Digital to Analog Converters Alexander Gurney Alexander Pitt Gautam Puri 1.

Digital to Analog Converters

Alexander GurneyAlexander PittGautam Puri

1

Digital to Analog Converters Alexander Gurney What is a DAC?

Applications of DACs

Alexander Pitt Types of DACsBinary Weighted ResistorR-2R Ladder

Gautam Puri SpecificationsResolutionSpeedLinearitySettling TimeReference VoltagesErrors

2

What is a DAC? A DAC converts a binary digital signal into an

analog representation of the same signal Typically the analog signal is a voltage output,

though current output can also be used

0101

0011

0111

1001

1001

1010

1011 DAC

What is a DAC? – Alexander Gurney

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Reference Voltage

DACs rely on an input Reference Voltage to calculate the Output Signal


4

Binary to Analog Conversion

1011100110100111 10000110010101000011001000010000Digital Input Signal

Ana

log

Out

put

Sig

nal

Each sample is converted from binary to analog, between 0 and Vref for Unipolar, or Vref and –Vref for Bipolar


5

Sampling Frequency Sampling frequency is the number of data

points sampled per unit time Sampling frequency must be twice the

frequency of the sampled signal to avoid aliasing, per Nyquist criteria

A higher sampling frequency decreases the sampling period, allowing more data to be transmitted in the same amount of time


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Output is a Piecewise Function This is due to finite sampling frequency The analog value is calculated and “held” over

the sampling period This results in an imperfect reconstruction of

the original signal

Ideally Sampled Signal Output typical of a real, practical DAC due to sample & hold

DAC


7

An Example

4 Bit signal Unipolar Vref = 7V 8 Sample Points Sample Frequency = 1 hertz Duration 8 seconds

0001 0011 0110 1100 1011 0101 0010 0111


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Filtering

The analog signal generated by the DAC can be smoothed using a low pass filter

This removes the high frequencies required to sustain the sharp inclines making up the edges

0 bit

nth bit

n bit DAC011010010101010100101101010101011111100101000010101010111110011010101010101010101010111010101011110011000100101010101010001111

Digital Input

Filter

Piece-wise Continuous Output

Analog Continuous Output


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DACs in Audio

Digital AnalogMP3s ->3.5mm Audio OutHD Radio ->Signal received by speakerCDs ->RCA Audio Out


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DACs in Video

Digital AnalogDVDs ->Composite OutputOTA Broadcast ->Converter Box OutputYoutube ->Analog Monitor Input


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Types of Digital to Analog Converters

Binary Weighted Explanation Advantages and disadvantages

R-2R Ladder Explanation Example Advantages and disadvantages

DAC Types – Alex Pitt

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Binary Weighted DAC

Use transistors to switch between open and close

Use a summing op-amp circuit with gain

Adds resistors in parallel scaled by two to divide voltage on each branch by a power of two


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Vout =

Analog Out

Binary Weighted DAC

Circuit can be simplified by adding resistors in parallel to substitute for Rin. *Values for A, B, C and D are either 1 or 0.


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Binary Weighted DAC

R

B

R

B

R

B

R

BRV

R

RVV nnn

inin 1-n0321

fin

fout 242

MSB LSB

General equation B0 B1 B2 B3


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Binary Weighted DAC

Advantages Works well up to ~ 8-bit conversions

Disadvantages Needs large range of resistor values (2048:1 for

a 12-bit DAC) with high precision resistor values

Too much or too little current flowing through resistors Minimum/maximum opamp current Noise overwhelms current through larger resistance

values


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R-2R Ladder DAC

Requires only two resistance values (R and 2R)

Vref

4 bit converter

Each bit controls a switch between ground and the inverting input of the op amp.

The switch is connected to ground if the corresponding bit is zero.


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RF

R-2R Ladder Example

Convert 0001 to analog

V0V1V2V3

0 1 11

2

RV V V

R R

V1

1 2 21

2

RV V V

R R

2 3 31

2

RV V V

R R

Vref

V0


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1

1/ 2 1/ 2eqR RR R

RF

R-2R Ladder Example

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Convert 0001 to analog

01

8 refV V

2RR

V0

out 0R 1

V2R 16 refV V

Vref


RF

RF

R

Rf

R-2R Ladder

By adding resistance in series and in parallel we can derive an equation for the R-2R ladder.


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R-2R Ladder

By knowing how current flows through the ladder we can come up with a general equation for R-2R DACs.

MSB

LSB


21

f0123

fout 16842R

BBBBIRIV sum

R-2R Ladder

Rf

1

out ref0 2

nf i

n ii

R BV V

R

f0123

fout 16842R

BBBB

R

VRIV ref

sum

4-Bit Equation Substituting

General Equation


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R

VI ref

R-2R Ladder DAC

Advantages Only two resistor values Can use lower precision resistors


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Specifications of DACLets discuss some terms you’ll hear when dealing with DACs

Reference Voltage Resolution Speed Linearity Settling Time Some types of Errors

Specifications - Gautam Puri

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Reference Voltage Vref

The reference voltage determines the range of output voltages from the DAC

For a ‘Non-Multiplying DAC’, Vref is a constant value set internally by the manufacturer

For a ‘Multiplying DAC’, Vref is set externally and can be varied during operation

Vref also affects DAC resolution (which will be discussed later).


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Full scale voltage Full scale voltage is the output voltage when all

the bits of the digital input signal are 1s.

It is slightly less than reference voltage Vref

Vfs = Vref - VLSB

N

NVV

2

)12(reffs


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Resolution of a DAC is the change in output voltage for a change in the least significant bit (LSB) of the digital input

Resolution is specified in “bits”. Most DACs have a resolution of 8 to 16 bits

Example: A DAC with 10 bits has a resolution of

Higher resolution (more bits) = smoother output A DAC with 8 bits has 256 steps whereas one with 16 bits

has 65536 steps for the given voltage range and can thus offer smoother output

Resolution

LSBref

2Resolution V

VN

ref10ref

1024

1

2Resolution V

V


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Speed (Sampling frequency) Sampling frequency is the rate at which the DAC

accepts digital input and produces voltage output In order to avoid aliasing, the Nyquist criterion

requires that

Sampling frequency is limited by the input clock speed (depends on microcontroller) and the settling time of the DAC

maxsampling 2 ff


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Settling Time

It takes the DAC a finite amount of time to produce the exact analog voltage corresponding to the digital input

The settling time is the time interval from when the DAC commands the update of its output to when the voltage actually reaches ± ½ VLSB.

A faster DAC will have a smaller settling time

tsettle


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Linearity If the change in analog output voltage per unit

change in digital input remains constant over the entire range of operation, the DAC is said to be linear

Ideally the DAC should have a proportionality constant which results in a linear slope

Non-linearity is considered an error, and will be further discussed in the errors section

010101000011001000010000Digital Input Signal

Ana

log

Out

put S

igna

l


Ana

log

Out

put S

igna

l

010101000011001000010000Digital Input Signal

Ana

log

Out

put S

igna

l


Ana

log

Out

put S

igna

l

Linear Non-linear


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Types of DAC Errors Non-monotonic output error Non-linear output error

― Differential― Integral

Gain error Offset error Full scale error Resolution error Settling time and overshoot error


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Non-monotonic Output Error A monotonic function has a slope whose sign does not

change Non-monotonic error results when the analog output

changes direction for a step or a few steps of digital input In a closed loop control system this may cause the DAC to

toggle continuously between 2 input codes and the system will be unstable.


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Differential non-linear output error For a change in the LSB of input, the output of an

ideal DAC is VLSB

However in a non-linear DAC the output may not be exactly the LSB but rather a fraction (higher or lower) of it


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Differential non-linear output error Basically “differential” non-linearity expresses the

error in step size as a fraction of LSB The DNL is the maximum of these deviations over

the entire transfer function One must choose a DAC with DNL less than 1 LSB.

A DNL > 1 LSB will lead to non-monotonic behavior. This means that for certain steps in digital input, the output voltage will change in the opposite direction. This may cause a closed loop control system to become unstable as the system may end up oscillating back and forth between two points.


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Integral non-linear output error The integral non-linearity error is the difference

between the ideal and actual output. It can also be defined as the difference between ideal and a best fit line

INL occurs when the output is non-linear and thus unable to adhere to a straight line.

The maximum deviation from this line is called INL.


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Integral non-linear output error INL is expressed as fraction of LSB. INL cannot be calibrated out as the non-

linearity is unpredictable and one does not know where the maximum deviation from the ideal line will occur.

One must choose an ADC with an INL (maximum deviation) within the accuracy required.


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More important - DNL or INL ?

The DNL and INL are both important non-linear errors to be aware of.

In the case of an application such as an imaging one, where slight differences in color densities are important, the “differential” non-linearity error is more important.

In an application where the parameters vary more widely, such as speed of a vehicle, the “integral” non-linearity error may be of greater importance


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Gain Error The difference between the output voltage (or

current) with full scale input code and theideal voltage (or current) that should exist with a full scale input code2 Types of Gain Error 1. Low Gain: Step

Amplitude Less than Ideal

2. High Gain: Step Amplitude Greater than Ideal

Gain Error can be adjusted to zero by using an external potentiometer


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Offset Error It is the difference in ideal and actual output voltage at a

digital input of zero All output values will differ from the ideal values by that

same amount, hence the output is “offset” from the input Offset can be ‘positive’ or ‘negative’ It can be fixed by adding/subtracting the difference to the

digital input before passing through the DAC


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Full Scale Error It is a combination of gain and offset error It is measured at the full scale input


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Resolution Error If the resolution is not high enough, the DAC

cannot accurately output the required waveform Lower resolution results in higher resolution error

Low resolution (1 bit) Higher resolution (3 bits)


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Settling Time and Overshoot Error If settling time is too high, the DAC will not

produce the ideal output waveform fast enough and there will be a delay or lag.

This will also lower the maximum operating frequency of the DAC.


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References• Previous semester lecture slides• http://www.hitequest.com/Hardware/a_dac.ht

m http://www.national.com/appinfo/adc/files/ms101157.pdf

• http://www.noise.physx.u-szeged.hu/DigitalMeasurements/ADConversion/ADSpecs.pdf

• Scherz, Paul. Practical Electronics for Inventors. 2nd Edition, McGraw Hill. 2007.

• http://masteringelectronicsdesign.com/an-adc-and-dac-differential-non-linearity-dnl/

• http://masteringelectronicsdesign.com/an-adc-and-dac-integral-non-linearity-inl/

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http://www.hitequest.com/Hardware/a_dac.htm

http://www.hitequest.com/Hardware/a_dac.htm

http://www.national.com/appinfo/adc/files/ms101157.pdf

http://www.national.com/appinfo/adc/files/ms101157.pdf

http://www.noise.physx.u-szeged.hu/DigitalMeasurements/ADConversion/ADSpecs.pdf

http://www.noise.physx.u-szeged.hu/DigitalMeasurements/ADConversion/ADSpecs.pdf

http://masteringelectronicsdesign.com/an-adc-and-dac-differential-non-linearity-dnl/

http://masteringelectronicsdesign.com/an-adc-and-dac-differential-non-linearity-dnl/

http://masteringelectronicsdesign.com/an-adc-and-dac-integral-non-linearity-inl/

http://masteringelectronicsdesign.com/an-adc-and-dac-integral-non-linearity-inl/

Questions ?

Alexander Gurney

What is a DAC?

Alexander Pitt

Types of DACs

Guatam Puri

Specifications

44

Digital to Analog Converters Alexander Gurney Alexander Pitt Gautam Puri 1.

Documents

analog signal

practical dac

sample hold dac

binary weighted dac

binary digital signal

voltage output

analog conversion

analog representation