Electronic Design

# ENOB Isn’t Always The Best Figure Of Merit

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When you’re shopping for a new car, would you decide which model to buy solely on its gas mileage performance? While that may be an important factor, the number of passengers it can hold, safety features, and even the color are also key considerations. While this example may seem obvious, it is rarely the case that a single figure of merit can be used to make important decisions.

I’ve met several engineers, though, who focus on effective number of bits (ENOB) as the deciding figure of merit when selecting an analog-to-digital converter (ADC). In seminars I’ve given on data acquisition, I express my opinion that I wish engineers wouldn’t consider ENOB at all. While it is a simple figure of merit, it doesn’t tell you enough about what really matters, and it is inconsistently defined.

The Standard Approach
The IEEE-1241 standard, which defines how data converters are to be specified and tested, uses the concept of ENOB to describe an ADC’s performance. ENOB is a figure of merit that is calculated from the signal-to-noise plus distortion (SINAD, sometimes also referred to as THD+N, or total harmonic distortion plus noise) measurement done using fast Fourier transform (FFT) testing. It attempts to describe the converter’s performance in terms of an “ideal” converter. For example, you may have a 16-bit converter that has 92-dB SINAD that equates to an ideal converter of about 15 bits.

As a simple figure of merit, ENOB (or SINAD) has its place. But it doesn’t tell you what the non-idealities of the converter actually are.

Figure 1 shows an ideal 16-bit converter’s performance digitizing a sine wave. (I didn’t actually have ideal converters to generate the plots that follow. Instead, I created the data purely mathematically and then used ADCPro, Texas Instruments’ ADC evaluation tool, to analyze the data and create the graphs.) The ratio of signal power to that of noise (this excludes harmonics of the input signal) is the signal-to-noise ratio (SNR). You might recall that the ideal SNR of an N-bit data converter is given by:

SNR (dB) = 6.02N + 1.76

ENOB solves this equation for N, using the SINAD of the measured ADC:

SINAD is used instead of SNR because it includes the nonlinearities that cause distortion. The equation for an ideal converter, of course, would have no such nonlinearities. With a SINAD of 98.18 dB, the ADC of Figure 1 is indeed an ideal 16-bit converter.

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Now consider two non-ideal converters. The FFT in Figure 2 is from a converter that has ideal linearity, but is noisy. The FFT in Figure 3 is from a converter that has low noise, but is nonlinear. It deviates from ideal linearity by ±2 least significant bits (LSBs), an integral nonlinearity (INL) of ±2 LSB.

Both converters from Figures 2 and 3 have an ENOB of 13.8 bits. Neither is a particularly good 16-bit converter. But if you have to choose one converter for your application, which one is better? In the Figure 2 case, you may have a perfectly usable converter, if you are going to post-process the data by averaging or digital filtering.

The converter in Figure 3 has serious linearity problems, which could affect many measurements. If you only looked at ENOB, you may not understand the limitations of the converter and how they may impact your system or how you could potentially work around them.

Depending upon the type of converter you are looking at, the measurement and specification of ENOB may not be what you think. The method approved by the IEEE is a dynamic measurement, which requires a sine-wave input. This applies well for comparing dynamic performance for many different converter architectures.

However, manufacturers of delta-sigma converters for use in dc measurement applications have defined their own equation for ENOB, which in fact is a noise measurement. Since noise reflects the certainty with which a measurement can be made, focusing on it as a figure of merit for this class of converter certainly makes sense. However, note that this is measuring something completely different than the test described by the IEEE, so you really can’t use it to compare this class of converter with the ENOB of converters calculated using the dynamic method. So why call it ENOB?

In this case, ENOB reflects the number of bit positions in each ADC code that are numerically unaffected by RMS noise. In doing this, the full-scale range of the converter is compared to its noise and results in:

where M is the number of bits the converter has, and σ is the standard deviation, or RMS noise, of a number of conversions made from the same dc input value. With this, then, you can solve for M as the ENOB:

What’s interesting about this equation is that if σ gets sufficiently small, the log term becomes negative, which results in an ENOB that is higher than the number of bits that the converter has!

So, beware when using ENOB as a deciding factor in choosing a data converter. Make sure you know which method is being used to find the ENOB. Look beyond the ENOB number at specifications such as SNR, THD, and INL to determine if the converter will do what you require in your system. You’d consider more than one figure of merit if you were buying a car. Make sure you do the same when you’re buying a data converter.

References
1. “IEEE Standard for Terminology and Test Methods for ADCs,” IEEE Standard 1241-2000, ieeexplore.ieee.org/xpls/abs_all.jsp?tp=&isnumber=20108&arnumber=929859&punumber=7400