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# Analog-to-digital converter (ADC), calculation of resolution and dynamic range

25/03/2022

An analog-to-digital converter is an A/D converter, ADC for short, which converts an analog signal into a digital signal. The analog voltage input at the input terminal is processed by the four processes of sampling, holding, quantization and encoding, and then converted into the corresponding binary digital output.

Sampling is the use of analog switches to convert continuously changing analog quantities into discrete digital quantities. Since the digital quantities formed after sampling have a narrow width, the narrow pulse can be broadened through the hold circuit to form a trapezoidal wave. Quantization is to convert each voltage value in a ladder-shaped analog signal into an integer multiple of a certain minimum unit, which is convenient for digital expression. Encoding is to represent the result of quantization (that is, integer multiples) with binary numbers. This process realizes the analog-to-digital conversion.

## Resolution and dynamic range

ADC resolution is the number of bits used to represent the analog input signal. In order to reproduce the analog signal more accurately, the resolution must be improved, and the use of a higher resolution ADC also reduces the quantization error. But the cost goes up.

Dynamic range (DR) is defined as the range from the noise floor of the device to its specified maximum output level, usually expressed in dB. The dynamic range of the ADC refers to the signal amplitude range that the ADC can distinguish; the resolution number (N) of the ADC determines the dynamic range of the ADC, which represents the range of the input signal level that the ADC can measure. DR can be defined as: Since the RMS amplitude of the signal in a given time window depends on how the signal amplitude changes within the time window, the DR change of the ADC depends on the characteristics of the input signal. For a constant DC input within its full-scale range (FSR), an ideal N-bit ADC can measure the maximum and minimum RMS amplitudes of FSR and FSR/2N, respectively. Therefore, the DR of ADC is: For the sine wave signal input, the minimum measurable RMS amplitude of the sine wave input signal is limited by the quantization error. The DR of the ideal ADC for the sine wave input signal is:

DR=6.02N+1.76dB

Assuming that the dynamic range of the ADC is 60dB, the resolvable signal amplitude is x to 1000x. Usually the dynamic range is very important, because if the signal is too large, it will cause the ADC input to over-range; if the signal is too small, it will be drowned in the quantization noise of the converter.

## SNR and SNR

The signal-to-noise ratio (SNR) of the digital-to-analog converter refers to the ratio of the input signal power to the noise power. It is used to quantify the noise in the data converter. SNR can also be measured by the RMS value of the signal amplitude and the noise amplitude, in dB As a unit. Under the condition of full-scale sine wave input, the theoretical maximum SNR of ADC is derived from the quantization noise, and the expression is:

SNR=6.02N+1.76dB

Here N is the number of bits of an ideal ADC. For the sine wave input of an ideal N-bit data converter (without considering harmonic distortion), the best SNR that can be achieved over the entire Nyquist bandwidth.

But for the actual ADC, in addition to the quantization noise, the SNR of the data converter is also limited by its own thermal noise and sampling clock phase noise. There are three main sources of noise:

• Quantization noise

• Jitter or sampling uncertain noise

Signal to Noise And Distortion (SINAD) refers to the RMS signal power and total noise power and the power of all other frequency components at the output (excluding DC) plus the power of all other harmonic components when a sine wave is input. The ratio of RMS and.

SNDR is one of the key parameters used to measure the dynamic performance of data converters. It includes all noise and spurs on the Nyquist bandwidth. The expression of SNDR is: Among them, the signal power is the average power of the useful signal, noise and distortion components. The unit of SNDR is decibel (dB). SNDR compares all bad frequency components with the input frequency, reflects the quality of the input signal, and measures the dynamic performance of the data converter as a whole. The larger the SNDR, the smaller the noise and spurious ratio in the input power.

## ADC effective number of bits

The effective number of bits (ENOB) is a parameter used to measure the conversion quality (in bits) of a data converter over the Nyquist bandwidth of the input signal.

ENOB here assumes that the converter has theoretically perfect performance without distortion. The only noise generated is quantization noise, so SNR is equal to SNDR, that is, SNR(dBFS) = 6.02N+1.76dB. Therefore, ENOB is also another expression of SNDR: However, for non-ideal data converters, SNDR and ENOB will degrade, including noise and other defects, such as device thermal noise, missing output codes, harmonics, AC/DC nonlinearity, gain/offset errors, and aperture clocks Phase noise or jitter. Noise on external bias reference sources and power rails will also reduce ENOB.

Total harmonic distortion (THD) measures the distortion component of a signal, expressed in decibels (dB) relative to the fundamental wave. For ADCs, total harmonic distortion (THD) is the ratio of the RMS sum of the selected input signal harmonics to the fundamental. When measuring, only harmonics within the Nyquist limit are included.

Similar to the degradation of THD as the input frequency increases due to non-linearity, the ENOB value will also degrade as the frequency increases. ENOB comes from SNDR, and SNDR is associated with THD and SNR. To understand the accurate ENOB of the data converter, you need to read the detailed specifications and prescribed conditions in the data sheet.

## ENOB in practice

Most analog data converter IC manufacturers generally tend to promote ENOB under ideal conditions, especially the ENOB value contained in the title of the data sheet. However, a large number of system engineers and purchasing managers are still curious about why the measured ENOB value is different from the ideal value contained in the data sheet?

In actual use, because the ADC itself has noise and errors, its output not only has quantization noise, but also high-order harmonics caused by distortion, so this SNR value has never been reached. Calculate the effective N of the ADC: ENOB = (SNR–1.76)/6.02 dB.

Assuming that the device is a 12-bit ADC, ENOB may only be 10 bits. But it should be noted that this does not mean that deleting the last two bits of the ADC can be used as an ideal 10-bit ADC. Here, ENOB means that the SNDR of a 12-bit non-ideal ADC is equal to the SNR of an ideal 10-bit ADC.

## Some understanding points about ENOB:

• The "number of digits" (12-bit or 14-bit) shown in the title of the general data converter data sheet refers to the number of digits or voltage resolution. This has nothing to do with ENOB.

• ENOB is mainly a function of noise, non-linearity, and input frequency.

• ENOB will be degraded due to various external uncertain factors (such as clock source, power supply, etc.).

• ENOB is calculated over the entire Nyquist bandwidth (DC to fs/2).

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