f in nt s ) b 3R R 2 3α 2 P 2 cos 2π f s 2 3f in nt s b 3R R 2 3α 2 P 2 = b 3A 2 a 1 A a 3A 3 α 2 1 Coefficient of cos 2π f s 2 3f in nt s

27 Coefficient of HD3 27/31 AWG Y(n) Z(n) DSP DAC HPF ADC D in Y = a 1 D in + a 3 D in 3 Z = b 1 Y + b 3 Y 3 Coefficient of ADC HD3 = b 3A 2 a 1 A a 3A 3 α 2 1 When filter α = 1, ADC HD3 Cancelled When filter α 1, Accurate measurement of ADC HD3

28 Attenuation Effect of HPF 28/ Attenuation by a factor of 1/10 with HPF is easy

29 OUTLINE 29/31 Reserch background Phase-switching algorithm Proposed solution Theoretical Analysis Conclusion

30 Conclusion 30/31 We have proposed high-frequency low-distortion signal generation algorithm with AWG. Needs only a simple analog HPF. No need for AWG nonlinearity identification Simulation shows that measurement error of ADC HD3 is as low as 1.7%.

31 Thank you for your kind attention! Accurate measurement has been very important from thousands years ago. 度量衡統一 by 始皇帝

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