Characteristics of Analogue to Digital Converters


The resolution of the converter indicates the number of discrete values it can produce. It is usually expressed in bits. For example, an ADC that encodes an analogue input to one of 256 discrete values has a resolution of eight bits, since
                   28 = 256.
Resolution can also be defined electrically, and expressed in volts. The voltage resolution of an ADC is equal to its overall voltage measurement range divided by the number of discrete values
For example.........

Full scale measurement range = 0 to 10 volts
ADC resolution is 12 bits: 212 = 4096 quantization levels
ADC voltage resolution is: (10-0)/4096 = 0.00244 volts = 2.44 mV

Full scale measurement range = -10 to +10 volts
ADC resolution is 14 bits: 214 = 16384 quantization levels
ADC voltage resolution is: (10-(-10))/16384 = 20/16384 = 0.00122 volts = 1.22 mV
In practice, the 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 analogue 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 S/N ratio should be around 6 dB per bit of resolution required.

   Accuracy depends on the error in the conversion. If the ADC is not broken, this error has two components: quantization error and (assuming the ADC is intended to be linear) non-linearity. 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 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.
   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.

Sampling rate
   The analogue signal is continuous in time and it is necessary to convert this to a flow of digital values. It is therefore required to define the rate at which new digital values are sampled from the analogue signal. The rate of new values is called the sampling rate or sampling frequency of the converter.
   A continuously varying band limited signal can be sampled (that is, the signal values at intervals of time T, the sampling time, are measured and stored) and then the original signal can be exactly reproduced from the discrete-time values by an interpolation formula. The accuracy is however limited by quantization error. However, this faithful reproduction is only possible if the sampling rate is higher than twice the highest frequency of the signal. This is essentially what is embodied in the Shannon-Nyquist sampling theorem.
   Since a practical ADC cannot make an instantaneous conversion, the input value must necessarily be held constant during the time that the converter performs a conversion (called the conversion time). An input circuit called a sample and hold performs this task—in most cases by using a capacitor to store the analogue voltage at the input, and using an electronic switch or gate to disconnect the capacitor from the input. Many ADC integrated circuits include the sample and hold subsystem internally.

All ADCs work by sampling their input at discrete intervals of time. Their output is therefore an incomplete picture of the behaviour of the input. There is no way of knowing, by looking at the output, what the input was doing between one sampling instant and the next. If the input is known to be changing slowly compared to the sampling rate, then it can be assumed that the value of the signal between two sample instants was somewhere between the two sampled values. If, however, the input signal is changing fast compared to the sample rate, then this assumption is not valid.
   If the digital values produced by the ADC are, at some later stage in the system, converted back to analogue values by a digital to analogue converter or DAC, it is desirable that the output of the DAC be a faithful representation of the original signal. If the input signal is changing much faster than the sample rate, then this will not be the case, and spurious signals called aliases will be produced at the output of the DAC. The frequency of the aliased signal is the difference between the signal frequency and the sampling rate. For example, a 2 kHz sine wave being sampled at 1.5 kHz would be reconstructed as a 500 Hz sine wave. This problem is called aliasing.
   To avoid aliasing, the input to an ADC must be low-pass filtered to remove frequencies above half the sampling rate. This filter is called an anti-aliasing filter, and is essential for a practical ADC system.
   Although aliasing in most systems is unwanted, it should also be noted that it can be exploited to provide simultaneous down-mixing of a band-limited high frequency signal


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