Analog circuits - Total Harmonic Distortion (THD)

Total Harmonic distortion (THD) is one of the important specification for a ADC. THD determines the amount of distortion that can happen on the output signal of the ADC. When we provide a signal input to the ADC, the internal op-amp configuration introduces non-linearity to the signal which causes the harmonics to occur at the output. To define what is harmonic, for a given fundamental frequency 'F', the harmonics are 2F, 3F, 4F, 5F. So, the question comes to mind on how many harmonics are to be considered as there could be multiples of fundamental frequency. This is decided by the amplitude of the harmonics. The harmonics which are very high compared to the noise floor in a design are to be considered as significant harmonics. If A1 is the amplitude of the fundamental frequency and A2, A3, A4, .. are the amplitudes of the harmonics, THD is calculated using the formulae,

Total Harmonic distortion, THD = LOG (SQRT((A2^2)+( A3^2)+ (A4^2)+( A5^2))/A1)

In the above equation, we have used harmonic amplitudes only till A5, but the count could be higher.

The unit for measurement of THD is dBc. So, the next doubt in the minds of the designer engineer comes to mind on how to know the THD value as we are not sure how many harmonics would be present. The designer need not worry as the manufacturers have characterized the non-linearity of their devices and given a graph for us in their datasheets.

AD7991 from analog Devices is a 12-bit resolution ADC with 4 analog inputs and a serial output as the conversion output. This can be interfaced to processor or a micro controller. Below are the 

snapshots from the AD7991 datasheet which shows the THD values. We can clearly see that till sixth harmonic have been considered for the THD calculation.

Tips for the designer:

1. THD should be as low as possible.

2. THD is dependent on the analog signal input frequency. As the input freqenucy increases, the THD also increases.

3. THD is dependent on the source resistance. Here source meant the one which generates the analog signal. If the source resistance is high, the THD increases.In this case, reducing the source resistance is important. For this, we have to use a input buffer to achieve the required impedance.