In this series:

- From Analog to Digital – Part 1: Introduction
- From Analog to Digital – Part 2: The Conversion Process
- From Analog to Digital – Part 3: Signal Sampling
- From Analog to Digital – Part 4a: Signal Bandwidth
- From Analog to Digital – Part 4b: Signal Bandwidth
- From Analog to Digital – Part 5: Signal Conditioning
- From Analog to Digital – Part 6a: ADC Performance
- From Analog to Digital – Part 6c: ADC Performance
- From Analog to Digital – Part 7: Precautions
- From Analog to Digital – Conclusion

In the first part of this blog on ADC performance, we discussed how the quantization error of an ADC resulted in a broadband noise component superimposed over an ideally digitized signal. We also examined how that noise component could be characterized in relation to its signal in terms of a signal-to-noise ratio (SNR) figure and how it would appear when displayed in the frequency domain. In the second part of this blog, we will examine additional performance deviations of ADCs and how they are measured, characterized, and displayed in the frequency domain.

## Harmonic Distortion

We've previously seen that systematic quantization errors generated by the quantizer of an ADC results in a broadband noise component that appears as a constant "noise floor" in the frequency domain representation of the digitized signal. This broadband spreading in the frequency domain is due to the fact that the quantizer error is completely uncorrelated to the input signal and will happen regardless of the amplitude, frequency, or shape of the signal.

We've also seen that another source of quantization error is caused by the uneven distribution of lines in the ADC's quantization grid. Contrary to the rapid error generated by discrete jumps to the nearest sampling value of the quantizer (which caused the broadband noise component of the ADC), the uneven distribution of the quantization grid lines creates errors that vary much more slowly and are correlated to the input signal.

This can easily be illustrated by the quantization grid shown the figure below. The straight blue line represents the ideal conversion mapping between the input signal and the quantized output. The purple line represents the nonlinear conversion mapping (grossly exaggerated) caused by the uneven distribution of the quantizer's horizontal grid lines.

Submitting the sine wave signal (blue) to the input of the quantizer results in the distorted wave (purple) at its output (both digitized output and corresponding continuous analog value). The distortion created by the quantizer will be systematic and will track the incoming waveform, regardless of its frequency.

Because the distortion is correlated to the signal and will repeat from cycle to cycle for a periodic signal, it creates what is known as harmonic distortion. When we analyze the digitized signal in the frequency domain, we observe that the distortion causes frequency components that are multiples of the signal's fundamental frequency. The fundamental frequency component (F) represents the sine wave signal at the input of the quantizer and the harmonic components (H1 to HN) are the distortion components created by the quantizer, located in frequencies that are multiples of F.

As mentioned earlier, the harmonic distortion created by the quantizer will track the incoming waveform, regardless of its frequency. This means that the distortion components will be susceptible to aliasing, like any other digitized signal. As shown in the following figure, the higher frequency harmonic components located in the second (and upper) Nyquist zone(s) will be folded back to the first Nyquist zone, where they will appear as non-harmonic components because they are no longer located at frequencies that are multiples of F.

The nonlinear mapping of the quantizer's conversion grid is not the only source of an ADC's harmonic distortion. In part 2 of this series, we mentioned that the ADC process is implemented in two steps: the use of a sample-and-hold (S/H) unit followed by quantization. Like the quantizer, the S/H is not an ideal component and it can generate a form of distortion that is very similar to the one produced by the non-linearities of the quantizer.

The S/H is used to sample and freeze the analog signal for the duration of the quantization process, but executing it properly can be very demanding. In order to properly sample a signal, the S/H must move from the previously frozen value to the next sampled value extremely rapidly and accurately. This can be very difficult to do, especially for signals with very large and rapid amplitude variations. In the event that the S/H is incapable of properly tracking such incoming signals, it will create non-linearities at its output that will be correlated to the signal (repetitive from cycle to cycle). It will also create harmonic distortion similar to the one previously described. This type of distortion will typically increase when a signal has strong high frequency components.

## Total Harmonic Distortion (THD) of an ADC

The measure of an ADC's total harmonic distortion (THD), regardless of whether the harmonics of the signal are aliased or not, is one of the main characteristics provided by ADC manufacturers. It is determined by computing the ratio of the RMS energy of the fundamental over the square root of the sum of the squared RMS energies of the harmonics. Only a limited set of significant harmonics are typically used in the computation.

THD measurements are normally performed using a signal that is very close to the maximum amplitude supported by the ADC (called its full-scale). These measurements are usually provided for a few typical and standard input frequencies. They are also sometimes shown using curves that plot the THD response for signals which span most of the ADC's frequency bandwidth and are performed with wide sampling rate variations.

## Conclusion

In this second part of our blog on ADC performance, we examined the impact of uneven spacing in the ADC's internal quantization grid on its harmonic distortion characteristics. We also discussed how the same type of distortion could also be attributed to the ADC's S/H inability to properly track large high frequency signals. Finally, we presented the standard equation used by ADC manufacturers to compute a device's total harmonic distortion characteristics.

In the third and last part of this blog, we'll examine how other similar ADC parameters like spurious components, dynamic range, and effective number of bits are computed.