Analog-to-digital converter

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4-channel stereo multiplexed analog-to-digital converter WM8775SEDS made by Wolfson Microelectronics placed on an X-Fi Fatal1ty Pro sound card.

An analog-to-digital converter (ADC, A/D, or A to D) is a device that converts a continuous physical quantity (usually voltage) to a digital number that represents the quantity's amplitude.

The conversion involves quantization of the input, so it necessarily introduces a small amount of error. Instead of doing a single conversion, an ADC often performs the conversions ("samples" the input) periodically. The result is a sequence of digital values that have been converted from a continuous-time and continuous-amplitude analog signal to a discrete-time and discrete-amplitude digital signal.

An ADC is defined by its bandwidth (the range of frequencies it can measure) and its signal to noise ratio (how accurately it can measure a signal relative to the noise it introduces). The actual bandwidth of an ADC is characterized primarily by its sampling rate, and to a lesser extent by how it handles errors such as aliasing. The dynamic range of an ADC is influenced by many factors, including the resolution (the number of output levels it can quantize a signal to), linearity and accuracy (how well the quantization levels match the true analog signal) and jitter (small timing errors that introduce additional noise). The dynamic range of an ADC is often summarized in terms of its effective number of bits (ENOB), the number of bits of each measure it returns that are on average not noise. An ideal ADC has an ENOB equal to its resolution. ADCs are chosen to match the bandwidth and required signal to noise ratio of the signal to be quantized. If an ADC operates at a sampling rate greater than twice the bandwidth of the signal, then perfect reconstruction is possible given an ideal ADC and neglecting quantization error. The presence of quantization error limits the dynamic range of even an ideal ADC, however, if the dynamic range of the ADC exceeds that of the input signal, its effects may be neglected resulting in an essentially perfect digital representation of the input signal.

An ADC may also provide an isolated measurement such as an electronic device that converts an input analog voltage or current to a digital number proportional to the magnitude of the voltage or current. However, some non-electronic or only partially electronic devices, such as rotary encoders, can also be considered ADCs. The digital output may use different coding schemes. Typically the digital output will be a two's complement binary number that is proportional to the input, but there are other possibilities. An encoder, for example, might output a Gray code.

The inverse operation is performed by a digital-to-analog converter (DAC).

Concepts[edit]

Resolution[edit]

Fig. 1. An 8-level ADC coding scheme.

The resolution of the converter indicates the number of discrete values it can produce over the range of analog values. The resolution determines the magnitude of the quantization error and therefore determines the maximum possible average signal to noise ratio for an ideal ADC without the use of oversampling. The values are usually stored electronically in binary form, so the resolution is usually expressed in bits. In consequence, the number of discrete values available, or "levels", is assumed to be 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 28 = 256. The values can represent the ranges from 0 to 255 (i.e. unsigned integer) or from −128 to 127 (i.e. signed integer), depending on the application.

Resolution can also be defined electrically, and expressed in volts. The minimum change in voltage required to guarantee a change in the output code level is called the least significant bit (LSB) voltage. The resolution Q of the ADC is equal to the LSB voltage. The voltage resolution of an ADC is equal to its overall voltage measurement range divided by the number of discrete values:

Q = \dfrac{E_ \mathrm {FSR}}{{2^M}},

where M is the ADC's resolution in bits and EFSR is the full scale voltage range (also called 'span'). EFSR is given by

E_ \mathrm {FSR} = V_ \mathrm {RefHi} - V_ \mathrm {RefLow}, \,

where VRefHi and VRefLow are the upper and lower extremes, respectively, of the voltages that can be coded.

Normally, the number of voltage intervals is given by

N = 2^M, \,

where M is the ADC's resolution in bits.[1]

That is, one voltage interval is assigned in between two consecutive code levels.

Example:

In practice, the useful resolution of a converter is limited by the best signal-to-noise ratio (SNR) that can be achieved for a digitized signal. An ADC can resolve a signal to only a certain number of bits of resolution, called the effective number of bits (ENOB). One effective bit of resolution changes the signal-to-noise ratio of the digitized signal by 6 dB, if the resolution is limited by the ADC. If a preamplifier has been used prior to A/D conversion, the noise introduced by the amplifier can be an important contributing factor towards the overall SNR.

Comparison of quantizing a sinusoid to 64 levels (6 bits) and 256 levels (8 bits). The additive noise created by 6-bit quantization is 12 dB greater than the noise created by 8-bit quantization. When the spectral distribution is flat, as in this example, the 12 dB difference manifests as a measurable difference in the noise floors.

Quantization error[edit]

Main article: Quantization error

Quantization error is the noise introduced by quantization in an ideal ADC. It is a rounding error between the analog input voltage to the ADC and the output digitized value. The noise is non-linear and signal-dependent.

In an ideal analog-to-digital converter, where the quantization error is uniformly distributed between −1/2 LSB and +1/2 LSB, and the signal has a uniform distribution covering all quantization levels, the Signal-to-quantization-noise ratio (SQNR) can be calculated from

\mathrm{SQNR} = 20 \log_{10}(2^Q) \approx 6.02 \cdot Q\ \mathrm{dB} \,\! [2]

Where Q is the number of quantization bits. For example, a 16-bit ADC has a maximum signal-to-noise ratio of 6.02 × 16 = 96.3 dB, and therefore the quantization error is 96.3 dB below the maximum level. Quantization error is distributed from DC to the Nyquist frequency, consequently if part of the ADC's bandwidth is not used (as in oversampling), some of the quantization error will fall out of band, effectively improving the SQNR. In an oversampled system, noise shaping can be used to further increase SQNR by forcing more quantization error out of the band.

Dither[edit]

Main article: dither

In ADCs, performance can usually be improved using dither. This is a very small amount of random noise (white noise), which is added to the input before conversion.

Its effect is to cause the state of the LSB to randomly oscillate between 0 and 1 in the presence of very low levels of input, rather than sticking at a fixed value. Rather than the signal simply getting cut off altogether at this low level (which is only being quantized to a resolution of 1 bit), it extends the effective range of signals that the ADC can convert, at the expense of a slight increase in noise – effectively the quantization error is diffused across a series of noise values which is far less objectionable than a hard cutoff. The result is an accurate representation of the signal over time. A suitable filter at the output of the system can thus recover this small signal variation.

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 may cause the least significant bit to "stick" at 0 or 1. With dithering, the true level of the audio may be calculated by averaging the actual quantized sample with a series of other samples [the dither] that are recorded over 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.

Accuracy[edit]

An ADC has several sources of errors. Quantization error and (assuming the ADC is intended to be linear) non-linearity are intrinsic to any analog-to-digital conversion.

These errors are measured in a unit called the least significant bit (LSB). 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%.

Non-linearity[edit]

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). These non-linearities reduce the dynamic range of the signals that can be digitized by the ADC, also reducing the effective resolution of the ADC.

Jitter[edit]

When digitizing a sine wave x(t)=A \sin{(2 \pi f_0 t)}, the use of a non-ideal sampling clock will result in some uncertainty in when samples are recorded. Provided that the actual sampling time uncertainty due to the clock jitter is \Delta t, the error caused by this phenomenon can be estimated as E_{ap} \le |x'(t) \Delta t| \le 2A \pi f_0 \Delta t. This will result in additional recorded noise that will reduce the effective number of bits (ENOB) below that predicted by quantization error alone.

The error is zero for DC, small at low frequencies, but significant when high frequencies have high amplitudes. This effect can be ignored if it is drowned out by the quantizing error. Jitter requirements can be calculated using the following formula: \Delta t < \frac{1}{2^q \pi f_0}, where q is the number of ADC bits.

Output size
(bits)
Signal Frequency
1 Hz1 kHz10 kHz1 MHz10 MHz100 MHz1 GHz
81,243 µs1.24 µs124 ns1.24 ns124 ps12.4 ps1.24 ps
10311 µs311 ns31.1 ns311 ps31.1 ps3.11 ps0.31 ps
1277.7 µs77.7 ns7.77 ns77.7 ps7.77 ps0.78 ps0.08 ps
1419.4 µs19.4 ns1.94 ns19.4 ps1.94 ps0.19 ps0.02 ps
164.86 µs4.86 ns486 ps4.86 ps0.49 ps0.05 ps
181.21 ns121 ps6.32 ps1.21 ps0.12 ps
20304 ps30.4 ps1.58 ps0.16 ps

Clock jitter is caused by phase noise.[3][4] The resolution of ADCs with a digitization bandwidth between 1 MHz and 1 GHz is limited by jitter.[5]

When sampling audio signals at 44.1 kHz, the anti-aliasing filter should have eliminated all frequencies above 22 kHz. The input frequency (in this case, < 22 kHz), not the ADC clock frequency, is the determining factor with respect to jitter performance.[6]

Sampling rate[edit]

Main article: Sampling rate

The analog 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 analog signal. The rate of new values is called the sampling rate or sampling frequency of the converter.

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 analog 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.

Aliasing[edit]

Main article: Aliasing
See also: Undersampling

An ADC works by sampling the value of the input at discrete intervals in time. Provided that the input is sampled above the Nyquist rate, defined as twice the highest frequency of interest, then all frequencies in the signal can be reconstructed. If frequencies above half the Nyquist rate are sampled, they are incorrectly detected as lower frequencies, a process referred to as aliasing. Aliasing occurs because instantaneously sampling a function at two or fewer times per cycle results in missed cycles, and therefore the appearance of an incorrectly lower frequency. For example, a 2 kHz sine wave being sampled at 1.5 kHz would be reconstructed as a 500 Hz sine wave.

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. In applications where protection against aliasing is essential, oversampling may be used to greatly reduce or even eliminate it.

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 undersampling and frequency mixer). The alias is effectively the lower heterodyne of the signal frequency and sampling frequency.[7]

Oversampling[edit]

Main article: Oversampling

Signals are often sampled at the minimum rate required, for economy, with the result that the quantization noise introduced is white noise spread over the whole pass band of the converter. If a signal is sampled at a rate much higher than the Nyquist frequency and then digitally filtered to limit it to the signal bandwidth there are the following advantages:

Oversampling is typically used in audio frequency ADCs where the required sampling rate (typically 44.1 or 48 kHz) is very low compared to the clock speed of typical transistor circuits (>1 MHz). In this case, by using the extra bandwidth to distribute quantization error onto out of band frequencies, the accuracy of the ADC can be greatly increased at no cost. Furthermore, as any aliased signals are also typically out of band, aliasing can often be completely eliminated using very low cost filters.

Relative speed and precision[edit]

The speed of an ADC varies by type. The Wilkinson ADC is limited by the clock rate which is processable by current digital circuits. Currently,[when?] frequencies up to 300 MHz are possible.[8] For a successive-approximation ADC, the conversion time scales with the logarithm of the resolution, e.g. the number of bits. Thus for high resolution, it is possible that the successive-approximation ADC is faster than the Wilkinson. However, the time consuming steps in the Wilkinson are digital, while those in the successive-approximation are analog. Since analog is inherently slower than digital, as the resolution increases, the time required also increases. Thus there are competing processes at work. Flash ADCs are certainly the fastest type of the three. The conversion is basically performed in a single parallel step. For an 8-bit unit, conversion takes place in a few tens of nanoseconds.

There is, as expected, somewhat of a tradeoff between speed and precision. Flash ADCs have drifts and uncertainties associated with the comparator levels. This results in poor linearity. For successive-approximation ADCs, poor linearity is also present, but less so than for flash ADCs. Here, non-linearity arises from accumulating errors from the subtraction processes. Wilkinson ADCs have the highest linearity of the three. These have the best differential non-linearity. The other types require channel smoothing to achieve the level of the Wilkinson.[9][10]

The sliding scale principle[edit]

The sliding scale or randomizing method can be employed to greatly improve the linearity of any type of ADC, but especially flash and successive approximation types. For any ADC the mapping from input voltage to digital output value is not exactly a floor or ceiling function as it should be. Under normal conditions, a pulse of a particular amplitude is always converted to a digital value. The problem lies in that the ranges of analog values for the digitized values are not all of the same width, and the differential linearity decreases proportionally with the divergence from the average width. The sliding scale principle uses an averaging effect to overcome this phenomenon. A random, but known analog voltage is added to the sampled input voltage. It is then converted to digital form, and the equivalent digital amount is subtracted, thus restoring it to its original value. The advantage is that the conversion has taken place at a random point. The statistical distribution of the final levels is decided by a weighted average over a region of the range of the ADC. This in turn desensitizes it to the width of any specific level.[11][12]

ADC types[edit]

These are the most common ways of implementing an electronic ADC:

There can be other ADCs that use a combination of electronics and other technologies:

Commercial analog-to-digital converters[edit]

Commercial ADCs are usually implemented as integrated circuits.

Most converters sample with 6 to 24 bits of resolution, and produce fewer than 1 megasample per second. Thermal noise generated by passive components such as resistors masks the measurement when higher resolution is desired. For audio applications and in room temperatures, such noise is usually a little less than 1 μV (microvolt) of white noise. If the MSB corresponds to a standard 2 V of output signal, this translates to a noise-limited performance that is less than 20~21 bits, and obviates the need for any dithering. As of February 2002, Mega- and giga-sample per second converters are available. Mega-sample 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 is 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 0 to 5 V. 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 I/O 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.

Applications[edit]

Music recording[edit]

Analog-to-digital converters are integral to current music reproduction technology. People produce much music on computers using an analog recording and therefore need analog-to-digital converters to create the pulse-code modulation (PCM) data streams that go onto compact discs and digital music files.

The current crop of analog-to-digital converters utilized in music can sample at rates up to 192 kilohertz. Considerable literature exists on these matters, but commercial considerations often play a significant role. Most[citation needed] high-profile recording studios record in 24-bit/192-176.4 kHz pulse-code modulation (PCM) or in Direct Stream Digital (DSD) formats, and then downsample or decimate the signal for Red-Book CD production (44.1 kHz) or to 48 kHz for commonly used radio and television broadcast applications.

Digital signal processing[edit]

People must use ADCs to process, store, or transport virtually any analog signal in digital form. TV tuner cards, for example, use fast video analog-to-digital converters. Slow on-chip 8, 10, 12, or 16 bit analog-to-digital converters are common in microcontrollers. Digital storage oscilloscopes need very fast analog-to-digital converters, also crucial for software defined radio and their new applications.

Scientific instruments[edit]

Digital imaging systems commonly use analog-to-digital converters in digitizing pixels.

Some radar systems commonly use analog-to-digital converters to convert signal strength to digital values for subsequent signal processing. Many other in situ and remote sensing systems commonly use analogous technology.

The number of binary bits in the resulting digitized numeric values reflects the resolution, the number of unique discrete levels of quantization (signal processing). The correspondence between the analog signal and the digital signal depends on the quantization error. The quantization process must occur at an adequate speed, a constraint that may limit the resolution of the digital signal.

Many sensors produce an analog signal; temperature, pressure, pH, light intensity etc. All these signals can be amplified and fed to an ADC to produce a digital number proportional to the input signal.

Electrical Symbol[edit]

ADC Symbol.svg

Testing[edit]

Testing an Analog to Digital Converter requires an analog input source, hardware to send control signals and capture digital data output. Some ADCs also require an accurate source of reference signal.

The key parameters to test a SAR ADC are the following:

  1. DC Offset Error
  2. DC Gain Error
  3. Signal to Noise Ratio (SNR)
  4. Total Harmonic Distortion (THD)
  5. Integral Non Linearity (INL)
  6. Differential Non Linearity (DNL)
  7. Spurious Free Dynamic Range
  8. Power Dissipation

See also[edit]

Notes[edit]

  1. ^ "PRINCIPLES OF DATA ACQUISITION AND CONVERSION". Burr-Brown. Retrieved 1994-05-01. 
  2. ^ Lathi, B.P. (1998). Modern Digital and Analog Communication Systems (3rd edition). Oxford University Press. 
  3. ^ Maxim App 800: "Design a Low-Jitter Clock for High-Speed Data Converters". maxim-ic.com (July 17, 2002).
  4. ^ "Jitter effects on Analog to Digital and Digital to Analog Converters". Retrieved 19 August 2012. 
  5. ^ Löhning, Michael and Fettweis, Gerhard (2007). "The effects of aperture jitter and clock jitter in wideband ADCs". Computer Standards & Interfaces archive 29 (1): 11–18. doi:10.1016/j.csi.2005.12.005. 
  6. ^ Redmayne, Derek and Steer, Alison (8 December 2008) Understanding the effect of clock jitter on high-speed ADCs. eetimes.com
  7. ^ "RF-Sampling and GSPS ADCs - Breakthrough ADCs Revolutionize Radio Architectures". Texas Instruments. Retrieved 4 November 2013. 
  8. ^ 310 Msps ADC by Linear Technology, http://www.linear.com/product/LTC2158-14.
  9. ^ Knoll (1989, pp. 664–665)
  10. ^ Nicholson (1974, pp. 313–315)
  11. ^ Knoll (1989, pp. 665–666)
  12. ^ Nicholson (1974, pp. 315–316)
  13. ^ Atmel Application Note AVR400: Low Cost A/D Converter. atmel.com
  14. ^ Knoll (1989, pp. 663–664)
  15. ^ Nicholson (1974, pp. 309–310)
  16. ^ Vogel, Christian (2005). "The Impact of Combined Channel Mismatch Effects in Time-interleaved ADCs". IEEE Transactions on Instrumentation and Measurement 55 (1): 415–427. doi:10.1109/TIM.2004.834046. 
  17. ^ Analog Devices MT-028 Tutorial: "Voltage-to-Frequency Converters" by Walt Kester and James Bryant 2009, apparently adapted from Kester, Walter Allan (2005) Data conversion handbook, Newnes, p. 274, ISBN 0750678410.
  18. ^ Microchip AN795 "Voltage to Frequency / Frequency to Voltage Converter" p. 4: "13-bit A/D converter"
  19. ^ Carr, Joseph J. (1996) Elements of electronic instrumentation and measurement, Prentice Hall, p. 402, ISBN 0133416860.
  20. ^ "Voltage-to-Frequency Analog-to-Digital Converters". globalspec.com
  21. ^ Pease, Robert A. (1991) Troubleshooting Analog Circuits, Newnes, p. 130, ISBN 0750694998.

References[edit]

Further reading[edit]

External links[edit]