2ndyr dig comm lect1 day1

8/4/2019 2ndYr Dig Comm Lect1 Day1

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Analog signal processing Vs Digital Signal Processing

In analog processing system the information is represented as an analog quantity. ie; something

that varies continuously with time. This "something" can be voltage , current etc.. . for example, the

signal that comes out of a microphone is analog in nature. The varying voltage from the microphone

is processed using an analog signal processing system known as "amplifier" , and reproduced

through a speaker.

Where in Digital Signal Processing system , the information is represented in digital format.

The signals that are to be processed is converted into numerical form before any processing. This

conversion is known as sampling. The information contained in an analog signal is first converted to

digital samples which are equally spaced in time. The figure below shows an analog signal and its

sampled version.

Each of these samples are converted in to a numerical value and stored in the computer's memory.

Processing is then done on these samples. The sampling in a Digital Signal Processing system is

governed by a theorem known as sampling theorem.

Sampling theorem

According to sampling theorem, an analog signal can be exactly reconstructed from its samples

if the sampling rate is at least twice the highest frequency component present in the signal. This

means, if the signal contains the highest frequency component of 1KHz, the sampling rate must be

at least 2 Kilo Samples/ Second. This sampling rate is also known as Nyquist rate. What if

sampling theorem is not satisfied..? violation of sampling theorem means , sampling the signal at a

sample rate less than Nyquist rate. This leads to unacceptable distortion in the signal . this distortion

is known as aliasing. Due to aliasing , the components present in the input signal whose frequency

is higher Nyquist frequency will be sampled as a signal of lower frequency. And this aliased

samples in turn corrupts the original signal which is lower than Nyquist frequency. Due to the

presence of aliasing , a signal that contains frequency components higher than Nyquist frequencycan not be reconstructed from it's samples. The effect of aliasing is shown in the figure below.


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The signal shown in black color is the original signal. While the signal shown in violate color is the

aliased signal because of improper sampling. From the figure it is obvious that the aliased signal

will be present in the sampled data as a lower frequency signal. And this will affect the original

content at that frequency.

It should be noted that the information in between two consecutive samples is lost forever. But

still the entire signal can be reconstructed from the samples as long as Sampling theorem is

satisfied.

Sampling and quantization

Sampling can be viewed theoretically as multiplying the original signal with a train of pulses

with unit amplitude. This leaves the original signal with information at descrete points with

magnitude of signal present in the original signal at that position. This is illustrated in the figurebelow.

This can be implemented using an AND gate as shown below.


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Now samples of the input signal is taken at discrete points. But in order to manipulate the signal

with a microprocessor or micro controller, these pulses has to be converted in to numbers. Before

this conversion, the pulses are quantized to some finite number of quantization levels. For example,

if the quantization levels are 0,1,2,3, etc... , a pulse with magnitude between 1 and 2 will be

quantized to either 1 or 2. This in fact introduces a noise in the sampled signal. Such noise in known

as quantization noise.

Quantization (signal processing)

Discrete signal

Digital signal (after quantization has occurred)

In digital signal processing, quantization is the process of approximating a continuous range of

values (or a very large set of possible discrete values) by a relatively small set of discrete symbols orinteger values. More specifically, a signal can be multi dimensional and quantization need not be

applied to all dimensions. Discrete signals (a common mathematical model) need not be quantized,

which can be a point of confusion.

A common use of quantization is in the conversion of a discrete signal (a sampledcontinuous

signal) into a digital signal by quantizing. Both of these steps (sampling and quantizing) are

performed in analog to digital converters with the quantization level specified inbits. A specific

example would be compact disc (CD) audio which is sampled at 44,100Hz and quantized with 16

bits (2 bytes) which can be one of 65,536 (i.e. 216) possible values per sample.

In electronics, adaptive quantization is a quantization process that varies the step size based on thechanges of the input signal, as a means of efficient compression.Two approaches commonly used

are forward adaptive quantization and backward adaptive quantization.
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Mathematical description

Quantization is referred to as scalar quantization, since it operates on scalar (as opposed to multi

dimensionalvector) input data. In general, a scalar quantization operator can be represented as

whereng an integer result that is sometimes referred to as the quantization index,

f(x) and g(i) are arbitrary real valued functions.

The integer valued quantization index i is the representation that is typically stored or transmitted,

and then the final interpretation is constructed using g(i) when the data is later interpreted.

In computer audio and most other applications, a method known as uniform quantization is the most

common. There are two common variations of uniform quantization, called mid rise and mid tread

uniform quantizers.

Ifx is a real valued number between 1 and 1, a mid rise uniform quantization operator that uses Mbits of precision to represent each quantization index can be expressed as

.

In this case thef(x) and g(i) operators are just multiplying scale factors (one multiplier being the

inverse of the other) along with an offset in g(i) function to place the representation value in the

middle of the input region for each quantization index. The value 2 (M 1) is often referred to as

the quantization step size. Using this quantization law and assuming thatquantization noise is

approximately uniformly distributed over the quantization step size (an assumption typicallyaccurate for rapidly varyingx or highM) and further assuming that the input signalx to be

quantized is approximately uniformly distributed over the entire interval from 1 to 1, the signal to

noise ratio (SNR) of the quantization can be computed as

.

From this equation, it is often said that the SNR is approximately 6 dB per bit.

For mid tread uniform quantization, the offset of 0.5 would be added within the floor function

instead of outside of it.

Sometimes, mid rise quantization is used without adding the offset of 0.5. This reduces the signal to

noise ratio by approximately 6.02 dB, but may be acceptable for the sake of simplicity when the step

size is small.

In digital telephony, two popular quantization schemes are the 'A law ' (dominant in Europe) and '

law' (dominant inNorth AmericaandJapan). These schemes map discrete analog values to an 8 bit

scale that is nearly linear for small values and then increases logarithmically as amplitude grows.

Because the human ear's perception ofloudness is roughly logarithmic, this provides a higher signal

to noise ratio over the range of audible sound intensities for a given number of bits.
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NyquistShannon sampling theorem

Fig: Hypothetical spectrum of a bandlimited signal as a function of frequency

The NyquistShannon sampling theorem is a fundamental result in the field ofinformation

theory, in particulartelecommunications andsignal processing.Samplingis the process of

converting a signal (for example, a function of continuous time or space) into a numeric sequence (a

function of discrete time or space). The theorem states:[1]

If a functionx(t) contains no frequencies higher thanBcps, it is completely determined

by giving its ordinates at a series of points spaced 1/(2B) seconds apart.

In essence the theorem shows that an analog signal that has been sampled can be perfectly

reconstructed from the samples if the sampling rate exceeds 2B samples per second, whereB is the

highest frequency in the original signal. If a signal contains a component at exactlyB hertz, then

samples spaced at exactly 1/(2B) seconds do not completely determine the signal, Shannon's

statement notwithstanding.

More recent statements of the theorem are sometimes careful to exclude the equality condition; that

is, the condition is ifx(t) contains no frequencies higher than or equal toB; this condition is

equivalent to Shannon's except when the function includes a steady sinusoidal component at exactly

frequencyB.

The assumptions necessary to prove the theorem form a mathematical model that is only an

idealization of any real world situation. The conclusion that perfect reconstruction is possible is

mathematically correct for the model but only an approximation for actual signals and actualsampling techniques.

The theorem also leads to a formula for reconstruction of the original signal. The constructive proof

of the theorem leads to an understanding of the aliasing that can occur when a sampling system does

not satisfy the conditions of the theorem.

The NyquistShannon sampling theorem is also known to be a sufficient condition. The field of

Compressed sensing provides a stricter sampling condition when the underlying signal is known to

be sparse. Compressed sensing specifically yields a sub Nyquist sampling criterion.
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Downsampling

When a signal isdownsampled, the sampling theorem can be invoked via the artifice of resampling

a hypothetical continuous time reconstruction. The Nyquist criterion must still be satisfied withrespect to the new lower sampling frequency in order to avoid aliasing. To meet the requirements of

the theorem, the signal must usually pass through a low pass filter of appropriate cutoff frequency

as part of the downsampling operation. This low pass filter, which prevents aliasing, is called an

anti aliasing filter .

Critical frequency

Fig: A family of sinusoids at the critical frequency, all having the same sample sequences of alternating +1

and 1. That is, they all are aliases of each other, even though their frequency is not above half the sample

rate.

The Nyquist rate is defined as twice the bandwidth of the continuous time signal. The sampling

frequency must be strictly greaterthan the Nyquist rate of the signal to achieve unambiguous

representation of the signal. This constraint is equivalent to requiring that the system's Nyquist

frequency (also known as critical frequency, and equal to half the sample rate) be strictly greater

than the bandwidth of the signal. If the signal contains a frequency component at precisely the

Nyquist frequency then the corresponding component of the sample values cannot have sufficient

information to reconstruct the Nyquist frequency component in the continuous time signal because

of phase ambiguity. In such a case, there would be an infinite number of possible and different

sinusoids (of varying amplitude and phase) of the Nyquist frequency component that are

represented by the discrete samples.

As an example, consider this family of signals at the critical frequency:

Where the samples

are in every case just alternating 1 and +1, for any phase . There is no way to determine either the

amplitude or the phase of the continuous time sinusoid x(t) thatx(nT) was sampled from. This

ambiguity is the reason for the strictinequality of the sampling theorem's condition.
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Analog to digital converterAn analog to digital converter (abbreviated ADC, A/D or A to D) is a device which converts

continuoussignals to discretedigital numbers. The reverse operation is performed by a digital to

analog converter (DAC).

Typically, an ADC is anelectronic device that converts an input analog voltage (or current) to a

digital number. 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, such

as binary, Gray code or two's complement binary.

Concepts

Resolution

The resolution of the converter indicates the number of discrete values it can produce over the rangeof analog values. The values are usually stored electronically in binaryform, so the resolution is

usually expressed in bits. 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 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 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 per step (volts per output code),

EFSR

is the full scale voltage range = VRefHi

VRefLo

,

M is the ADC's resolution in bits, and

N is the number of intervals, given by the number of available levels (output codes), which is:

N= 2M

Some examples may help:

Example 1

Full scale measurement range = 0 to 10 volts

ADC resolution is 12 bits: 212 = 4096 quantization levels (codes)

ADC voltage resolution is: (10V 0V) / 4096 codes = 10V / 4096 codes

0.00244 volts/code 2.44 mV/code
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Example 2

Full scale measurement range = 10 to +10 volts


ADC voltage resolution is: (10V ( 10V)) / 16384 codes = 20V / 16384 codes

0.00122 volts/code 1.22 mV/code

Example 3

Full scale measurement range = 0 to 8 volts


ADC voltage resolution is: (8 V 0 V)/8 codes = 8 V/8 codes = 1 volts/code = 1000

mV/code

In practice, the smallest output code ("0" in an unsigned system) represents a voltage range which is

0.5X of the ADC voltage resolution (Q)(meaning half wide of the ADC voltage Q ) while the

largest output code represents a voltage range which is 1.5X of the ADC voltage resolution

(meaning 50% wider than the ADC voltage resolution). The otherN 2 codes are all equal in width

and represent the ADC voltage resolution (Q) calculated above. Doing this centers the code on aninput voltage that represents theMth division of the input voltage range. For example, in Example 3,

with the 3 bit ADC spanning an 8 V range, each of the Ndivisions 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 Msteps are

equal width. This practice is called "Mid Rise with Offset" operation.

In practice, the useful resolution of a converter is limited by the best signal to noise ratio 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 animportant contributing factor towards the overall SNR.

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 piecewise constant and therefore non linear operation). The term linearas 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.,
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that the output value kis used for the range of input values from

m(k+ b)

to

m(k+ 1 + b),

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 .

Non linear ADCs

If theprobability density function of a signal being digitized isuniform, then the signal to noise

ratio relative to the quantization noise is the best possible. Because this is often not the case, 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 companders used in some tape recorders and other

communication systems, and is related to entropymaximization. (Never confuse companders 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 systems to increase the dynamic

range of the representable values while retaining fine granular fidelity in the low amplitude region.

An eight bit a law or the law logarithmic ADC covers the widedynamic rangeand 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 linearityis intrinsic to any analog to digital conversion. There is also a so called

aperture errorwhich is due to a clockjitterand is revealed when digitizing a time variant signal

(not a constant value).

These errors are measured in a unit called theLSB, 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

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 auniform distribution. Its RMS value is

thestandard deviationof this distribution, given by . In the eight bitADC 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.
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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, resulting in 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) anddifferential 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.

Digital Ramp ADC

Conversion from analog to digital form inherently involves comparator action where the value of theanalog voltage at some point in time is compared with some standard. A common way to do that is

to apply the analog voltage to one terminal of a comparator and trigger a binary counter which

drives a DAC. The output of the DAC is applied to the other terminal of the comparator. Since the

output of the DAC is increasing with the counter, it will trigger the comparator at some point when

its voltage exceeds the analog input. The transition of the comparator stops the binary counter,

which at that point holds the digital value corresponding to the analog voltage.
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Successive Approximation ADC

Illustration of 4 bit SAC with 1 volt step size (after Tocci, Digital Systems).

The successive approximation ADC is much

faster than the digital ramp ADC because it uses

digital logic to converge on the value closest to

the input voltage. A comparatorand a DAC areused in the process.
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Flash ADCIllustrated is a 3 bit flash ADC with resolution 1 volt (after Tocci). The resistor net and comparators

provide an input to the combinational logic circuit, so the conversion time is just the propagation

delay through the network it is not limited by the clock rate or some convergence sequence. It is

the fastest type of ADC available, but requires a comparator for each value of output (63 for 6 bit,

255 for 8 bit, etc.) Such ADCs are available in IC form up to 8 bit and 10 bit flash ADCs (1023

comparators) are planned. The encoder logic executes a truth table to convert the ladder of inputs to

the binary number output.
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Digital to analog converterIn electronics, a digital to analog converter (DAC or D to A ) is a device for converting a digital

(usually binary) code to an analog signal (current, voltage or electric charge).

Ananalog to digital converter (ADC) performs the reverse operation.

Basic ideal operation

Ideally sampled signal. Signal of a typical interpolating DAC output

A DAC converts an abstract finite precision number (usually a fixed point binary number) into a

concrete physical quantity (e.g., avoltage or a pressure). In particular, DACs are often used to

convert finite precision time series data to a continually varying physical signal.

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

processed by a reconstruction filter uses some form ofinterpolation to fill in data between the

impulses. Other DAC methods (e.g., methods based onDelta sigma modulation ) produce a pulse

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

signal.

By theNyquistShannon sampling theorem, sampled data can be reconstructed perfectly providedthat its bandwidth meets certain requirements (e.g., a baseband signal withbandwidth less than the

Nyquist frequency). However, even with an ideal reconstruction filter, digital sampling introduces

quantization error that makes perfect reconstruction practically impossible. Increasing the digital

resolution (i.e., increasing the number ofbits used in each sample) or introducing samplingdither

can reduce this error.

Practical operation

Instead of impulses, usually the sequence of numbers update the analogue voltage at uniform

sampling intervals.

These numbers are written to the DAC, typically with a clock signal that causes each number to be

latched in sequence, at which time the DAC output voltage changes rapidly from the previous value

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

constant or 'staircase' shaped output. This is equivalent to azero order hold operation and has an

effect on the frequency response of the reconstructed signal.
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Piecewise constant signal typical of a zero order (non interpolating) DAC output.

The fact that practical DACs output a sequence of piecewise constant values or rectangular pulses

would cause multiple harmonics above the nyquist frequency. These are typically removed with a

low pass filter acting as a reconstruction filter.

However, this filter means that there is an inherent effect of the zero order hold on the effective

frequency response of the DAC resulting in a mild roll off of gain at the higher frequencies (often a

3.9224 dB loss at the Nyquist frequency) and depending on the filter, phase distortion. This high

frequency roll off is the output characteristic of the DAC, and is not an inherent property of the

sampled data.

Applications

Audio

Most modern audio signals are stored in digital form (for example MP3s and CDs) and in order to

be heard through speakers they must be converted into an analog signal. DACs are therefore found

in CD players,digital music players, and PC sound cards.

Specialist stand alone DACs can also be found in high end hi fi systems. These normally take the

digital output of aCD player(or dedicated transport) and convert the signal into aline level output

that can then be fed into apre amplifier stage.

Similar digital to analog converters can be found in digital speakerssuch as USB speakers, and in

sound cards.

Video

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 are more commonly used than

digital, but this may change as flat panel displayswith DVIand/or HDMI connections become more

widespread. A video DAC is, however, incorporated in any Digital Video Player with analog

outputs. The DAC is usually integrated with some memory (RAM), which contains conversion

tables forgamma correction, contrast and brightness, to make a device called aRAMDAC.

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

an analog signal digitally.
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DAC types

The most common types of electronic DACs are:

Four Bit D/A ConverterOne way to achieveD/A conversion is to use asumming amplifier.

This approach is not satisfactory for a large number of bits because it requires too much

precision in the summing resistors. This problem is overcome in the R 2R network DAC.

Summing Amplifier

This is an example of an inverting amplifier

of gain=1 with multiple inputs. More than

two inputs can be used, for example in an

audio mixer circuit. The input resistors can

be unequal, giving a weighted sum.
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R 2R Ladder DAC

The summing amplifier with the R 2R ladder of

resistances shown produces the output

where the D's take the value 0 or 1. The digital inputs

could be TTL voltages which close the switcheson a

logical 1 and leave it grounded for a logical 0. This is

illustrated for 4 bits, but can be extended to any number

with just the resistance values R and 2R.

R 2R Ladder DAC Details

the Pulse Width Modulator, the simplest DAC type. A stable current or voltage is switched

into a low pass analog filter with a duration determined by the digital input code. This

technique is often used for electric motor speed control, and is now becoming common in

high fidelity audio.

Oversampling DACs or Interpolating DACs such as the Delta Sigma DAC , use a pulse

density conversion technique. Theoversampling technique allows for the use of a lower

resolution DAC internally. A simple 1 bit DAC is often chosen because the oversampled

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

feedbackloop, in a technique called delta sigma modulation . This results in an effective

high pass filter acting on the quantization (signal processing) noise, thus steering this noise

out of the low frequencies of interest into the high frequencies of little interest, which is

called noise shaping (very high frequencies because of the oversampling). The quantization

noise at these high frequencies are removed or greatly attenuated by use of an analog low

pass filter at the output (sometimes a simple RC low pass circuit is sufficient). Most veryhigh resolution DACs (greater than 16 bits) are of this type due to its high linearity and low

cost. Higher oversampling rates can either relax the specifications of the output low pass

filter and enable further suppression of quantization noise. Speeds of greater than 100

thousand samples per second (for example, 192kHz) and resolutions of 24 bits are attainable

with Delta Sigma DACs. A short comparison with pulse width modulation shows that a1 bit

DAC with a simple first order integrator would 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 a low pass filter with afrequency

response inversely proportional to frequency and using one such integrator in the noise

shaping loop is a first order delta sigma modulator. Multiple higher order topologies (such asMASH) are used to achieve higher degrees of noise shaping with a stable topology.

the Binary Weighted DAC, which contains one resistor or current source for each bit of the

DAC connected to a summing point. These precise voltages or currents sum to the correct

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 converter is usually

limited to 8 bit resolution or less.

the R 2R ladder DAC, which is a binary weighted DAC that uses a repeating cascaded

structure of resistor values R and 2R. This improves the precision due to the relative ease of

producing equal valued matched resistors (or current sources). However, wide convertersperform slowly due to increasingly large RC constants for each added R 2R link.

the Thermometer coded DAC, which contains an equal resistor or current source segment

for each possible value of DAC output. An 8 bit thermometer DAC would have 255

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 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.

the Segmented DAC, which combines the thermometer coded principle for the mostsignificant 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 the use 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 at the beginning of the analog signal chain, which makes them 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 to reproduce.

This is usually stated as the number ofbits it uses, which is the base twologarithm of the
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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 (28) levels. Resolution is related to the Effective Number of

Bits (ENOB) which is a measurement of the actual resolution attained by the DAC.

Maximum sampling frequency: This is a measurement of the maximum speed at which the

DACs circuitry can operate and still produce the correct output. As stated in the Nyquist

Shannon sampling theorem, a signal must be sampled at over twice thefrequency of thedesired signal. For instance, to reproduce signals in all theaudible spectrum, which includes

frequencies of up to 20 kHz, it is necessary to use DACs that operate at over 40 kHz. The

CD standard samples audio at 44.1 kHz, thus DACs of this frequency are often used. A

common frequency in cheap computer sound cards is 48 kHz many work at only this

frequency, offering the use of other sample rates only through (often poor) internal

resampling.

monotonicity: This refers to the ability of DACs analog output to increase with an increase

in digital code or the converse. 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 by the

DAC. It is expressed as a percentage of the total power of unwantedharmonicdistortion and

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 and smallest

signals the DAC can reproduce expressed in decibels. This is usually related to DAC

resolution and noise floor.

Other measurements, such asPhase distortion and Sampling Period Instability, can also be very

important for some applications.
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2ndyr dig comm lect1 day1

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