2 SNR Enhancement by Summation of ADCs

In audio ADCs, oversampling decreases quantization noise in the band of interest, which results in improved SNR. The theoretical value of signal-to-noise ratio of an N-bit ADC can be expressed as

Where N is the number of bits. By oversampling, the SNR can be increased and a designer can quantify the improvement of SNR by using the following equation

where OSR (oversampling ratio) is the ratio of sampling frequency to twice the input frequency, which is also known as the Nyquist frequency. This ratio is given by

The preceding equation shows that SNR improves by 3 dB per octave. So, if OSR = 2, then the SNR improves by 3 dB; if OSR = 4, the SNR improves by 6 dB.

The TLV320ADC5140 and TLV320ADC6140 devices from TI’s Audio ADC portfolio features the Dynamic Range Enhancer (DRE) algorithm that can be used to improve the far-field recording performance by improving the dynamic range of the ADC channel at low signal levels. The DRE is a digitally-assisted algorithm that dynamically adjusts the front-end programmable gain amplifier (PGA) to improve the signal-to-noise ratio of low-level signals while preventing high-level signals from saturating the PGA and ADC.

The two methods described in earlier sections are embedded in the design of ADCs. There is another method to improve the dynamic range which is similar to the oversampling method. In this method, instead of oversampling, two or four or more ADCs are used in parallel. In this approach, the same input is fed to all ADCs, as the inputs are all tied together, the outputs are summed and averaged to yield an improved dynamic range. In Figure 2-1, two identical ADCs are connected at the input, receiving the same voltage. The outputs are summed in the digital domain and averaged using back-end digital processing within an FPGA or digital signal processor.

Figure 2-1 Connecting Two Identical ADCs and Summing ADC Outputs

Equation 1 through Equation 9 show how using this approach improves dynamic range. When two signals with the same frequency and phase are summed, the signals sum in terms of voltage. The result of this summation is

However, random signals, (such as noise, which have different frequencies and phases), sum in terms of power. Noise from two separate converters or channels are white and random, which means that the noise is predominantly uncorrelated from one channel or device to the other. Since noise signals are random, the signals must be treated by statistical means. The result for summation of two noise sources are

Figure 2-1 shows a circuit with two identical ADCs. Two identical ADCs are used, the same input is applied to both ADCs, and the output of each is sent to be summed and averaged in the digital domain. The input of each ADC consists of the input signal as well as the noise. The two outputs can be summed using the following equation

In the preceding equation, both inputs are identical. The summation of the these signals doubles the signal level which is equivalent to a 6-dB increase in signal level, whereas the summation of uncorrelated noise sources increases the noise level by a factor of 1.4 or 3 dB. Overall, there is a 3-dB improvement in dynamic range. This concept can be expanded to more parallel devices and SNR can be improved even more. For example, if four ADCs are used in parallel, the outcome is a 6-dB increase in SNR. Considering Equation 1, which calculates the SNR based on number of bits, the effective number of bits (ENOB) can be calculated using

With the 3-dB improvement of SNR, the new ENOB’ is calculated as

Where SNR’=SNR+3 for two converters used in parallel. Replacing SNR’ in Equation 8, results in the following equation.

For each doubling of the number of devices used in parallel, the effective number of bits increases by approximately 0.5, improving the SNR by 3 dB.