As the Bode plot is the foundation for understanding the operational amplifier (op amp) AC parameters, the Fourier series plot is the basis for the converter AC parameters. In both cases, the magnitude and phase-versus.-time data is being transformed into a magnitude and phase vs. frequency display.

The case for the converters is more complex because the transition between the analog domain and the digital domain must be accomplished. While the Fourier series representation of a signal is well described in the mathematical literature, it is not that well realized in standard test equipment. Therefore, it may not be as intuitive as the Bode plot.

The classical Fourier series representation of a signal in the time domain is well defined when the function can be stated in a mathematical expression. But when the function is only known as the digital output from an ADC, a Fast Fourier Transform (FFT) is necessary. This procedure was originally published as the Cooley-Tukey algorithm in 1965 and is realized in many computer programs.

The interest here is in the results. This yields the magnitude of each frequency in the signal bandwidth. From this result you can calculate several performance parameters.

A plot with typical FFT results is shown in Figure 1. This plot was copied from the data sheet of the ADS8325, a 16-bit 250 ksamples-per-second ADC. With a full scale sine wave input at 10 kHz, the FFT shows spikes at each multiple of the applied signal through 40 kHz.

Figure 1: FFT analysis of the ADS8325 output

By inspection, the spurious free dynamic range (SFDR) in this example is approximately 75 dB. The applied signal at 10 kHz is 0 dB, and the third harmonic at 30 kHz is about -75 dB. This is the highest spur, and the SFDR is the difference between these two magnitudes. Since it is not possible to determine frequency in the ADC output, any signal below -75dB must be suspected as noise and ignored.

Part three in this series, "Signal Chain Basics: Analog and the Digital World," described the quantization noise associated with a perfect converter. This calculates to a signal-to-noise ratio (SNR) of:

Since no converter will be without noise, the actual SNR is determined from the FFT as:

Any circuit will have some form of nonlinearity which will produce signals at the harmonics (integer multiples) of the applied signal.

As the harmonics continue to infinity, there must be some reasonable limit to the number of harmonics considered. There are several standards for this limit. One standard, IEEE Std.1241, recommends using harmonics up to nine. For a total harmonic distortion (THD) number to be meaningful, the number of harmonics must be given.

The last descriptive term derived from the FFT is SINAD, or signal-to-noise-and-distortion.

About the author



William P. (Bill) Klein is a Senior Applications Engineer with the High Performance Analog group at Texas Instruments. Bill joined TI through its acquisition of Burr-Brown in August 2000. His experience as an analog circuit designer covers over 40 years in fields ranging from mineral exploration to medical nuclear imaging. One current role Bill has is hosting the Analog e-LAB Web Cast, presenting real world solutions to real world problems in analog circuit design. In addition to a BSEE from Arizona State University and registration as a Professional Engineer in the State of Arizona, he has authored numerous magazine articles, application notes and conference papers.

Previous installments of this series:

• "SIGNAL CHAIN BASICS (Part 14): Analog/digital converter—static parameters", www.planetanalog.com/features/showArticle.jhtml;?articleID=207800114, click here
• "SIGNAL CHAIN BASICS (Part 13): Putting the Bode plot to use", www.planetanalog.com/features/showArticle.jhtml;?articleID=207403561, click here
• "SIGNAL CHAIN BASICS (Part 12): The Bode plot, an essential ac-parameter display tool", www.planetanalog.com/features/showArticle.jhtml;?articleID=207403561, click here
• "SIGNAL CHAIN BASICS (Part 11): Introducing voltage- and power-conditioning circuits", www.planetanalog.com/features/showArticle.jhtml;?articleID=207001505, click here
• "SIGNAL CHAIN BASICS (Part 10): Exploring the Delta-Sigma Converter", www.planetanalog.com/features/showArticle.jhtml;?articleID=206903892, click here
• "SIGNAL CHAIN BASICS (Part 9): SAR Converter Operation Explored", www.planetanalog.com/features/showArticle.jhtml;?articleID=206901015, click here
• "SIGNAL CHAIN BASICS (Part 8): Flash- and Pipeline-Converter Operation Explored", www.planetanalog.com/features/showArticle.jhtml;?articleID=206504289, click here
• "SIGNAL CHAIN BASICS (Part 7): Op Amp Performance Specification--Bias Current", www.planetanalog.com/features/showArticle.jhtml;?articleID=206101908, click here
• "SIGNAL CHAIN BASICS (Part 6): Op Amp Input Voltage Offset", www.planetanalog.com/features/showArticle.jhtml;?articleID=205901111, click here
• "SIGNAL CHAIN BASICS (Part 5): Introduction to the Instrumentation Amplifier", www.planetanalog.com/features/showArticle.jhtml;?articleID=205208593, click here
• "SIGNAL CHAIN BASICS (Part 4): Introduction to analog/digital converter (ADC) types", www.planetanalog.com/features/showArticle.jhtml;?articleID=204803631, click here
• "SIGNAL CHAIN BASICS (Part 3): Analog and the digital world", www.planetanalog.com/features/showArticle.jhtml;?articleID=204400376, click here
• "SIGNAL CHAIN BASICS (Part 2): Op Amp--Basic operations", www.planetanalog.com/features/showArticle.jhtml;?articleID=203101699, click here
• "SIGNAL CHAIN BASICS: Operational Amplifier--The Basic Building Block", www.planetanalog.com/features/showArticle.jhtml;?articleID=202801320, click here