Selecting the Optimum Test Ton

Abstract: An earlier applicaTIon note, "Coherent Sampling vs. Window Sampling," covered the basics of coherent sampling. It showed differences between tests performed with coherent sampling and windowed sampling condiTIons. The following technical discussion is a follow-up note, which deals with the proper selecTIon of test tones and instruments to successfully test and evaluate a high-speed ADC's AC performance.

ALSO SEE:

• ApplicaTIon Note: Coherent Sampling Calculator (CSC)
• Coherent Sampling Calculator (XLS, 81K)

As discussed in the earlier Application Note 1040: Coherent Sampling vs. Window Sampling, a variety of approaches may be used to evaluate dynamic performance parameters, such as signal-to-noise ratio (SNR), signal-to-noise and distortion (SINAD), total harmonic distortion (THD), intermodulation distortion (IMD) and spurious-free dynamic range (SFDR) of high speed data converters. However, the concept of coherent sampling, a frequency-based sinewave test, yields more accurate and repeatable test results than using a windowing method.

In sinewave-testing a high-speed analog-to-digital converter (ADC), it is not only imperative to sample the applied waveform continuously to avoid unwanted artifacts in the FFT spectrum, but to precisely select the sampling frequency (fSAMPLE), the input test tone (fIN), and the size of the data record (NRECORD). For any given clock frequency there exist certain input test tones, which can hide ADC errors, while other frequencies reveal ADC errors. These frequencies can vary by only a fraction of a percent and yield vastly different results. The optimum input test tone is one for, which there are NRECORD distinct phases sampled, which are uniformly distributed between 0 and 2π radians. Taking this knowledge into account, coherent sampling can be described as the sampling of a periodic signal, where an integer number of its cycles fit into a predefined sampling window. Mathematically, this is expressed by

fIN = (NWINDOW / NRECORD) × fSAMPLE,

where fIN is a continuous sinusoidal input signal, fSAMPLE is the ADC's clock/sample frequency, NWINDOW represents an integer number of cycles within the sampling window, and NRECORD is the number of data points targeted for the sampling window or FFT.

Additionally it is important to choose NRECORD large enough to produce at least one representative sample of every frequency bin² of the converter. Given that the input tone is chosen as previously discussed, an ideal converter's transfer curve (excluding random noise) requires the minimum value for NRECORD to be π2N, where N is the resolution of the data converter under test.

There are two common ways to calculate the desired input tone. Following are examples of these two methods based on coherent sampling. Assuming that an ADC, such as the MAX1190, is driven with a 120MHz clock, and a near optimum input frequency of 17MHz is to be analyzed with an 8192-point FFT record, the following two steps provide guidance in selecting the appropriate input test tone.

1. Start with fIN = 17MHz and fSAMPLE = 120MHz to determine the window size NWINDOW (remember that according to the previous discussion, NWINDOW has to be an integer odd or mutually prime number) for an 8192-point data record NRECORD.
   
   NWINDOW = int (fIN / fSAMPLE) × NRECORD
   NWINDOW = int (17MHz / 120MHz) × 8192 = 1160
2. Based on the above result for NWINDOW, the next closest mutually prime (odd) number is 1163 (1161). Use either of these numbers to compute the final, near-optimum input test tone as follows
   
   fIN = fSAMPLE × (NWINDOW / NRECORD)
   fIN(MUTUALLY_PRIME) = 120MHz × (1163 / 8192) = 17.0361328MHz
   fIN(ODD) = 120MHz × (1161 / 8192) = 17.0068359MHz

Unfortunately, this very method will require a high-resolution signal synthesizer capable of supporting all the digits necessary to get an accurate reading on the input frequency. A different approach, which offsets the clock frequency from its exact value of 120MHz, yet still, obeying the rules for coherent sampling, can overcome such stringent demand. The next five steps show that the need for a high-resolution instrument is relaxed by 'distributing' the number of required digits between input and sampling frequency.

1. Determine the resolution of the sampling frequency that fits into an 8192-point record by
   
   Δf = fSAMPLE / NRECORD
   Δf = 120MHz / 8192 = 14.6484375kHz
   
   
2. Some of commonly available signal generators in the market may not offer enough resolution to offer this many digits to accurately capture both input and sampling frequency. To bypass this requirement and still meet the coherent sampling condition, it is recommended to select Δf based on the next highest integer number.
   
   Δf = int (fSAMPLE / NRECORD) = 15kHz
   
   
3. Based on the new Δf, the exact sampling frequency computes to
   
   fSAMPLE = Δf × NRECORD
   fSAMPLE = 15kHz × 8192 = 122.880MHz
   
   
4. Δf also helps to determine the size of NWINDOW. Again, use the next highest integer odd (or mutually prime) number, determined by the desired input test tone and Δf.
   
   NWINDOW = int (fIN / Δf)
   NWINDOW = 17MHz / 15kHz = 1133
   
   
5. Based on these findings, the near optimum input test tone fIN calculates as follows
   
   fIN = fSAMPLE × (NWINDOW / NRECORD)
   fIN = 122.88MHz (1133 / 8192) = 16.995MHz

Equipment and Set-Up Recommendations for a Successful High-Speed ADC TestTable 1 lists some recommended hardware instruments and software products, which have proven to be quite valuable for data capture and analysis of high-speed ADC dynamic performance parameters.

Table 1. Equipment and software tool recommendations for high-speed ADC testing
Type Of Equipment