How to improve ADC resolution and reduce noise

allAnalog-to-digital converters(ADCs) have an amount of "input-referred noise" that can be simulated as a noise source in series with the input of a noiseless ADC. Input referred noise is not the same as quantization noise, which only appears when the ADC is processing an ac signal. In most cases, lower input noise is better, but in some cases, input noise can actually help achieve higher resolution.

 

What is input-referred noise?

The actual ADC deviates from the ideal ADC in many ways. Input-referred noise is certainly not ideal, and its effect on the overall transfer function of the ADC is shown in Figure 1. As the analog input voltage increases, the "ideal" ADC (shown in Figure 1A) maintains a constant output code until the transition region is reached, at which point the output code immediately jumps to the next value and remains at that value until the next transition region is reached.

 

Theoretically, an ideal ADC would have a "code transition" noise of 0 and a transition region width equal to 0. The actual ADC has a certain amount of code transition noise, so the transition region width depends on the amount of noise referred to the input (as shown in Figure 1B). Figure 1B shows the code transition noise with a width of approximately 1 LSB (least significant bit) peak-to-peak.

Figure 1: Input referred noise and its effect on the ADC transfer function

 

Due to resistor noise and "kT/C" noise, all ADC internal circuitry generates a certain amount of rms (RMS) noise. This noise is present even with a DC input signal, which is responsible for the code transition noise. Today, code transition noise is often referred to as "input-referred noise" rather than the term "code transition noise."

 

Referred to the input Noise is typically characterized by a histogram of several output samples with the ADC input as a dc value. The output of most high-speed or high-resolution ADCs is a series of codes centered on the nominal value of the dc input (see Figure 2). To measure its value, the input of the ADC is grounded or connected to a deeply decoupled voltage source, and a large number of output samples are taken and represented as a histogram (sometimes referred to as a "ground input" histogram). Since the noise is roughly Gaussian distributed, the standard deviation σ of the histogram can be calculated, which corresponds to the effective input rms noise.

Figure 2: Effect of input-referred noise on ADC "ground input" histogram (ADC has a small amount of DNL)

 

Although the ADC's inherent differential nonlinearity (DNL) can cause its noise distribution to deviate slightly from the ideal Gaussian distribution (partial DNL is shown in the Figure 2 example), it is at least roughly Gaussian. If the DNL is large, the σ values for several different DC input voltages should be calculated and then averaged. For example, if the code distribution has large and unique peaks and valleys, this indicates a poor ADC design or, more likely, a faulty PCB layout, poor grounding, or improper power supply decoupling (see Figure 3). When the dc input sweeps over the ADC input voltage range, if the distribution width changes sharply, this also indicates a problem.

Figure 3: Histogram of poorly designed ADCs and/or poorly placed, grounded, and decoupled ground inputs

 

 

Increase ADC Resolution and Reduce Noise?

The effect of input-referred noise can be reduced by digital averaging. Suppose one16-bit ADCIt has 15-bit noise-free resolution and a sample rate of 100 kSPS. For each output sample, if the two samples are averaged, the effective sampling rate drops to 50 kSPS, the SNR increases by 3 dB, and the noise-free number increases to 15.5 bits.

 

If the four samples are averaged, the sampling rate drops to 25 kSPS, the SNR increases by 6 dB, and the noise-free bits increase to 16 bits. In fact, if 16 samples are averaged, the output sample rate drops to 6.25 kSPS, SNR increases by another 6 dB, and the number of noise-free bits increases to 17 bits. To take advantage of the additional "resolution", the averaging algorithm must be performed on a larger significant number of digits.

 

The averaging process also helps to eliminate the DNL error of the ADC transfer function, which can be illustrated by the following simple example: assuming that the ADC has an outcode at quantization level "k", although code "k" is lost due to large DNL error, the average of two adjacent codes k – 1 and k + 1 is equal to k. Therefore, this technique can be leveraged to effectively improve the dynamic range of the ADC at the cost of a reduced overall output sample rate and the need for additional digital hardware.

 

However, it should be noted that the mean does not correct for the intrinsic integral nonlinearity of the ADC. Now consider a situation where the ADC has very low input-referred noise and the histogram always shows a clear code, what does the digital mean do for such an ADC? The answer is simple – it doesn't work! The answer is always the same, regardless of how many samples are averaged. But as long as enough noise is added to the input signal so that there is more than one code in the histogram, the averaging method will be effective. Therefore, a small amount of noise may be a good thing (at least for the averaging method), but the higher the noise present at the input, the greater the number of averaging samples required to achieve the same resolution.