Information AboutAnalog-to-digital Converter |
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An analog-to-digital converter (abbreviated '''ADC''', '''A/D''' or '''A to D''') is an electronic integrated circuit, which converts continuous Signals to discrete Digital numbers. The reverse operation is performed by a Digital-to-analog Converter ('''DAC'''). Typically, an ADC is an Electronic device that converts an input analog Voltage (or current) to a Digital number. The digital output may be using different coding schemes, such as Binary and Two's Complement binary. However, some non-electronic or only partially electronic devices, such as Rotary Encoder s, can also be considered ADCs. RESOLUTION The Resolution of the converter indicates the number of discrete values it can produce over the range of analog values. The values are usually stored electronically in Binary form, so the resolution is usually expressed in Bit s. In consequence, the number of discrete values available, or "levels", is usually a power of two. For example, an ADC with a resolution of 8 bits can encode an analog input to one in 256 different levels, since . The values can represent the ranges 0 to 255 or -128 to 127, for example, depending on the application. Resolution can also be defined electrically, and expressed in Volt s. The voltage resolution of an ADC is equal to its overall voltage measurement range divided by the number of discrete intervals as in the formula: Where Q is resolution in volts, EFSR is the full scale voltage range, and M is resolution in bits. The number of intervals is given by the number of available levels minus one. Some examples may help:
In practice, the useful resolution of the converter is limited by the Signal-to-noise Ratio of the signal in question. If there is too much noise present in the analog input, it will be impossible to accurately resolve beyond a certain number of bits of resolution, the "effective number of bits" (ENOB). While the ADC will produce a result, the result is not accurate, since its lower bits are simply measuring noise. The Signal-to-noise Ratio should be around 6 dB per bit of resolution required. RESPONSE TYPE Linear ADCs Most ADCs are of a type known as Linear , although analog-to-digital conversion is an inherently non-linear process (since the mapping of a continuous space to a discrete space is a non-invertible and therefore non-linear operation). The term ''linear'' as used here means that the range of the input values that map to each output value has a linear relationship with the output value, i.e., that the output value ''k'' is used for the range of input values from m to m where ''m'' and ''b'' are constants. Here ''b'' is typically 0 or −0.5. When ''b'' = 0, the ADC islhljhkjhkred to as ''mid-rise'', and when ''b'' = −0.5 it is referred to as ''mid-tread''. Non-linear ADCs If the Probability Density Function of a signal being digitized is Uniform , then the signal-to-noise ratio relative to the quantization noise is the best possible. Because of this, it's usual to pass the signal through its Cumulative Distribution Function (CDF) before the quantization. This is good because the regions that are more important get quantized with a better resolution. In the dequantization process, the inverse CDF is needed. This is the same principle behind the Compander s used in some tape-recorders and other communication systems, and is related to Entropy maximization. (Never confuse Compander s with Compressors !) For example, a voice signal has a Laplacian Distribution . This means that the region around the lowest levels, near 0, carries more information than the regions with higher amplitudes. Because of this, logarithmic ADCs are very common in Voice Communication System s to increase the dynamic'' Italic Text '' range of the representable values while retaining fine-granular fidelity in the low-amplitude region. An eight-bit A-law or the μ-law logarithmic ADC covers the wide Dynamic Range and has a high resolution in the critical low-amplitude region, that would otherwise require a 12-bit linear ADC. ACCURACY An ADC has several sources of errors. Quantization error and (assuming the ADC is intended to be linear) non- Linearity is intrinsic to any analog-to-digital conversion. There is also a so-called ''aperture error'' which is due to a clock Jitter and is revealed when digitizing a signal (not a single value). These errors are measured in a unit called the ''LSB'', which is an abbreviation for Least Significant Bit . In the above example of an eight-bit ADC, an error of one LSB is 1/256 of the full signal range, or about 0.4%. Quantization error See Also: Quantization noise Quantization error is due to the finite resolution of the ADC, and is an unavoidable imperfection in all types of ADC. The Magnitude of the quantization error at the sampling instant is between zero and half of one LSB. In the general case, the original signal is much larger than one LSB. When this happens, the Quantization Error is not correlated with the signal, and has a Uniform Distribution . Its RMS value is the Standard Deviation of this distribution, given by . In the eight-bit ADC example, this represents 0.113% of the full signal range. At lower levels the quantizing error becomes dependent of the input signal. And the result is distortion. This distortion is created after the anti-aliasing filter, and if these distortions are above 1/2 the sample rate they will alias back into the audio band. In order to make the quantizing error independent of the input signal, noise with an amplitude of 1 quantization step is added to the signal. This slightly reduces signal to noise ratio, but completely eliminates the distortion. It is known as dither. Non-linearity All ADCs suffer from non-linearity errors caused by their physical imperfections, causing their output to deviate from a linear function (or some other function, in the case of a deliberately non-linear ADC) of their input. These errors can sometimes be mitigated by Calibration , or prevented by testing. Important parameters for linearity are integral non-linearity (INL) and '''differential non-linearity''' (DNL). therefore you need to do a careful calculation when you do the convergence Aperture error |
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