Application Note 728: 2001 Defining Testing Dynamic Parameters Hi

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Application Note 728: 2001 Defining Testing Dynamic Parameters Hi

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CONVERSION/SAMPLING CIRCUITS HIGH-SPEED SIGNAL PROCESSING
Application Note 728: 2001
Defining Testing Dynamic Parameters High-Speed ADCs, Part first part this article series discusses commonly known definitions most crucial high-speed data converters this case analog-to-digital converter short ADCs) used communications, instrumentation data acquisition applications. purpose this article help reader gain better understanding common parameters such signal-to-noise ratio (SNR), signal-to-noise-and-distortion (SINAD), total harmonic distortion (THD) spurious-free dynamic range (SFDR). second part this article series (see "Dynamic Testing High-Speed ADCs" further reading), these parameter definitions test measuring them real-world test scenarios.
Additional Information: Dynamic Testing High-Speed ADCs, Part Dynamic specifications ADCs very important high-speed applications such digital communications, ultrasound imaging, instrumentation, digitization. following discussion provides definition mathematical foundation each parameter, offers useful techniques evaluating dynamic performance high-speed ADCs, explains dynamic parameters correlate with performance. Part this two-part discussion covers definition these specifications:
Signal-to-noise ratio (SNR) Signal-to-noise distortion ratio (SINAD) Effective number bits (ENOB) Total harmonic distortion (THD) Spurious-free dynamic range (SFDR) Two-tone intermodulation distortion (TTIMD) Multi-tone intermodulation distortion (MTIMD) Voltage standing-wave ratio (VSWR)
explaining measure these parameters, Part provides insight into practical aspects dynamic performance testing. Note that some specifications allow more than approach measurement even definition. Thus, test techniques Part represent method mandatory. methods described extended altered necessary suit application hand.
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When testing high-speed converters, emulates operation spectrum analyzer used quantify linearity analog circuits. this instrument test procedure, dynamic specifications usually expressed frequency domain, using Fast Fourier Transform (FFT). both cases, data output represents magnitude this FFT. example (Figure consider plot 80Msps, 10-bit designed optimized ultrasound imaging digitization baseband/IF frequencies. Such plots contain impressive amounts information generated quickly. However, make FFT, must understand parameters defined.
Figure 8192-point plot MAX1448.
Signal-to-Noise Ratio (SNR) waveform perfectly reconstructed from digital samples, ratio (root mean square) full-scale analog input quantization error (AQUANTIZATION[rms] ALSB/ AREF/[2N value sine wave half peak-to-peak value divided quantization error difference between analog waveform digitally reconstructed replica, which characterized staircase-shaped transfer curve. difference function resembles sawtooth wave that oscillates once sample between levels +1/2LSB -1/2LSB (LSB being least-significant bit). difference function's value peak value (1/2LSB) divided ideal N-bit converter, defined
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Most dynamic specifications expressed ratio relative measurements rather than absolute units. Thus, signal-to-noise ratio ideal ADC, driven full-scale sinusoidal input with power equal AREF/(2 decibels,
diminished many noise sources addition quantization noise (See Appendix data converter's resolution quantization level both help establish noise floor. actual sinusoidal input signal therefore described where ASIGNAL[rms] represents amplitude analog input signal, ATOTAL_NOISE[rms] noise sources (thermal noise, quantization noise, etc.) that limit converter's dynamic performance. Applying this definition 10-bit such MAX1448 yields typical value 58.4dB 40MHz Nyquist frequency (fSAMPLE 80Msps). This represents ~62dB exhibited ideal 10-bit ADC. driven sinusoidal input with amplitude equal ADC's full-scale input, maximum theoretical where fMAX describes maximum bandwidth input tone, fSAMPLE converter's sampling frequency. From this equation, note that increases sampling frequency increases beyond Nyquist rate fMAX). Called processing gain, this effect caused spreading quantization noise power (which fixed independent bandwidth) sampling frequency increases. This "oversampling" helps minimize effect noise, which falls into Nyquist bandwidth fMAX. Signal-to-Noise Distortion Ratio (SINAD) sinusoidal input signals, SINAD defined ratio signal noise (including first harmonics THD: usually through 5th-order harmonics). given sampling rate input frequency, SINAD provides ratio analog input signal noise plus distortion. SINAD describes quality ADC's dynamic range, expressed ratio maximum amplitude output signal smallest increment output signal that converter produce. Mathematically, SINAD described
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where ASIGNAL[rms] depicts output signal level ANOISE+HD[rms] describes spectral components below Nyquist frequency, excluding quality SINAD also depends amplitude frequency sinusoidal input tone. Effective Number Bits (ENOB) actual (versus ideal) ADCs, specification often used place SINAD ENOB, which global indication accuracy specific input frequency sampling rate. calculated from converter's digital data record log2 ratio measured ideal error: where number digitized bits, AMEASURED_ERROR[rms] averaged noise, AIDEAL_ERROR[rms] quantization noise error, expressed AFS/[2N converter's full-scale input range determined reference voltage AREF.
ENOB generally depends amplitude frequency applied sinusoidal input tone, both must specified this particular test. This method compares noise produced under test quantization noise ideal with same resolution bits. actual 10-bit with sine-wave input given frequency amplitude ENOB bits, then produces same noise level that input would ideal 9-bit ADC.
Directly related SINAD, ENOB frequently expressed error ideal consists solely noise. actual converters, however, measured error includes quantization noise along with aberrations such missing output codes, AC/DC nonlinearity, aperture uncertainty (jitter). Noise reference powersupply lines also degrades ENOB. Total Harmonic Distortion (THD) Dynamic errors integral nonlinearities contribute harmonic distortion whenever samples periodic signal. pure sine-wave inputs, output harmonic-distortion components found spectral values whose nonaliased frequencies integer multiples
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applied sinusoidal input tone. amplitudes nonaliased frequencies, which depend amplitude frequency applied input sine wave, generally given dBratio with respect amplitude applied sine-wave input. Their frequencies usually expressed multiple frequency applied sinusoidal input signal. harmonics output signal's Fast Fourier Transform (FFT) spectrum. harmonics included definition, first three most cases) represent major contribution output distortion given converter. communications RF/IF applications, often more important figure merit ADCs than DCnonlinearity specifications that describe converter's static performance. given where A[fIN]rms fundamental amplitude, AHD_2[rms] through AHD_N[rms] represent amplitudes Nth-order harmonics. choice harmonic components included usually trade-off between desire include harmonics with significant portion harmonic-distortion energy, exclusion Discrete Fourier Transform (DFT) frequency bins, whose energy content mainly dominated random noise (see Appendix Unless otherwise specified (refer manufacturer's specification data sheet), normally consists lowest four nine harmonics (2nd through 10th harmonics, inclusive) sinusoidal analog input tone. Note that manufacturers specify their values either decibels (dB) decibels with reference carrier frequency fundamental (dBc). Both units common use, defined with respect analog input tone. Spurious-Free Dynamic Range (SFDR) term spurious-free dynamic range usually applied cases which harmonic distortion spurious signals regarded undesirable spurs output spectrum sampled pure-sinusoidal input tone. SFDR indicates usable dynamic range ADC, beyond which spectral analysis poses special detection thresholding problems. Though similar THD, SFDR addresses converter's in-band harmonic characteristics. Spurious-free dynamic range ratio amplitude fundamental (the maximum signal component) value largest distortion component specified frequency range. well-designed systems, this spur should harmonic fundamental. SFDR important because noise harmonics restrict data converter's dynamic range. bandpass converter, example, spurs interpreted adjacent channel information. other applications, signals interest such low-level radar signals cannot distinguished from harmonic content. help determine SFDR value, spectrum analyzer with integrated digital-to-analog converter (DAC) reconstruction recommended. usual procedure apply near full-scale input signal (the preferred input-tone amplitude -0.5dB -1dB FS), measure response, then acquire measure amplitude largest spurious component. SFDR ratio first second measurement. SFDR also determined inspecting spectrum (plot) under test.
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spectrally pure sine-wave inputs, SFDR ratio amplitude averaged value fundamental frequency (A[fIN]) amplitude averaged value largest-amplitude harmonic (AHD_MAX[rms]) spurious signal component (ASPUR_MAX[rms]) observed over entire Nyquist band.
general, SFDR function amplitude frequency (A[fIN], fIN) analog input tone and, some cases, even sampling frequency (fSAMPLE) converter under test. Therefore, when testing spurious-free dynamic range, should specify sampling frequency well input frequency amplitude. Two-Tone Intermodulation Distortion (Two-Tone IMD) generally caused modulation, occur when samples signal composed multiple) sine-wave signals. spectral components occur both (fIMF_SUM) difference (fIMF_DIFF) frequencies possible integer multiples fundamental (input frequency tone) signal-group frequencies. two-tone test, input test frequencies fIN1 fIN2 (fIN2 fIN1) values that numbers bins away from Nyquist frequencies (fSAMPLE/2). These settings guarantee that difference between input tones always even number bins. resulting spectrum (Figure averaged amplitude spectrum A[fIMF]rms. amplitudes two-tone input signal found specified difference frequencies:
where positive integers. condition that greater than zero creates 2nd-order (fIN1+fIN2 fIN1-fIN2) 3rd-order (2fIN1+fIN2, 2fIN1-fIN2, fIN1+2fIN2, fIN12fIN2, 3fIN1 3fIN2) intermodulation products. Because test parameters generally application-specific, particular guidelines necessary available) specify frequencies signal amplitudes used intermodulation tests. size |fIN2-fIN1| depends entirely application information desired. Note that small differences input tones cause intermodulation frequencies clustered around harmonic distortion components fIN1 fIN2. Two-tone intermodulation distortion generally function amplitudes (A[fIN1]rms A[fIN2]rms) frequencies (fIN1 fIN2) input components. must therefore specify input tones amplitudes which two-tone measurements performed. essential that input test signal virtually free intermodulation harmonic
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distortion. ADCs larger dynamic range wider bandwidth, this condition increasingly difficult achieve.
Figure This plot illustrates two-tone spectrum with 2nd- 3rd-order products.
signal generators, containing output-leveling circuitry linked balanced isolated outputs other coupling circuits, easily generate effects. Therefore, avoid intermodulation distortion test signal, should operate power splitters/combiners (used combine split input tones) well within their linear range. Figure depicts two-tone with 2nd- 3rd-order products 10-bit, 80Msps ADC. best results, two-tone envelope this chosen -0.5dB amplitude input tones normalized -6.5dB
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Figure Two-tone intermodulation distortion MAX1448, with fSAMPLE 82.345MHz.
Multi-Tone Intermodulation Distortion (Multi-Tone IMD) Multi-tone intermodulation distortion tests often used system design determine limits signal dynamic range, useful frequency bands different signal groups, where input signal's noise floor mask small intermodulation components given ADC. measurement single-tone harmonic distortion useful obtaining general ideas about linearity given ADC, such data does lead directly models predicting useful measures intermodulation performance independent input-signal tones. typical test procedure features computer-controlled that generates signal composed sine waves binary center frequencies. tone amplitudes increased uniformly, beginning noise floor continuing full-scale level which clipping begins, gaps between tones serve observation points analyze resulting IMD. Such tests provide results similar that noise-power ratio (NPR) test (see Appendix They allow better simulation expected signal-group waveforms, however. Voltage Standing-Wave Ratio (VSWR) Seldom specified data sheets high-speed data converters, VSWR ratio mismatch between actual impedance desired expected impedance. calculated applying test signal measuring reflection coefficient input
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terminal. Calculated follows, VSWR directly related reflection coefficient simple terminating impedance where depicts input termination impedance, represents transmission line impedance (nominally compensate circuit inaccuracies measurement, recommended calibration standards available (typically short, open, Conclusion preceding discussion been review most important dynamic specifications high-speed data converters. will conclude Part which offers detailed insight into tools most suitable capturing data records using those records testing dynamic performance parameters defined above. addition test setup information, Part provides samples MATLAB© LabWindows/CVI© source code, enabling designers analyze dynamic performance capturing data records quickly processing them efficiently. MATLAB registered trademark Mathworks Inc. LabWindows/CVI registered trademark National Instruments Inc. Appendices Appendix term "noise" rather ambiguous qualified type. general, includes effects nonlinearities (INL, DNL), random fixed-pattern effects, sampling-time error. Total noise (ATOTAL_NOISE[rms]) deviation output signal (converted input units) from input signal, excluding deviations caused differential gain phase errors, DC-level shifts. Notable examples such effects, defined here noise, include quantization error, harmonic intermodulation distortion, spurious distortion. Appendix Testing high-speed ADCs their dynamic performance often requires frequency transform captured data record, using Discrete Fourier Transform (DFT) Fast Fourier Transform (FFT) analysis. produces same results DFT, minimizes computation requirements taking advantage computational symmetries redundancies within analysis. speeding computation, this approach enables spectral analysis virtual real time. Provided that periodic input signal sampled frequently enough (i.e., fMAX, where fMAX maximum bandwidth sinusoidal-input test tone, bandwidth data converter tested), equation pair defined
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acquired data record usually contains sinusoidal input signals, harmonics, intermodulation products, other spurious signals that must analyzed properly characterize ADC. Assuming that input signals periodic, data record containing integral number cycles sinusoidal input signals will contain spectral components frequencies other than those corresponding chosen input tones. Also known spectral leakage, these components should avoided because they mask spurious performance itself. precise characterization, spectral leakage must kept minimum choosing proper input tones (with respect fSAMPLE) low-noise high-precision signal sources. avoid spectral leakage completely, method coherent sampling recommended. Coherent sampling requires that input- clock-frequency generators phase-locked that choose input frequency based this relationship: fIN/fSAMPLE NWINDOW/NRECORD, where desired input frequency, fSAMPLE clock frequency data converter under test, NWINDOW number cycles data window make samples unique, choose prime numbers), NRECORD data record length (for 8192-point FFT, data record contains 8192 points). Because ratio fSAMPLE integer value, signal clock sources must have adequate frequency tuning resolution prevent spectral leakage. Appendix Noise-power ratio (NPR) figure merit that defines spectral power contributed errors, such THD, small frequency band within baseband composite input signal being processed analyzed. this test, generates random noise whose spectrum approximately uniform predetermined cutoff frequency less than half sampling frequency. Then, notch filter removes narrow band frequencies from noise. improve measurement, notch depth recommended least 10dB 15dB greater than value being measured. Compared overall noise bandwidth, notch width should narrow. With this notched noise applied input, computes frequency spectrum resulting code sequence then calculates ratio average power spectral density inside notched frequency band that outside notched band.
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Literature Sources Low-Voltage/Low-Power Integrated Circuits Systems-Low-Voltage Mixed-Signal Circuits, Sanchez-Sinencio Andreou, IEEE Press Marketing, 1999. MAX1448 data sheet Rev. 7/00, Maxim Integrated Products. MAX1448EVKIT data sheet Rev. 7/00, Maxim Integrated Products. Analog Integrated Circuit Design, Johns Martin, John Wiley Sons Inc., 1997. Integrated Analog-to-Digital Digital-to-Analog Converters, Plasche, Kluwer Academic Publishers, 1994. Analog-Digital Conversion Handbook, Engineering Staff Analog Devices Inc., Prentice Hall Publishers, 1986. similar version this article appeared November 2000 issue Microwaves
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Application Note 728: 2001 Defining Testing Dynamic Parameters Hi

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