### Abstract

The sine wave test of an analog-to-digital converter (ADC) metals to excite the ADC with a pure sine wave, look for the sine wave which best fits the output in least squares (LS) sense, and analyze the difference. This is described in the IEEE standards 1241-2000 and 1057-1994. Least squares is the "best" fitting method most of us can imagine, and it yields very good results indeed. Its known properties are achieved when the error (the deviation of the samples from the true sine wave) is random, white (the error samples are all independent), with zero mean Gaussian distribution. Then, the LS fit coincides with the maximum likelihood estimate of the parameters. However, in sine wave testing of ADCs, these assumptions are far from being true. The quantization error is partly deterministic, and the sample values are strongly interdependent. For sine waves covering less than, say, 20 quantum levels, this makes the sine wave fit worse than expected, and since small changes in the sine wave affect the residuals significantly, especially close to the peaks, ADC error analysis may become misleading. Processing of the residuals [e.g., the calculation of the effective number of bits, (ENOB)] can exhibit serious errors. This paper describes this phenomenon, analyzes its consequences, and suggests modified processing of samples and residuals to reduce the errors to negligible level.

Original language | English |
---|---|

Pages (from-to) | 1978-1983 |

Number of pages | 6 |

Journal | IEEE Transactions on Instrumentation and Measurement |

Volume | 54 |

Issue number | 5 |

DOIs | |

Publication status | Published - Oct 2005 |

### Fingerprint

### Keywords

- Analog-to-digital converter
- Analog-to-digital converter (ADC) test
- Effective number of bits (ENOB)
- Four-parameter method
- IEEE Standard 1057-1994
- IEEE Standard 1241-2000
- Least squares (LS)
- Sine wave fitting
- Three-parameter method

### ASJC Scopus subject areas

- Electrical and Electronic Engineering
- Instrumentation

### Cite this

*IEEE Transactions on Instrumentation and Measurement*,

*54*(5), 1978-1983. https://doi.org/10.1109/TIM.2005.855082

**Improved determination of the best fitting sine wave in ADC testing.** / Kollár, I.; Blair, Jerome J.

Research output: Contribution to journal › Article

*IEEE Transactions on Instrumentation and Measurement*, vol. 54, no. 5, pp. 1978-1983. https://doi.org/10.1109/TIM.2005.855082

}

TY - JOUR

T1 - Improved determination of the best fitting sine wave in ADC testing

AU - Kollár, I.

AU - Blair, Jerome J.

PY - 2005/10

Y1 - 2005/10

N2 - The sine wave test of an analog-to-digital converter (ADC) metals to excite the ADC with a pure sine wave, look for the sine wave which best fits the output in least squares (LS) sense, and analyze the difference. This is described in the IEEE standards 1241-2000 and 1057-1994. Least squares is the "best" fitting method most of us can imagine, and it yields very good results indeed. Its known properties are achieved when the error (the deviation of the samples from the true sine wave) is random, white (the error samples are all independent), with zero mean Gaussian distribution. Then, the LS fit coincides with the maximum likelihood estimate of the parameters. However, in sine wave testing of ADCs, these assumptions are far from being true. The quantization error is partly deterministic, and the sample values are strongly interdependent. For sine waves covering less than, say, 20 quantum levels, this makes the sine wave fit worse than expected, and since small changes in the sine wave affect the residuals significantly, especially close to the peaks, ADC error analysis may become misleading. Processing of the residuals [e.g., the calculation of the effective number of bits, (ENOB)] can exhibit serious errors. This paper describes this phenomenon, analyzes its consequences, and suggests modified processing of samples and residuals to reduce the errors to negligible level.

AB - The sine wave test of an analog-to-digital converter (ADC) metals to excite the ADC with a pure sine wave, look for the sine wave which best fits the output in least squares (LS) sense, and analyze the difference. This is described in the IEEE standards 1241-2000 and 1057-1994. Least squares is the "best" fitting method most of us can imagine, and it yields very good results indeed. Its known properties are achieved when the error (the deviation of the samples from the true sine wave) is random, white (the error samples are all independent), with zero mean Gaussian distribution. Then, the LS fit coincides with the maximum likelihood estimate of the parameters. However, in sine wave testing of ADCs, these assumptions are far from being true. The quantization error is partly deterministic, and the sample values are strongly interdependent. For sine waves covering less than, say, 20 quantum levels, this makes the sine wave fit worse than expected, and since small changes in the sine wave affect the residuals significantly, especially close to the peaks, ADC error analysis may become misleading. Processing of the residuals [e.g., the calculation of the effective number of bits, (ENOB)] can exhibit serious errors. This paper describes this phenomenon, analyzes its consequences, and suggests modified processing of samples and residuals to reduce the errors to negligible level.

KW - Analog-to-digital converter

KW - Analog-to-digital converter (ADC) test

KW - Effective number of bits (ENOB)

KW - Four-parameter method

KW - IEEE Standard 1057-1994

KW - IEEE Standard 1241-2000

KW - Least squares (LS)

KW - Sine wave fitting

KW - Three-parameter method

UR - http://www.scopus.com/inward/record.url?scp=27644534850&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=27644534850&partnerID=8YFLogxK

U2 - 10.1109/TIM.2005.855082

DO - 10.1109/TIM.2005.855082

M3 - Article

AN - SCOPUS:27644534850

VL - 54

SP - 1978

EP - 1983

JO - IEEE Transactions on Instrumentation and Measurement

JF - IEEE Transactions on Instrumentation and Measurement

SN - 0018-9456

IS - 5

ER -