(1) A basic concept
Decibel (dB): An amplitude unit defined by logarithm. For voltage values, dB is given in 20log (VA/VB); for power values, it is given in 10log (PA/PB). dBc is the dB value relative to a carrier signal; dBm is the dB value relative to 1mW. For dBm, the load resistance in the specification must be known (for example, 1mW is provided to 50Ω) to determine the equivalent voltage or current value.
(2) Definition of static indicators
1. Quantization Error
The quantization error is the basic error, which is illustrated by a simple 3bit ADC. The input voltage is digitized and divided into 8 discrete levels, represented by codes 000b to 111b, and each code spans the voltage range of Vref/8. The code size is generally defined as a Least Significant Bit (LSB). If it is assumed that Vref=8V, the voltage change between each code represents 1V. In other words, there is an error between the actual voltage generating the specified code and the voltage representing the code. Generally speaking, adding 0.5LSB offset to the input will result in a quantization error of plus or minus 0.5LSB at the ideal transition point.
2. Offset Gain Error
The difference between the ideal output of the device and the actual output is defined as the offset error, which exists in all digital codes. In practice, the offset error will cause a fixed offset between the transfer function or analog input voltage and the corresponding numerical output code. The usual method of calculating the offset error is to measure the voltage of the first digital code transition or "zero" transition and compare it with the theoretical zero voltage. The gain error is the difference between the estimated transfer function and the actual slope. The gain error is usually calculated at the last or last transfer code conversion point of the analog-to-digital converter.
In order to find the zero point and the last converted code point to calculate the offset and gain errors, a variety of measurement methods can be used. The two most commonly used are the code average method and the voltage jitter method. Code average measurement is to continuously increase the input voltage of the device, and then detect the conversion output result. Every time you increase the input voltage, you will get some conversion codes. Use the sum of these codes to calculate an average value, measure the input voltage that produces these average conversion codes, and calculate the device offset and gain. The voltage jitter method is similar to the code average method. The difference is that it uses a dynamic feedback loop to control the input voltage of the device. The input voltage is adjusted according to the difference between the converted code and the expected code until the difference between the two codes is zero. When the expected conversion code is close to the input voltage or changes near the conversion point, measure the average value of the applied "jitter" voltage and calculate the offset and gain.
3. Differential nonlinearity (DNL)
See the previous article.
4. Integral nonlinearity (INL)
See the previous article.
(3) Definition of dynamic indicators
1. Effective number of bits (ENOB): The test index (bits) related to the analog-to-digital converter (ADC) and the input frequency fIN. With the increase of fIN, the overall noise (especially the distortion component) will increase, thus reducing ENOB and SINAD performance. See also: Signal to Noise + Distortion Ratio (SINAD). The relationship between ENOB and SINAD is:
Note: The difference between digits and effective digits
Because the signal-to-noise ratio of an ideal ADC (containing only quantization noise) can have a formula:
SNR = (1.76 + 6.02*N)dB
It is calculated that the noise only contains quantization noise. If the ADC has no other noise but only quantization noise, the number of sampling bits N is the same as the effective number of bits Neff.
However, there are some other noises in the actual situation, so the number of bits N calculated by the above formula is the effective number of bits, which is less than N (sampling number of bits), and here is the difference between the number of sampling bits and the effective number of bits.
That is, the number of sampling bits N is the processing accuracy that the ADC can reach when there is only quantization error;
The effective number of bits Neff is the processing accuracy that the ADC can reach in actual processing.
2. Resolution: When an analog signal is quantized, it is expressed by a limited discrete voltage level, and the resolution is used to express the number of discrete levels of the signal. In order to recover the analog signal more accurately, the resolution must be increased. Resolution is usually defined as the number of bits, and conversion with higher resolution can reduce quantization noise.
3. Root Mean Square (RMS): Represents the effective value or effective DC value of an AC signal. For a sine wave, the RMS is 0.707 times the peak value, or 0.354 times the peak-to-peak value.
4. Spurious-free dynamic range (SFDR): the RMS value of the sine wave fIN (for ADC means the input sine wave, for ADC/DAC means the reconstructed output sine wave) and the spurious signal observed in the frequency domain The ratio of the RMS value of, the typical value is expressed in decibels. SFDR is very important in some communication systems that require maximum converter dynamic range.
The spurious-free dynamic range indicates the ability of the analog-to-digital converter to detect the smallest signal while inputting a large signal, which is also a very important performance parameter in practical applications. When the converter is used in the case where the oversampling rate is very high or the spectrum performance of the converter is very important, the index of spurious-free dynamic range is a very important parameter that marks the system performance.
5. Total Harmonic Distortion (THD): The ratio of the RMS value of the distortion that appears at the input (DAC is the output) frequency integer multiples (harmonic) to the RMS value of the input (or output) sine wave. Only the harmonics within the Nyquist frequency limit are included in the measurement, and the typical value is expressed in decibels:
In the formula, V2 to Vx are the harmonics of the fundamental wave V1.
6. Signal to noise + distortion ratio (SINAD): DC to Nyquist frequency band, sine wave fIN (for ADC means the input sine wave, for ADC/DAC means the reconstructed output sine wave) RMS value The ratio to the RMS value of the converter noise, including harmonic components. Typical values are expressed in decibels. Please also refer to the notes on root mean square (RMS) and total harmonic distortion.
7. dBFS (dB Full Scale): is a digital signal level unit, referred to as full-scale relative level. Full Scale refers to the position of 0 dBFS, 0 dBFS is the maximum encoding level, the actual corresponding value of 0 dBFS of different ADCs is different, and it is also the reference level for the full scale of the digital peak meter. For the digital signal, the maximum value of the code of the largest analog signal that the ADC can handle is 0 dBFS. The ratio of the code of the actual digital signal amplitude to the amplitude represented by the signal code of this maximum value is the full-scale relative level ( dBFS). Because the position where the maximum value is specified as 0, the full-scale relative level of the signal actually processed by a slice of ADC is all negative.
How to find the dBFS of a 12-bit ADC chip:
dBFS = 20 * log10 (sampled signal / 1111 1111 1111).
Therefore, fin = -1dBFS is often seen in ADC data files; this can be calculated by the above formula, where the amplitude of -1dBFS fin is equivalent to 0.8913 of the full-scale input amplitude.
8. TWO-TONE IMD (two-tone intermodulation distortion): two-tone intermodulation distortion
TWO-TONE IMD is the harmonic distortion generated at the (fin1 -fin2) and (fin1 +fin2) frequency points of the two input signals fin1 and fin2 when the ADC processes the mixed signal of two sine waves.
As shown below: