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, Gray code or two's complement binary. However, some non-electronic or only partially electronic devices, such as rotary encoders, can also be considered ADCs.
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 intervals as in the formula:
The number of intervals is given by the number of available levels (output codes), which is:
Some examples may help:
In practice, the smallest output code ("0" in an unsigned system) represents a voltage range which is 0.5X (half-wide) of the ADC voltage resolution (Q) while the largest output code represents a voltage range which is 1.5X (50% wider) of the ADC voltage resolution. The other N − 2 codes are all equal in width and represent the ADC voltage resolution (Q) calculated above. Doing this centers the code on an input voltage that represents the Mth division of the input voltage range. For example, in Example 3, with the 3-bit ADC spanning an 8 V range, each of the N divisions would represent 1 V, except the 1st ("0" code) which is 0.5 V wide, and the last ("7" code) which is 1.5 V wide. Doing this the "1" code spans a voltage range from 0.5 to 1.5 V, the "2" code spans a voltage range from 1.5 to 2.5 V, etc. Thus, if the input signal is at 3/8ths of the full-scale voltage, then the ADC outputs the "3" code, and will do so as long as the voltage stays within the range of 2.5/8ths and 3.5/8ths. This practice is called "Mid-Tread" operation. This type of ADC can be modeled mathematically as:
The exception to this convention seems to be the Microchip PIC processor, where all M steps are equal width. This practice is called "Mid-Rise with Offset" operation.
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). If a preamplifier has been used prior to A/D conversion, the noise introduced by the amplifier is an important contributing factor towards the overall SNR. 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.
where m and b are constants. Here b is typically 0 or −0.5. When b = 0, the ADC is referred to as mid-rise, and when b = −0.5 it is referred to as mid-tread.
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 systems to increase the dynamic range of the representable values while retaining fine-granular fidelity in the low-amplitude region.
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.
At lower levels the quantizing error becomes dependent of the input signal, resulting in 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.
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.
One can see that the error is relatively small at low frequencies, but can become significant at high frequencies.
This effect can be ignored if it is relatively small as compared with quantizing error. Jitter requirements can be calculated using the following formula: , where q is a number of ADC bits.
|ADCresolutionin bit||input frequency|
|1 Hz||44.1 kHz||192 kHz||1 MHz||10 MHz||100 MHz||1 GHz|
|8||1243 µs||28.2 ns||6.48 ns||1.24 ns||124 ps||12.4 ps||1.24 ps|
|10||311 µs||7.05 ns||1.62 ns||311 ps||31.1 ps||3.11 ps||0.31 ps|
|12||77.7 µs||1.76 ns||405 ps||77.7 ps||7.77 ps||0.78 ps||0.08 ps|
|14||19.4 µs||441 ps||101 ps||19.4 ps||1.94 ps||0.19 ps||0.02 ps|
|16||4.86 µs||110 ps||25.3 ps||4.86 ps||0.49 ps||0.05 ps||–|
|18||1.21 µs||27.5 ps||6.32 ps||1.21 ps||0.12 ps||–||–|
|20||304 ns||6.88 ps||1.58 ps||0.16 ps||–||–||–|
|24||19.0 ns||0.43 ps||0.10 ps||–||–||–||–|
A continuously varying bandlimited 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 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.
If the digital values produced by the ADC are, at some later stage in the system, converted back to analog values by a digital to analog 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 sinewave being sampled at 1.5 kHz would be reconstructed as a 500 Hz sinewave. 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 that is applied to analog signals with higher frequency content.
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 (see frequency mixer).
An audio signal of very low level (with respect to the bit depth of the ADC) sampled without dither sounds extremely distorted and unpleasant. Without dither the low level always yields a '1' from the A to D. With dithering, the true level of the audio is still recorded as a series of values over time, rather than a series of separate bits at one instant in time.
A virtually identical process, also called dither or dithering, is often used when quantizing photographic images to a fewer number of bits per pixel—the image becomes noisier but to the eye looks far more realistic than the quantized image, which otherwise becomes banded. This analogous process may help to visualize the effect of dither on an analogue audio signal that is converted to digital.
Dithering is also used in integrating systems such as electricity meters. Since the values are added together, the dithering produces results that are more exact than the LSB of the analog-to-digital converter.
Note that dither can only increase the resolution of a sampler, it cannot improve the linearity, and thus accuracy does not necessarily improve.
Nonelectronic ADCs usually use some scheme similar to one of the above.
Most converters sample with 6 to 24 bits of resolution, and produce fewer than 1 megasample per second. It is rare to get more than 24 bits of resolution because of thermal noise generated by passive components such as resistors. For audio applications and in room temperatures, such noise is usually a little less than 1 μV (microvolt) of white noise. If the Most Significant Bit corresponds to a standard 2 volts of output signal, this translates to a noise-limited performance that is less than 20~21 bits, and obviates the need for any dithering. Mega- and gigasample converters are available, though (Feb 2002). Megasample converters are required in digital video cameras, video capture cards, and TV tuner cards to convert full-speed analog video to digital video files. Commercial converters usually have ±0.5 to ±1.5 LSB error in their output.
In many cases the most expensive part of an integrated circuit is the pins, because they make the package larger, and each pin has to be connected to the integrated circuit's silicon. To save pins, it's common for slow ADCs to send their data one bit at a time over a serial interface to the computer, with the next bit coming out when a clock signal changes state, say from zero to 5V. This saves quite a few pins on the ADC package, and in many cases, does not make the overall design any more complex. (Even microprocessors which use memory-mapped IO only need a few bits of a port to implement a serial bus to an ADC.)
Commercial ADCs often have several inputs that feed the same converter, usually through an analog multiplexer. Different models of ADC may include sample and hold circuits, instrumentation amplifiers or differential inputs, where the quantity measured is the difference between two voltages.
ADCs are integral to current music reproduction technology. Since much music production is done on computers, when an analog recording is used, an ADC is needed to create the PCM data stream that goes onto a compact disc.
The current crop of AD converters utilized in music can sample at rates up to 192 kilohertz. Many people in the business consider this an overkill and pure marketing hype, due to the Nyquist-Shannon sampling theorem. Simply put, they say the analog waveform does not have enough information in it to necessitate such high sampling rates, and typical recording techniques for high-fidelity audio are usually sampled at either 44.1 kHz (the standard for CD) or 48 kHz (commonly used for radio/TV broadcast applications). However, this kind of bandwidth headroom allows the use of cheaper or faster anti-aliasing filters of less severe filtering slopes. The proponents of oversampling assert that such shallower anti-aliasing filters produce less deleterious effects on sound quality, exactly because of their gentler slopes. Others prefer entirely filterless AD conversion, arguing that aliasing is less detrimental to sound perception than pre-conversion brickwall filtering. Considerable literature exists on these matters, but commercial considerations often play a significant role. Most high-profile recording studios record in 24-bit/192-176.4 kHz PCM or in DSD formats, and then downsample or decimate the signal for Red-Book CD production.
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