Analog-to-Digital Converter (ADC)


An ideal ADC uniquely represents all analog inputs within a certain range by a limited number of digital output codes. Each digital code represents a fraction of the total analog input range. Since the analog scale is continuous, while the digital codes are discrete, there is a quantization process that introduces an error. As the number of discrete codes increases, the corresponding step width gets smaller and the transfer function approaches an ideal straight line. The steps are designed to have transitions such that the midpoint of each step corresponds to the point on this ideal line.

The width of one step is defined as 1 LSB (one least significant bit) and this is often used as the reference unit for other quantities in the specification. It is also a measure of the resolution of the converter since it defines the number of divisions or units of the full analog range. Hence, 1/2 LSB represents an analog quantity equal to one half of the analog resolution.

The resolution of an ADC is usually expressed as the number of bits in its digital output code. For example, an ADC with an n-bit resolution has 2n possible digital codes which define 2n step levels. However, since the first (zero) step and the last step are only one half of a full width, the full-scale range (FSR) is divided into 2n – 1 step widths.

1 LSB = FSR/(2n – 1) for an n-bit converter


Enter:


Result:




ADC Characteriscitcs



ENOB

Effective number of bits (ENOB) is a measure of the dynamic range of an ADC. The resolution of an ADC is specified by the number of bits used to represent the input analog value, in principle giving 2N signal levels for an N-bit signal. However, all real ADC circuits introduce noise and distortion. ENOB specifies the resolution of an ideal ADC circuit that would have the same resolution as the circuit under consideration.

ENOB is based on the equation for an ideal ADC’s SNR:

SNR (dB) = 6.02 × N + 1.76 dB

where N is the ADC’s resolution. A real world ADC never achieves this SNR due to its own noise and errors. You can rearrange the equation to calculate an ADC’s effective N, or ENOB as we commonly call it:

ENOB = (SNR – 1.76)/6.02 dB.

Ideal ADC - Enter:


Result:



An ADC datasheet will indicate the ENOB uder certain condition. SNR can be obtain as follows:

SNR (dB) = 6.02 × N + 1.76 dB




ADC Resolution

The resolution of an ADC is usually expressed as the number of bits in its digital output code. For example, an ADC with an n-bit resolution has 2n possible digital codes which define 2n step levels. However, since the first (zero) step and the last step are only one half of a full width, the full-scale range (FSR) is divided into 2n – 1 step widths.

1 LSB = FSR / (2n - 1)

for an n-bit converter

The Ideal Transfer Function (ADC)




Signal Characteristics

Signal-to-noise and distortion ratio (SNR) is a measure of the quality of a signal. It is a measure used in science and engineering that compares the level of a desired signal to the level of background noise. It is defined as the ratio of signal power to the noise power, often expressed in decibels. A ratio higher than 1:1 (greater than 0 dB) indicates more signal than noise. While SNR is commonly quoted for electrical signals, it can be applied to any form of signal (such as isotope levels in an ice core or biochemical signaling between cells).

By definition SNR is computed as a ratio of signal and noise powers:

Rsignal is the internal impedance of the signal source.
Rnoise is the internal impedance of the noise source.
If Rsignal = Rnoise, then

Assuming Rsignal = Rnoise Computer SNR:




Result:




The quantization error as a function of time is shown in more detail in the figure. A simple sawtooth waveform provides a sufficiently accurate model for analysis. The equation of the sawtooth error is given by:

Signal to noise ratio can be computed as follows:

SNR = Psignal / Pnoise = μ / σ






Result:








POWER SUPPLY NOISE

The analog power supply is used as the reference voltage for conversion. As the ADC output is the ratio between the analog signal voltage and the supply voltage, any noise on the analog reference will cause a change in the converted digital value.










VSTEP = VREF / 2n

VERROR = VSTEP * Difference






ANALOG INPUT SIGNAL NOISE

The analog signal to be converted may have some noise superimposed on it. There may be a high frequency noise signal. It is recommended to connect a 10nf capacitor to the analog input signal. You can also add a low pass filter but this will affect FAIN, so you should use this only if the input signal frequency is low.

FAIN is the frequency of the analog input signal.








OFFSET ERROR

The offset error as shown in Figure 3 is defined as the difference between the nominal and actual offset points. For an ADC, the offset point is the midstep value when the digital output is zero, and for a DAC it is the step value when the digital input is zero. This error affects all codes by the same amount and can usually be compensated for by a trimming process. If trimming is not possible, this error is referred to as the zero-scale error.