Report in Adc and Dac

8/3/2019 Report in Adc and Dac

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REPORT IN ADC AND DAC

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1-Analog-to-digital converter:

Analog to Digital Converters (A/Ds)What Are They?

Some Properties Of A/D Converters

Where Do You Use A/Ds?You are at: Bits&Bytes - Interface Circuits - Analog To Digital Converters (A/Ds)Return to Table of Contents

A/D Converters

Analog-to-Digital converters - a.k.a. A/D converters - are widely used by many

engineers and scientists of all types, often without their realizing it. Whenever

they make a measurement of a voltage, and that measurement is taken into a

computer, an A/D is used.

If you're going to take measurements - and just about every engineer will do a

lot of that - then you will be better off if you understand some of the basic ideas

behind A/D converters. There are two simple goals for this lesson.

Given an A/D converter with a given range and number of bits,

To be able to calculate the resolution of the converter.

Given an A/D converter in the laboratory,

To be able to determine the resolution of the converter and the number of bits

used in the converter.

What Are A/D Converters?

A/D converters are electrical circuits that have the following characteristics.

The input to the A/D converter is a voltage.o A/D converters may be designed for voltages from 0 to 10v, from -5

to +5v, etc., but they almost always take a voltage input. (Some rare

exceptions occur with current inputs!) In any event, the input is ananalog voltage signal for most cases.

The output of the A/D converter is a binary signal, and that binary signalencodes the analog input voltage. So, the output is some sort of digital

number.
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A comparator can be used as a simple one-bit A/D converter. Although a

converter with just one bit isn't particularly useful, you can begin to see how an

A/D converter works by puttering with it for a moment. If you read the lesson on

comparators you encountered a simluation of a comparator. That simulator is

reproduced below. Click hereif you want to read the lesson on comparators.

Comparator Simulator

Sim1 Here is the comparator simulator. You can think of a comparator as a one-bit

A/D converter. The input is an analog signal, and the output is a one bit digital

representation of the analog signal. In the simulator, you can control a simulated

voltage source that is the input the the comparator, and the digital output bit is

indicated with a simulated LED. Notice the following.

The input can range from zero (0) to ten (10) volts. When the input voltage goes above five (5) volts, the output is a binary one

(1) and the LED lights. When the input voltage is less than five volts, the

output is a binary zero (0) and the LED does not light.

Properties of A/D Converters

The comparator simulation reveals a few important facts about A/D

converters.

An A/D converter has a range. The simulator has a range from 0v to 10v, ora total of ten (10) volts. The total range of an A/D is the difference

between the highest and lowest voltages the A/D can convert.

An A/D has a resolution that is determined by the largest count that theA/D's counter/register can hold.

The largest count is determined by the number of bits in the counter.
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o If there are N bits in the counter, the largest count is 2N-1.o In the comparator, there is only one bit, and the largest count is 1,

and there are only two different outputs that are possible.

Clearly, if you want a more accurate conversion the converter will need tohave a lot more than just one bit. Let's look at another simulation. This simulation

is a four-bit A/D converter.

Four Bit A/D Converter Simulator

Sim2 Here is a simulation of a four bit A/D converter. Note the following:

As in the comparator simulation, we assume that the input voltage can rangefrom zero (0) to ten (10) volts.

We have added some "fine control" with two buttons that "nudge" thevoltage up or down, but not beyond the 0-10v range.

Try the simulator first, and then we will examine what happens in a little more

detail.

Now, consider the following observations about the converter above.

There are four bits in the simulation converter. The range is from 0v to 10v, or 10v total range. With four bits, there are 16 different count values (0 through 15). Thus, 10v is divided into 16 different parts, each part being:

o 10/16 = 0.625 volts wide.Now, let's consider an example question.

Example


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E1 How many bits would you need to divide 10 v into .01 v intervals? To get the

answer to the question consider the following.

If you divide 10 v into .01 v intervals you need 1000 intervals.

If you need 1000 intervals you need to think about a power of 2 that islarger than 1000.

o The smallest power of 2 that is larger than 1000 is 210 which is equalto 1024.

That means that you need 10 bits in the converter, and the the count in thecounter/register will run from 0 to 1023.

And that leads us to observe that real converters often go to 10.23v, not10v because that gives perfect .01v increments between resolvable voltages.

o And another converter might run from -5.12v to +5.11v for the samereason.

Almost all A/D converters use a scheme in which the analog voltage is first

converted into a binary integer (a "count", as in the simulator above) when the

conversion is done. In some cases, there may be some software that gives you the

actual count - the binary integer. In other cases the conversion might be

converted - using software - to a a numerical value or a character representation

of a numerical value.

Example

E2 A GPIB (IEEE-488) voltmeter is used to measure a DC voltage. The

instrument uses an A/D converter that generates a binary number. Within the

instrument, that binary number is converted to a string of characters which is, in

turn, transmitted to a computer connected to the instrument.

To illustrate the concept in the example, consider the revised simulator

below. In this simulator, the conversion algorithm - from the count in the registerto an analog voltage - is given by:

Vmeas = Count*0.625o Note: .625 = 10/16 = Range/#Counts

Here is the simulation.


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Four Bit A/D Converter Simulator (Revised)

Sim3 Here is a revised simulation of a four bit A/D converter. Note the following:

Vmeas = Count*0.625o Vmeas is displayed on the simulation.

Of course, the simulation only raises a few more issues.

The largest issue is that the computed voltage is always lower than theactual voltage.

o The average error would probably be less if we used a different wayto compute the computed voltage.

o The formula for the computed voltage is: Vmeas = Count*0.625

Using this expression for the calculated voltage, we can plot the calculated

voltage as a function of the count. That's shown in the figure below.


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Even more interesting is the plot of the calculated voltage against the voltage

input that is being measured. That's shown next. We've also included a plot (the

blue line) that shows what the output would be ideally (And that might take many,

many bits in the converter!). Notice that the calculated voltage is always lower

than the voltage input using the calculation method we assumed above. Note also

that the largest error occurs just before the converter switches when the voltageis rising. For example, as the voltage rises from 0v to 3v, there is a time when the

converter output switches from 0v to 0.625v. The largest error occurs justbefore that point, so a bound on the error is:

Error < 0.625


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We can reduce the error if we calculate the voltage differently. We can

examine what happens if we use a different expression for the computed voltage.

We will use:

Vmeas = Count*0.625 + 0.3125The result is shown in the next simulator.

Now, here is a plot of the calculated voltage against the voltage input that is

measured. Notice that the error limit is half of what it was using the first

calculation method.


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The conclusion is that the way the voltage is computed can affect the average

error when an A/D is used to measure voltage values.

Whenever you buy an A/D converter, or a voltmeter, or a data acquisition

unit, you need to be cognizant of how the data presented to the user is actually

computed. That's not usually a problem in instruments, but there are A/D

computer cards that use the first method above to calculate voltage, and you

should be aware of that when it happens. It is less important when the number of

bits in the converter is higher, but when you have high requirements for accuractyyou should be thinking of what might be taking place.

The Effect of Number of Bits

The number of bits used in the counter also affects the accuracy of the

conversion. Again, we will use a simulation to show the effect of the number of

bits.

Six Bit A/D Converter Simulator

Sim4 Here is a simulation of a six bit A/D converter.


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Run the simulator, and compare results with the four bit simulators above.

We can think a little bit about error in an A/D. First, note that the errorlimit depends upon the range and the number of bits.

If there are N bits, the number of divisions is 2N-1. If the total range of voltage is VRange, then the size of a division is:

o SmallestDivision = VRange/2N The error is related to the Division size.

o If the calculated voltage is SmallestDivision*Count, the error is thesame size as the smallest division.

o If the calculated voltage is SmallestDivision*Count +SmallestDivision/2, the error is SmallestDivision/2, i.e. half the size

of the smallest division.

o See the simulations above for a better appreciation/understanding ofthe error.

We're not going to give you any more simulators with more bits. Actually,

we've almost reached the resolution limit for the screen. The simulators with the

"nudge buttons" just nudge the controls by a single pixel, and that is too much fora twelve bit converter, for example.

Example


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E3 A popular A/D board gives a count and requires you to perform the

computation shown in the line of C code shown below. The variable binary is the

count value that is returned.

MeasuredVolts = (((binary-2048)*20)/4096);

The A/D converts voltages from -10v to +10v. We can conclude the following.

o The converter has 12 bits. You get that conclusion by noting that thecount can vary from 0 to 4095. When the count is 0, MeasuredVolts =0.

Let's sum up a few points.

More is better when it comes to bits in an A/D. The indicated voltage willbe closer to the actual value of the voltage being measured when there are

more bits.

More is pricier when it comes to bits in an A/D. It takes more parts, andthey have to be made more accurately if there are more bits.

How Does An A/D Work?

While we have discussed A/D converters above, we haven't yet given you anyinsight into how you could build an A/D. Here we will discuss a simple way to build

an A/D. This might not be the fastest A/D possible, but it will start to give you

some insight into what happens inside an A/D.

The circuit is shown in the simulator below.

Simulator - Showing How You Might Construct An A/D

Sim 5 This simulator is a four bit A/D, and it consists of the following components.

A pulse generator that produces a sequence of 0's and 1's. A counter which counts the pulses and produces an increasing count.


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o The counter has a "Stop" input. When that input goes high, thecounter ceases to count.

A D/A which produces an analog signal proportional to the count output fromthe counter.

An adjustable input voltage source.

A comparator which produces a "1" when the D/A output is larger than theinput voltage.

o The output of the comparator is used to stop the counter.Here is the circuit.

Here is how the A/D Simulator works.

First, set a DC voltage from the adjustable source. Second, click the "Convert" button.

o The counter begins counting, and the count is displayed on the LEDsand the numerical value of the count is displayed.

o The digital count signals (four bits of signals in this case) form theinput to a D/A converter which produces an output voltage

proportional to the count.o The output voltage from the D/A is compared to the input voltage.o When the output voltage from the D/A becomes larger than the input

voltage the comparator develops a "Stop" signal that is used to stop

the counter.

o The count that remains in the counter is a digital representation ofthe input voltage.


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Try the simulator, using different voltages within the allowable range, i.e. 0-5v.

The simulator lets you see the inner workings of one type of A/D converter.

Note the following about any A/D converter.

The conversion takes time. In the simulator, there is a variable amount oftime until the counter reaches the correct count. We have slowed down the

simulator so you can see what happens, but even in the best A/Ds there is

some time that must elapse between the start of a conversion and the end

of a conversion. That time limits how many conversions can be done per

second. People have worked on that problem and there are other kinds of

converters that convert more quickly.

The conversion is not exact, and the accuracy depends upon the number ofbits in the counter.

The result of the conversion is an integer, and that integer still must betranslated into an equivalent voltage (although the conversion isn't hard to

do).

Practical A/Ds

Now, consider what happens in a typical application of an A/D. We'll look at a

voltmeter. In a voltmeter, this is what happens.

A voltage is applied to the voltmeter, and an A/D converts the voltage to acount.

The count is converted to a floating point number. The floating point number is displayed on an LCD or LED display.

If the voltmeter is connected to a computer (say through an IEEE-488 bus) the

following also takes place.

The floating point data is converted to a character representation totransmit over an IEEE-488 or internet connection.

You can see that there are a few conversions that have to take place in this

process. There are a number of other considerations here as well.


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The number of bits in the A/D converter will affect the accuracy of thevoltmeter. There is a lot of legend and lore in that area. Click hereto

examine that.

You need to be aware of how to make conversions. Actually, you need tobecome knowledgeable about the different representations as well as how toprogram those conversions in various programming environments like C, C++,

Visual Basic and LabView.

A/D converters are found in many places - including places where you might

not think that you would find them. Here are a few.

Voltmeters are digital today. To display a digital result for a voltagemeasurement the voltage is first converted to digital form in an A/D, and

then it is changed to a decimal format to be displayed.

A/Ds are used in digital thermometers, so if you've spent some time in thehospital, you've used an A/D.

And, you get the idea.

However, there is an important situation where you need to dig deeper into

how A/Ds operate, and how they interface with the software and hardware that isoften used in measurement and control situations. Let's think about a few typical

situations.

Assume that you are recording temperature at four points in a heat-treatingoven. You need to do the following.

o You need to get the data into a computer and you need to compute andrecord the average temperature (the four temperature data points).

You have three tanks used for chemical processing. You need to control thelevel of the liquid in the three tanks. Each tank has a small computer with anA/D board that measures and controls the liquid level in each tank and also

measures the temperature. Each computer has a network card that

connects it to an Ethernet LAN. There is a central computer on the LAN

and you need to send information from each of the control computers to the

central computer.
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o You need to take the data at each computer and you need to transmitit over the network to the central computer so that it can be

recorded there and be available for any computations that might be

necessary.

In both of these situations you need to consider how to manipulate the data

that you measure and want to store. Here are some of the considerations.

If you take data with an instrument connected to a computer (like a dataacquisition unit or a voltmeter) the instrument may be connected to the

computer with an IEEE-488 (GPIB) connection. (Click hereto learn more

about IEEE-488.) IEEE-488 connections have some considerations.

o Most IEEE-488 instruments convert data into strings of charactersand those strings are transmitted to the computer.

If you send data over a network, you must send strings of characters.The conclusion that you need to reach is that you need to be aware of how

data has to be converted in these kinds of situations. Let's look at the sequence

of operations you might face.

The A/D converter gets some raw data or information and it is in the formof an integer count. Often it is simply a binary number represented with

some fixed number of bits.

o The count could be a number like 10001000 (or 129 in decimalnumbers).

o If the A/D converter has eight (8) bits or less, the data will take asingle byte.

o If the A/D converter has more than eight bits (which is typical) thedata will take more than one byte. Usually, for most converters, the

data will take two bytes, since most converters are 10, 12 or more

bits.

The count is converted to a number that represents the voltage (or possiblysome other physical variable). That takes some computer code (And therewill probably be some sort of computing chip in the instrument.) and the

process results in a number that is probably a floating point number.

o The floating point number might be something like 3.1416v. If you transmit that floating point number you need to generate a string of

characters.
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o The string of characters might be something like a "3", a period ("."),a "1", a "4", etc.

o In many cases you may need to add one or more characters to signalthe end of a string. That could be a carriage return and a line feed,

for example.

Representing Instrument Data

Taking data with an instrument immediately leads you to consider several

things about data. Here is a sample.

If you take a lot of data, you need to know how the data is represented. If you take a lot of data, you need to know how the data is transmitted from

the instrument to a computer. If you take a lot of data, you need to know how the data you get will be

stored if you store it in a computer file.

Digital Voltmeters

Digital Voltmeters are a special case of A/Ds. Obviously, if voltage

measurements are taken and the results are displayed digitally with LED or LCD

displays, the instrument has to contain an A/D converter. Digital voltmeters have

some characteristics that you might need to understand. You canclick herefor

more material on digits in digital voltmeters.

Digital voltmeters usually have scales that are 0-0.3v, 0-3v, 0-30v, 0-300v,etc.

You need to learn a little terminology and the reasons for the terminology. Let's

take a look at a sample voltmeter.

Example

E4 Consider a voltmeter built around a 10 bit A/D converter. We will assume the

following.

The range of the voltmeter is from 0-3v, and it does DC voltagemeasurements. It does not measure negative voltages.
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Then, with 10 bits we can draw these inferences.

Ten bits will produce 210 intervals. That's 1024 intervals. If there are 1024 intervals over a range of 3v, each interval will be 3/1024 =

.00293v.

It is easier to compute the displayed voltage if the interval is adjusted to.003v.

o That would make the range 0-3.072v. (That's .003 x 1024.)o If you are measuring a voltage that varies around 3v, that would allow

you to keep the range the same, but still change the range when the

voltage got large enough. Manufacturers like to build in a little

"hysteresis" to prevent constant range changes in situations like that

and it might be especially hard on auto-ranging meters.

If you wanted to measure negative voltages and have the range be from -3vto +3v, you would have intervals of .006v, and the meter would measure from

-3.072v to +3.072v.

If you wanted to measure voltages on a 0-30v scale, you would probably use avoltage divider or some other way to reduce the voltage by a factor of

(exactly) 10 (i.e., multiply it by exactly 0.1) and then use the same converter

as on the 0-3v scale.

If we could use a 12 bit A/D, then some conclusions would change.

Twelve bits will produce 212 intervals. That's 4096 intervals. If there are 4096 intervals over a range of 3v, each interval will be 3/4096

= .000732v.

It is easier to compute the displayed voltage if the interval is adjusted to.0075v.

o That would make the range 0-3.072v - just as it was in the case of the10 bit converter,

o That produces the same advantages as you had with the 10 bitconverter.

If you wanted to measure negative voltages and have the range be from -3vto +3v, you would have intervals of .0015v, and the meter would measure

from -3.072v to +3.072v.

At this point, you should have a good idea about how the number of bits in an

A/D converter determines the accuracy of the converter - i.e. the resolution of

the converter.


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You also need to learn how to determine the resolution of an instrument in the

laboratory, and relate the resolution of lab instruments to what you know about

the number of bits in a converter. You canclick herefor an laboratory exercise

which leads you through getting the number of bits in the A/D converter inside a

voltmeter.
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2-Digital-to-analog converter:

Overview:

Ideally sampled signal.

A DAC converts anabstractfinite-precision number (usually afixed-pointbinary number) into a

physical quantity (e.g., avoltageor apressure). In particular, DACs are often used to convert

finite-precisiontime seriesdata to a continually varying physicalsignal.

A typical DAC converts the abstract numbers into a concrete sequence ofimpulsesthat are then

processed by areconstruction filterusing some form ofinterpolationto fill in data between theimpulses. Other DAC methods (e.g., methods based ondelta-sigma modulation) produce apulse-

density modulatedsignal that can then be filtered in a similar way to produce a smoothly varying

signal.

As per theNyquistShannon sampling theorem, a DAC can reconstruct the original signal from

the sampled data provided that its bandwidth meets certain requirements (e.g., abasebandsignal

withbandwidthless than theNyquist frequency). Digital sampling introducesquantization error

that manifests as low-level noise added to the reconstructed signal.

Practical operation:

Piecewise constant output of a conventional practical DAC.

Instead of impulses, usually the sequence of numbers update the analogue voltage at uniformsampling intervals.
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These numbers are written to the DAC, typically with aclock signalthat causes each number to

belatchedin sequence, at which time the DAC output voltage changes rapidly from the previousvalue to the value represented by the currently latched number. The effect of this is that the

output voltage is heldin time at the current value until the next input number is latched resulting

in apiecewise constantor 'staircase' shaped output. This is equivalent to azero-order hold

operation and has an effect on the frequency response of the reconstructed signal.

The fact that DACs output a sequence of piecewise constant values (known as zero-order holdinsample data textbooks) orrectangular pulsescauses multiple harmonics above theNyquist

frequency. Usually, these are removed with alow pass filteracting as a reconstruction filter in

applications that require it.

Applications:

A simplified functional diagram of an 8-bit DAC

Audio:

Most modern audio signals are stored in digital form (for exampleMP3sandCDs) and in order

to be heard through speakers they must be converted into an analog signal. DACs are thereforefound inCD players,digital music players, and PCsound cards.

Specialist standalone DACs can also be found in high-endhi-fisystems. These normally take thedigital output of a compatibleCD playeror dedicatedtransport(which is basically a CD player

with no internal DAC) and convert the signal into an analogline-leveloutput that can then be fed

into anamplifierto drive speakers.

Similar digital-to-analog converters can be found indigital speakerssuch asUSBspeakers, and

insound cards.

InVoIP(Voice over IP) applications, the source must first be digitized for transmission, so it

undergoes conversion via anAnalog-to-Digital Converter, and is then reconstructed into analog

using a DAC on the receiving party's end.
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Top-loading CD player and external digital-to-analog converter.

Video:

Video sampling tends to work on a completely different scale altogether thanks to the highlynonlinear response both of cathode ray tubes (for which the vast majority of digital video

foundation work was targeted) and the human eye, using a "gamma curve" to provide anappearance of evenly distributed brightness steps across the display's full dynamic range - hence

the need to use RAMDACs in computer video applications with deep enough colour resolutionto make engineering a hardcoded value into the DAC for each output level of each channel

impractical (e.g. an Atari ST or Sega Genesis would require 24 such values; a 24-bit video card

would need 768...). Given this inherent distortion, it is not unusual for a television or videoprojector to truthfully claim a linear contrast ratio (difference between darkest and brightest

output levels) of 1000:1 or greater, equivalent to 10 bits of audio precision even though it may

only accept signals with 8-bit precision and use an LCD panel that only represents 6 or 7 bits per

channel.

Video signals from a digital source, such as a computer, must be converted to analog form if theyare to be displayed on an analog monitor. As of 2007, analog inputs were more commonly used

than digital, but this changed asflat panel displayswithDVIand/orHDMIconnections became

more widespread.[citation needed] A video DAC is, however, incorporated in any digital video player

with analog outputs. The DAC is usually integrated with somememory(RAM), which containsconversion tables forgamma correction, contrast and brightness, to make a device called a

RAMDAC.

A device that is distantly related to the DAC is thedigitally controlled potentiometer, used to

control an analog signal digitally.

Mechanical:

An unusual application of digital-to-analog conversion was thewhiffletreeelectromechanicaldigital-to-analog converter linkage in theIBM Selectrictypewriter.[citation needed]
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DAC types:

The most common types of electronic DACs are:

Thepulse-width modulator, the simplest DAC type. A stablecurrentorvoltageisswitched into a low-passanalog filterwith a duration determined by the digital inputcode. This technique is often used for electric motor speed control, but has many other

applications as well.

Oversampling DACs or interpolating DACs such as the delta-sigma DAC, use a pulsedensity conversion technique. Theoversamplingtechnique allows for the use of a lower

resolution DAC internally. A simple1-bit DACis often chosen because the oversampled

result is inherently linear. The DAC is driven with apulse-density modulatedsignal,created with the use of alow-pass filter,step nonlinearity(the actual 1-bit DAC), and

negative feedbackloop, in a technique calleddelta-sigma modulation. This results in an

effectivehigh-pass filteracting on thequantization (signal processing)noise, thus

steering this noise out of the low frequencies of interest into the megahertz frequencies of

little interest, which is callednoise shaping. The quantization noise at these highfrequencies is removed or greatly attenuated by use of an analog low-pass filter at the

output (sometimes a simpleRC low-pass circuitis sufficient). Most very high resolutionDACs (greater than 16 bits) are of this type due to its highlinearityand low cost. Higher

oversampling rates can relax the specifications of the output low-pass filter and enable

further suppression of quantization noise. Speeds of greater than 100 thousand samplesper second (for example, 192 kHz) and resolutions of 24 bits are attainable with delta-

sigma DACs. A short comparison withpulse-width modulationshows that a1-bit DAC

with a simple first-orderintegratorwould have to run at 3 THz (which is physically

unrealizable) to achieve 24 meaningful bits of resolution, requiring a higher-order low-pass filter in the noise-shaping loop. A single integrator is alow-pass filterwith a

frequency responseinversely proportional to frequency and using one such integrator inthe noise-shaping loop is a first order delta-sigma modulator. Multiple higher ordertopologies (such asMASH) are used to achieve higher degrees of noise-shaping with a

stable topology.

The binary-weighted DAC, which contains oneresistororcurrent sourcefor each bit ofthe DAC connected to a summing point. These precise voltages or currents sum to thecorrect output value. This is one of the fastest conversion methods but suffers from poor

accuracy because of the high precision required for each individual voltage or current.

Such high-precision resistors and current sources are expensive, so this type of converteris usually limited to 8-bit resolution or less.

TheR-2R ladderDAC which is a binary-weighted DAC that uses a repeating cascadedstructure of resistor values R and 2R. This improves the precision due to the relative easeof producing equal valued-matched resistors (or current sources). However, wideconverters perform slowly due to increasingly large RC-constants for each added R-2R

link.

Thethermometer-codedDAC, which contains an equal resistor or current-sourcesegment for each possible value of DAC output. An 8-bit thermometer DAC would have255 segments, and a 16-bit thermometer DAC would have 65,535 segments. This is

perhaps the fastest and highest precision DAC architecture but at the expense of high
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cost. Conversion speeds of >1 billion samples per second have been reached with this

type of DAC.

Hybrid DACs, which use a combination of the above techniques in a single converter.Most DAC integrated circuits are of this type due to the difficulty of getting low cost,

high speed and high precision in one device.

oThe segmented DAC, which combines the thermometer-coded principle for themost significant bits and the binary-weighted principle for the least significant

bits. In this way, a compromise is obtained between precision (by the use of the

thermometer-coded principle) and number of resistors or current sources (by theuse of the binary-weighted principle). The full binary-weighted design means 0%

segmentation, the full thermometer-coded design means 100% segmentation.

DAC performance:

DACs are very important to system performance. The most important characteristics of these

devices are:

Resolution: This is the number of possible output levels the DAC is designed toreproduce. This is usually stated as the number ofbitsit uses, which is the base twologarithmof the number of levels. For instance a 1 bit DAC is designed to reproduce 2

(21) levels while an 8 bit DAC is designed for 256 (2

8) levels. Resolution is related to the

Effective number of bitswhichis a measurement of the actual resolution attained by theDAC. Resolution determinescolor depthin video applications andaudio bit depthin

audio applications.

Maximumsampling rate: This is a measurement of the maximum speed at which theDACs circuitry can operate and still produce the correct output. As stated in theNyquistShannon sampling theoremdefines a relationship between the sampling frequency and

bandwidthof the sampled signal. Monotonicity: This refers to the ability of a DAC's analog output to move only in the

direction that the digital input moves (i.e., if the input increases, the output doesn't dip

before asserting the correct output.) This characteristic is very important for DACs used

as a low frequency signal source or as a digitally programmable trim element.

THD+N: This is a measurement of the distortion and noise introduced to the signal bythe DAC. It is expressed as a percentage of the total power of unwantedharmonic

distortionand noise that accompany the desired signal. This is a very important DAC

characteristic for dynamic and small signal DAC applications.

Dynamic range: This is a measurement of the difference between the largest andsmallest signals the DAC can reproduce expressed indecibels. This is usually related to

resolution andnoise floor.

Other measurements, such asphase distortionandjitter, can also be very important for some

applications, some of which (e.g. wireless data transmission, composite video) may even rely onaccurate production of phase-adjusted signals.

Linear PCM audio sampling usually works on the basis of each bit of resolution being equivalentto 6 decibels of amplitude (a 2x increase in volume or precision).
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Non-linear PCM encodings (A-law / mu-law, ADPCM, NICAM) attempt to improve their

effective dynamic ranges by a variety of methods - logarithmic step sizes between the outputsignal strengths represented by each data bit (trading greater quantisation distortion of loud

signals for better performance of quiet signals)

DAC figures of merit:

Static performance:o Differential nonlinearity(DNL) shows how much two adjacent code analog

values deviate from the ideal 1 LSB step.[1]

o Integral nonlinearity(INL) shows how much the DAC transfer characteristicdeviates from an ideal one. That is, the ideal characteristic is usually a straightline; INL shows how much the actual voltage at a given code value differs from

that line, in LSBs (1 LSB steps).

o Gaino Offseto Noise is ultimately limited by thethermal noisegenerated by passive components

such as resistors. For audio applications and in room temperatures, such noise is

usually a little less than 1V(microvolt) ofwhite noise. This limits performanceto less than 20~21 bits even in 24-bit DACs.

Frequency domain performanceo Spurious-free dynamic range(SFDR) indicates in dB the ratio between the

powers of the converted main signal and the greatest undesired spur.

o Signal-to-noise and distortion ratio (SNDR) indicates in dB the ratio between thepowers of the converted main signal and the sum of the noise and the generated

harmonic spurs

o i-th harmonic distortion (HDi) indicates the power of the i-th harmonic of theconverted main signal

o Total harmonic distortion(THD) is the sum of the powers of all HDio If the maximum DNL error is less than 1 LSB, then the D/A converter is

guaranteed to be monotonic. However, many monotonic converters may have a

maximum DNL greater than 1 LSB.

Time domain performance:o Glitch energyo Response uncertaintyo Time nonlinearity (TNL)
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