# ADC Guide, Part 9: Total Harmonic Distortion

Up to now, this series has primarily discussed the DC specifications of an ADC. Now, we will talk about AC specifications like distortion and noise in the ADC.

Total Harmonic Distortion (THD) is, as the name suggests, the measure harmonic distortion present in a signal. It is the ratio of the sum of the powers of all harmonic components to the power of the fundamental frequency of the signal. THD relates to the linearity of the system.

In part 5 of this series , we took a brief look at how missing codes in an ADC can cause distortion in ADC output. Such distortion will cause harmonics of the input signal to appear in the output of the ADC. While it is true that ADC with missing codes will have a large amount of harmonic distortion, missing codes are not the only source of harmonic distortion. Harmonic distortion in an ADC output is caused by any nonlinearity present in the ADC characteristics. Every practical ADC has nonlinear characteristics. As a result, harmonics are present in the output of every practical ADC. While DNL and INL are the measures of nonlinearity in ADC characteristics, THD is the measure of the resulting harmonic distortions present in the output of an ADC. Click on image to enlarge.

Figure 1: FFT of output of an ADC with non linear characteristics –
resulting harmonics are clearly visible

In order to visualize the harmonic distortion in the output of an ADC, we would give a sine wave as an input to the ADC and plot Fourier Transform (a.k.a. FFT) of the digital output of the ADC. Figure 1 shows an example of the FFT of such an ADC output. Ideally, the FFT should have had a single frequency spike at the frequency of sine wave. Although the input signal’s frequency has the highest amplitude in the FFT plot (green stem in the FFT), there are other frequency contents seen in the plot. The input signal frequency is referred to as the fundamental frequency. Apart from the fundamental frequency component, there are spikes seen periodically in the FFT (blue stems). These are the harmonics of the input signal frequency.

The ADC used for the measurements in Figure 1 had considerable nonlinear characteristics. For a good ADC design, the output FFT of an ADC would look much cleaner. Figure 1-1 below shows one such example. We would need more precise tools and measuring equipment in order to characterize the distortion of such an ADC. Click on image to enlarge.

Figure 1-1: FFT of output of an ADC with fairly liner characteristics
– Very low harmonic content.

Total harmonic distortion is defined as the power of the harmonic content in the output of ADC with respect to the power at the fundamental frequency. It can either be expressed in decibels or percentage as per equations (1) and (2) respectively. Click on image to enlarge. Click on image to enlarge.

As can be seen in Figure 1 , the amplitude of the harmonics – and hence the power in the harmonic frequencies – generally reduces as we move to higher harmonics of the ADC. Therefore, while calculating the total harmonic distortion, only the first few harmonics need to be considered. ADC datasheets should specify the number of harmonics considered for calculating total harmonic distortion numbers in the datasheet.

Apart from the fundamental frequency and harmonic frequency components of an ADC, Figure 1 also shows the presence of some power at every other frequency component (marked in red). This corresponds to the noise present in the output of ADC.

In the next part of this series, we will talk about the noise specifications of an ADC.