General specifications of Data Converter

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Mrs. Vijaylakshmi S. JigajinniDept. of Instrumentation TechnologyBasaveshwar Engg. College,Bagalkot-587102

Fundamentals of Sampled Data Systems

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Analog-to-Digital converters (ADCs) translate analog quantities, wich are characteristic of most phenomen in the ‘’real world’’ to digital language, used in information processing, computing, data transmission, and control systems

Digital-to-Analog converters (DACs) are used in transforming transmitted or stored data, or the results of digital processing, back to ‘’real world’’ variables for control, information display, or further analog processing

General Specifications 1. Accuracy2. Error3. Linearity4. Resolution 5. Common mode rejection6. Monotonicity7. Code elongation/code

skipping8. Glitches9. Deglitchers10. High frequency roll off11. Conversion time

12. Conversion speed13. Cross talk14. Quantization error15. ADC dynamic specifications

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1. Accuracy:– Degree of conformity of a digital code representing the analogue voltage to its actual

(true) value;– Can express as the “degree of truth”.

Defn: closeness with which converters output approaches a true or standard value. It is usually expressed in terms of LSB.

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• Absolute accuracy is the measure of the DAC output voltage with respect to its expected value.

• Relative accuracy is the deviation of the actual from the ideal output voltage as a fraction of the full-scale voltage.

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Sources of Static Error

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2. Error Defn: deviation of converters output from actual output expected.

Static errors, that is those errors that affect the accuracy of the converter when it is converting static (dc) signals, can be completely described by just four terms.

These are :

Each can be expressed in LSB units or sometimes as a percentage of the FSR

offset error, gain error, integral nonlinearity and

differential nonlinearity.

Offset Error- ADC

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Nominal Offset Point

Actual Offset Point

001

010

011

000

Ideal Diagram

ActualDiagram

0 1 2 3

LSB21

LSB411Offset Error

Analog Output Value

Dig

ital O

utpu

t Cod

e

The offset error is defined as the difference between the nominal and actual offset points.

For a zero input if the output is non-zero then there is a offset error

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Digital Input

Desired/Ideal OutputOutput Voltage

Positive Offset

Negative Offset

In bipolar systems, the offset error shifts the transfer function but does not reduce the number of available codes.

Offset Error - DAC

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1

2

3

0

Ideal Diagram

Actual Diagram

000 001 010 011

LSB411

Digital Input Code

Offset Error

Nominal Offset Point

Actual Offset Point

Ana

log

Out

put V

alue

(LS

B)

For a DAC it is the step value when the digital input is zero. This error affects all codes by the same amount and can usually be compensated for by a trimming process. If trimming is not possible, this error is referred to as the zero-scale error.

Offset error occurs when the DAC output is not 0 V when the input code is all 0s.

Gain Error - ADC

10

101

110

111

000

Ideal Diagram

Actual Diagram

0 5 6 7

LSB21

Analog Input Value (LSB)

Dig

ital O

utpu

t Cod

e

Nominal Gain PointActual Gain Point

Gain Error

LSB43

The gain error is defined as the difference between the nominal and actual gain points on the transfer function after the offset error has been corrected to zero. For an ADC, the gain point is the midstep value when the digital output is full scale,

• Gain error:– Full-scale error minus the offset error, measured at the last ADC transition on

the transfer-function curve and compared with the ideal ADC transfer function;– May (or not) include errors in the voltage reference of the ADC.

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Gain Error - DAC

12

4

5

6

0

Ideal Diagram

000 100 101 110

LSB411

Digital Input Code

Offset ErrorAna

log

Out

put

Va

lue

(L

SB

)7

111

Actual Gain Point

Gain Error

Nominal Gain Point

For a DAC it is the step value when the digital input is full scale. This error represents a difference in the slope of the actual and ideal transfer functions This error can also usually be adjusted to zero by trimming.

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• Gain Error: Difference in slope of the ideal curve and the actual DAC output

High Gain Error: Actual slope greater than ideal

Low Gain Error: Actual slope less than ideal

Digital Input

Desired/Ideal Output

Ana

log

Out

put V

olta

ge

Low Gain

High Gain

Both offset and gain errors reduction techniques will imply partial loss of the ADC range.

Differential Nonlinearity (DNL) Error - ADC

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0

0 ... 001

654321

0 ... 010

0 ... 011

0 ... 100

0 ... 101

0 ... 110

0 ... 000

LSB1

LSB1

Differential Linearity Error

Differential Linearity Error

Analog Input Value (LSB)

Dig

ital O

utpu

t Cod

e

LSB21

LSB21

DNL is the difference between an actual step width (for an ADC) and the ideal value of 1 LSB. Therefore if the step width is exactly 1 LSB, then the differential nonlinearity error is zero.

If the DNL exceeds 1 LSB nonmonotonic (this means that the magnitude of the output gets smaller for an increase in the magnitude of the input)

If the DNL error of – 1 LSB there is also a possibility that there can be missing codes i.e., one or more of the possible 2n binary codes are never output.

• Differential Non-Linearity (DNL):– Determines how far an output code is from a neighbouring output code. The

distance is measured as a VIN converted to LSBs;

– No DNL error requires that:

• as the VIN is swept over its range, all output code combinations will appear at the converter output;

– DNL error < ± 1 LSB

ensures no missing codes.

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Differential Nonlinearity (DNL) Error - DAC

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1

2

3

4

5

6

0

LSB1

LSB1

DiferentialLinearity Error

Diferential Linearity Error

Digital Input Code

(LS

B)

LSB41

LSB41

0 ... 000 0 ... 1000 ... 010

0 ... 1010 ... 0110 ... 001

0 ... 110

Ana

log

Out

put V

alue

The differential nonlinearity error shown in Figure is the difference between an actual step height (for a DAC) and the ideal value of 1 LSB. Therefore if the step height is exactly 1 LSB, then the differential nonlinearity error is zero

Integral Nonlinerity (INL) Error - ADC

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0

001

654321

010

011

100

101

110

000

Analog Input Value (LSB)

Dig

ital O

utp

ut C

ode

7

111

At Transition001/010 (-1/4 LSB)

At Transition011/100 (-1/2 LSB)

Ideal Transition

Actual Transition

End-Point Lin. Error

The integral nonlinearity error shown in Figure is the deviation of the values on the actual transfer function from a straight line. This straight line can be either a best straight line which is drawn so as to minimize these deviations orit can be a line drawn between the end points of the transfer function once the gain and offset errors have been nullified (end-point linearity )

Integral Nonlinerity (INL) Error - DAC -

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000

1

110101100011011001

2

3

4

5

6

0

Digital Input Code

Ana

log

Out

put

Val

ue

(LS

B)

111

7

At Step001 (1/4 LSB)

At Step011 (1/2 LSB)

End-Point Lin. Error

The name integral nonlinearity derives from the fact that the summation of the differential nonlinearities from the bottom up to a particular step, determines the value of the integral nonlinearity at that step.

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• Integral Non-Linearity: Deviation of the actual DAC output from the ideal (Ideally all INL’s = 0)

Digital Input

Ideal Output

1VLSB Int. Non-Linearity = 1VLSB

Ana

log

Out

put V

olta

ge

Absolute Accuracy (Total) Error -ADC-

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0

001

654321

010

011

100

101

110

000

Analog Input Value (LSB)

Dig

ital O

utpu

t Cod

e

7

111

Total ErrorAt Step0 ... 001 (1/2 LSB)

Total ErrorAt Step 0 ... 101(-1 1/4 LSB)

The absolute accuracy or total error of an ADC as shown in Figure is the maximum value of the difference between an analog value and the ideal midstep value. It includes offset, gain, and integral linearity errors and also the quantization error in the case of an ADC

Absolute Accuracy (Total) Error -DAC-

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0 ... 000

1

0 ... 110

0 ... 101

0 ... 100

0 ... 011

0 ... 010

0 ... 001

2

3

4

5

6

0

Digital Input Code

Ana

log

Inpu

t Val

ue (

LSB

)

0 ... 111

7

Total Error At Step 0 ... 011 (1 1/4 LSB)

• DNL, INL and noise impact on the dynamic range:– INL, DNL and Noise errors cover the entire range;– Impact on the Effective Number of Bits (ENOB);– Not easily calibrated or corrected;– Affects accuracy.

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3. Linearity: Linearity error is the deviation from a straight

line output with increasing digital input codes.If a DAC output produces equal change in input for equal change in the input , it has 100%

linearity. Any deviation from this produces non-linearity.It is also expressed in ±LSB

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4. Resolution, R:– The smallest change to the analogue voltage that can be converted into a

digital code;

– The Least Significant Bit (LSB):

– The resolution only specifies the width of the digital output word, not the performance;

– Also called as step size or quantum• For ADC: it is the minimum change in input voltage required to produce 1 LSB change at

output. It is also expressed in no. of bits.

nR

21

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1FS

2Resolution

n

V

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• Resolution: is the amount of variance in output voltage for every change of the LSB in the digital input.

• How closely can we approximate the desired output signal(Higher Res. = finer detail=smaller Voltage divisions)

• A common DAC has a 8 - 12 bit Resolution

NLSB

VV

2Resolution Ref N = Number of

bits

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Better Resolution(3 bit)Poor Resolution(1 bit)

Vout

Desired Analog signal

Approximate output

2 V

olt.

Lev

els

Digital Input0 0

1

Digital Input

Vout

Desired Analog signal

Approximate output

8 V

olt.

Lev

els

000

001

010

011

100

101

110

111

110

101

100

011

010

001

000

5. Common mode rejection ratio

– Common mode range: it is the total range at which CMRR remains stable.

• Ex. If common mode signal is 6v and differential signal input is 4v then the common mode range is 10v.

Common mode reject ratio: it is the ability of a device to reject the effect of voltage applied to both input terminals simultaneously.

It is expressed as a ratio or as 20 log to base 10 of the ratio.

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• CMRR: is the ratio of common mode voltage (CMV) to the contribution to the output due to CMV alone.

» CMRR: 20 log 10 CMV/∆Vout

Where Vout is refferred to input

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Common mode voltage:is a voltage that appears in both input terminals of a device, with respect to its output reference (gnd).

CMV=1/2(v1+v2) for input v1 and v2Common mode error is any error at the output due to the common mode input voltage.

• 6. Monotonicity means that the magnitude of the output voltage increases every time the input digital code increases.

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• A monotonic converter is one whose output steps either increase or remain the same for correspondingly increasing input steps.

• When such converter skips or misses an output code by decreasing in the output level for a corresponding increasing input, it is said to be nonmonotonic.

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7. Code elongation and code skipping• Special cases of nonlinearity• An elongated code is the one in which digital

number represents two or more quantum levels, instead of 1-LSB change expected in a normal code.

• Also called as localized aberration• Appears when i/p signal is of high frequency• If a code is elongated for 1 LSB or resolution

then there will be skipping of immediate next.

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8. Glitches• Glitch: A transient spike in the output of a DAC that occurs when more than one bit changes in the input code.– Use a low pass filter to reduce the glitch – Use sample and hold circuit to reduce the glitch

• These are unwanted spike type outputs produced from DAC because of switching (on and off) time mismatch.

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9. Deglitcher

• are electronic circuits added at output stage for DACs to remove such glitch.

• Is a device that removes or reduces the effects of time skew pulses in D/A conversion.

• It consists of a S/H Circuit, which holds the DAC output constant until the switche reaches equilibrium.

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Ana

log

Out

put V

olta

ge

Digital Input

Perfect Agreement

7F 80

5V

Glitch

10. High frequency roll off• Is the departure of an ADC’s input circuits from an ideal transfer function, i.e the input circuit and track/hold circuits don’t have an infinite bandwidth.

• For proper signal reproducibility it has to satisfy the Nyquist sampling theorem.

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Input

Output

Ideal

Monotonic curvature causes even harmonic distortions

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Input

Output

Ideal

Compression causes odd harmonic distortions

Circuits that roll off the input bandwidth can distort high frequency inputs, which causes the monotonic curvature of transfer function i.e even harmonics and symmetrical compression which results in odd harmonics

11. Conversion Time/Speed

• Rate of conversion of a single digital input to its analog equivalent

• Conversion rate depends on– clock speed of input signal– settling time of converter

• When the input changes rapidly, the DAC conversion speed must be high.

• Also known as speed of conversion• It is the time it takes a converter to make a

total measurement from instant an input code or signal is impressed at the input, to the instant a corresponding signal or code appears at the output terminal.

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12.Cross talk

• It is the leakage voltage of signals between circuits or channels of a multi channel system or device, such as a multiplexer.

• Cross talk attenuation = 20 log10 [Vtest/Vout]• Decay rate is the maximum rate of change of

the output voltage to the HOLD mode.

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13. Quantization Error

• In addition to the errors of temperature, aging, fabrication and device limitation, there is also the error of quantization

• The error of quantization is one-half of a least significant bit. This is expressed as ±1/2LSB

• It is function of the number of bits in the converter.

• Can be reduced by increasing the resolution

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Sampling TheoryThe system shown in Figure is real-time system ; i.e., the signal to the ADC is continuously sampled at a rate equal to fS, and the ADC presents a new sample to the DSP at this rate.

In order to maintain real-time operation, the DSP must perform all its required computation within the sampling interval, 1/fS, and present an output sample to the DAC before arrival of the next sample from the ADC.

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The Nyquist Criteria

A continuous analog signal is sampled at discrete intervals, fS,which must be carefully chosen to ensure an accurate representation of the original analog signal

The Nyquist criteria requiries that the sampling frequency be at least twice the highest frequency contained in the signal, or information about the signal will be lost

If the sampling frequency is less than twice the maximum analog signal frequency, a phenomen know as aliasing will occur

Nyquist Theorem

For lossless digitization, the sampling rate should be at least twice the maximum frequency response.

• In mathematical terms:fs > 2*fm

• where fs is sampling frequency and fm is the maximum frequency in the signal

Nyquist Sampling Theorem

• To preserve all information in a signal, the signal must be sampled at a rate of twice the highest-frequency component of the signal.

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maxs f2 f

Quantization Process• Quantization Process

– Representing an analog signal having infinite resolution with a digital word having finite resolution

– Determines Maximum Achievable Dynamic Range– Results in Quantization Error/Noise

100

11

10

01

00

Dig

ital

Analog0 1/4 1/2 3/4 1 = FS

1LSB

Any Analog Input in this Range Gives the Same Digital Output Code

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Quantization Error ε

000

001

010

011

100

101

110

111

inV

2LSBV

2LSBV

7

8 refV

Dou

t

2 2LSB LSBV V

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Quantization Error (3-Bit Flash)

sample

sample

Am

plit

ud

eErr

or

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Dynamic specifications of ADC

ADC Specifications – AC performance

• 1. Signal-to-noise ratio (SNR):– Signal-to-noise ratio without distortion components;– Determines where the average noise floor of the converter is, setting an ADC

performance limit for noise.– It is the ratio of rms full scale analog input to its rms quantization error.– SNR increases with increase in full scale

» SNR = 20 log10(S/N)------- dB

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ADC Specifications – AC performance

• Signal-to-noise ratio (SNR):– For an n bit ADC sine wave input is given by:

– Can be improved with oversampling:• Lowers the average noise floor of the ADC;• Spreads the noise over more frequencies (equalise total noise).

][76.102.6 dBnSNR

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ADC Specifications – AC performance

• Signal-to-noise ratio (SNR):– Oversampling an ADC is a common principle to increase resolution;

– It reduces the noise at any one frequency point.

– A 2x oversampling reduces the noise floor by 3 dB, which corresponds to a ½ bit resolution increase;

– Oversampling by k times provides a SNR given by:

][2

log1076.102.6max

10 dBff

nSNR s

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ADC Specifications – AC performance

• 2. Signal-to-noise and distortion ratio (SINAD):– Similar to SNR;

– Includes the harmonic content [total harmonic distortion], from DC to the Nyquist frequency;

• SINAD = 20 log10[S/(N+D)]------dB

– Is defined as the ratio of the RMS value of an input sine wave to the RMS value of the noise of the converter;

– Writing the equation in terms of n, provides the number of bits that are obtained as a function of the RMS noise (effective number of bits, ENOB):

02.6/76.1 SINADn52

3. Spurious Free Dynamic Range (SFDR)

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Probably the most significant specification for an ADC used in a communicationsapplication is its spurious free dynamic range (SFDR).

SFDR of an ADC is defined as the ratio of the rms signal amplitude to the rms value of the peak spurious spectral content measured over the bandwidth of interest.

SFDR=20 log10[A rms/A(SPUR-max)rms] ------ dB

SFDR is generally plotted as a function of signal amplitude and may be expressedrelative to the signal amplitude (dBc) or the ADC full-scale (dBFS) as shown in Figure

ADC Specifications – AC performance

• Spurious-free dynamic range (SFDR):– Defined as the ratio of the RMS value of an input sine wave to the

RMS value of the largest trace observed in the frequency domain using a FFT plot;

– If the distortion component is much larger than the signal of interest, the ADC will not convert small input signals, thus limiting its dynamic range.

• 4. Total harmonic distortion (THD):– Gets increasingly worse as the input frequency increases;– Primary reason for ENOB degradation with frequency is that

SINAD decreases as the frequency increases toward the Nyquist limit, SINAD decreases.

– It is the ratio of the rms value of the fundamental signal to the mean value of root sum square (rss) of its harmonics.

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• 5. TDH +N: total harmonic distortion plus noise is the ratio of the rms value of the fundamental signal to the root sum square (rss) of its harmonics plus all the noise components (excluding dc).

• THD+N is equal to SINAD provided bandwidth for noise measurement should be same for both specifications– Noise components = quantization noise + thermal noise6. (ENOB) effective number of bits : it is one of the specification

which indicate ADC accuracy at specific input frequency and at specific sampling rate.

ENOB= (SINAD-1.76dB)/ 6.02

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Aperture Time, Aperture Delay Time, and aperture Jitter

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• Acquisition time : is the interval between SAMPLE command and the moment when the output begins to track the input regardless of previous state of output.

• Aperture time: it is the time it takes for A/D converter actually assign a binary number to that input analog signal.– It is the time instant a command signal is given

and the instant the digital code appears.– Usually < 50 nsec.

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Jitter in clock signal degrades the ADC signal-to-noise ratio.

58Time

Am

plitu

de

tt tt

Jitter

Jitter is generally defined as short-term, non-cumulative variation of the significant instant of a digital signal from its ideal position in time. Figure illustrates a sampling clock signal that contains jitter. Jitter generated by the clock is caused by various internal noise sources, such as thermal noise, phase noise, and spurious noise. A clock signal that has cycle-to-cycle variation in its duty cycle is said to exhibit jitter. Clock jitter causes an uncertainty in the precise sampling time, resulting in a reduction of dynamic performance.

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Digital to Analog Converters

-Common Applications

• Generic use• Circuit Components• Digital Audio • Function Generators/Oscilloscopes• Motor Controllers

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Digital to Analog Converters

-Common Applications-Generic

• Used when a continuous analog signal is required.

• Signal from DAC can be smoothed by a Low pass filter

0 bit

nth bit

n bit DAC011010010101010100101101010101011111100101000010101010111110011010101010101010101010111010101011110011000100101010101010001111

Digital Input

Filter

Piece-wise Continuous

Output

Analog Continuous

Output

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Digital to Analog Converters

-Common Applications-Circuit Components

• Voltage controlled Amplifier– digital input, External Reference Voltage as control

• Digitally operated attenuator– External Reference Voltage as input, digital control

• Programmable Filters– Digitally controlled cutoff frequencies

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Digital to Analog Converters

-Common Applications-Digital Audio

• CD Players• MP3 Players• Digital Telephone/Answering Machines

1. http://electronics.howstuffworks.com/cd.htm2. http://accessories.us.dell.com/sna/sna.aspx?c=us&cs=19&l=en&s=dhs&~topic=odg_dj

1 2 3

3. http://www.toshiba.com/taistsd/pages/prd_dtc_digphones.html

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Digital to Analog Converters

-Common Applications-Function Generators

• Digital Oscilloscopes– Digital Input– Analog Ouput

• Signal Generators– Sine wave generation– Square wave generation– Triangle wave generation– Random noise generation

1

1. http://www.electrorent.com/products/search/General_Purpose_Oscilloscopes.html

2

2. http://www.bkprecision.com/power_supplies_supply_generators.htm

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Digital to Analog Converters

-Common Applications-Motor Controllers

• Cruise Control• Valve Control • Motor Control

1

1. http://auto.howstuffworks.com/cruise-control.htm

2

2. http://www.emersonprocess.com/fisher/products/fieldvue/dvc/

3

3. http://www.thermionics.com/smc.htm

Applications of ADCBased on area of application divided into 4 types– Data transmission– Data processing– Data read out– Data storage

• Most popular applications are• Electronic weighing system• Digital voltmeter• Digital micrometer using LVDT

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Questions

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Questions

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