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Digital to Analog Converter. Nov. 1, 2005 Fabian Goericke, Keunhan Park, Geoffrey Williams. Outline. What is a DAC? Types of DAC Circuits Resistor-string DAC Binary weighted DAC R-2R Ladder DAC Specifications of DAC Errors Applications. What is a DAC?.

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digital to analog converter

Digital to Analog Converter

Nov. 1, 2005

Fabian Goericke, Keunhan Park, Geoffrey Williams

outline
Outline
  • What is a DAC?
  • Types of DAC Circuits
    • Resistor-string DAC
    • Binary weighted DAC
    • R-2R Ladder DAC
  • Specifications of DAC
  • Errors
  • Applications
what is a dac
What is a DAC?
  • A digital to analog converter (DAC) is a device that converts digital numbers (binary) into an analog voltage or current output.

1001

0101

0011

0111

1001

1010

1011

DAC

what is a dac4
What is a DAC?

Analog Output Signal

Digital Input Signal

types of dac circuits
Types of DAC Circuits

1. Resistor String

2. Binary Weighted Resistor

3. R-2R Ladder

slide6

Resistor String DAC

  • Components of a String DAC
  • Resistor String  supply discrete voltage levels
  • Selection Switches  connect the right voltage level to op-amp according to input bits
  • Op-amp  amplifies the discrete voltage levels to desired range, keeps the current low
slide7

Resistor String DAC

Resistor String

Example

slide8

Resistor String DAC

Selection Switches

1 1 0  6V

1 1 1  7V

1 0 0  4V

0 0 0  0V

slide9

Resistor String DAC

Advantages:

  • simple
  • fast for < 8 bits

Disadvantages:

  • high element count for higher resolutions, reason:

number of resistors:

number of switches:

  • slow for > 10 bits
slide10

R

2R

4R

2nR

Rf

-

Vout

+

Binary Weighted Resistor DAC

  • Basic Idea:
    • Use a summing op-amp circuit
    • Use transistors to switch between high and ground
    • Use resistors scaled by two to divide voltage on each branch by a power of two
binary weighted resistor dac
Binary Weighted Resistor DAC
  • non-inverting input on ground  virtual ground at inverting input
  • KIRCHHOFF’s current law and no input current into op-amp  I1 + I2 = 0
  • I1 = V1 / R + V2 / (2R) + V3 / (4R) + …
binary weighted resistor dac12
Binary Weighted Resistor DAC

Most significant bit

Least significant bit

Rf = R / 2

Vn = Vref, if bit is set

Vn = 0, if bit is clear

Terms have less influence

slide13

Binary Weighted Resistor DAC

  • Advantages
    • Simple
    • Fast
  • Disadvantages
    • Needs large range of resistor values (2000:1 for 12-bit) with high precision in low resistor values
    • Needs very small switch resistances
r 2r resistor ladder dac
R-2R Resistor Ladder DAC

Vref

Each bit controls a switch between

ground and the inverting input of the

op amp.

  • Simplest type of DAC
  • Requires only two precision resistance valuce (R and 2R)

The switch is connected to ground if

the corresponding bit is zero.

0

0

0

0

4 bit converter

r 2r dac example
R-2R DAC Example
  • Convert 0001 to analog

V0

V1

V0

V1

=

V2

V1

V0

V3

Vref

r 2r dac example16
R-2R DAC Example
  • Convert 0001 to analog

R

2R

Vref

V0

r 2r dac summary
R-2R DAC Summary
  • Conversion results for each bit
  • Conversion equation for N-bit DAC

for

slide18

R-2R DAC Summary

  • Advantages
    • Only two resistor values
    • Does not need the kind of precision as Binary weighted DACs
    • Easy to manufacture
    • Faster response time
  • Disadvantages
    • More confusing analysis
specification of dac
Specification of DAC
  • Resolution
  • Speed
  • Settling time
  • Linearity
  • Reference voltage
specification resolution
Specification - Resolution
  • 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 - 16 bit Resolution

N = Number of bits

specification speed
Specification - 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.
specification settling time
Specification – Settling Time
  • The time required for the input signal voltage to settle to the expected output voltage (within +/- ½ of VLSB).
  • Ideally, an instantaneous change in analog voltage would occur when a new binary word enters into DAC
  • Fast converters reduce slew time, but usually result in longer ring time.

tslew

tring

tdelay

specification linearity
Specification – Linearity
  • The difference between the desired analog output and the actual output over the full range of expected values.
specification linearity24

Linearity(Ideal Case)

NON-Linearity(Real World)

Desired Output

Desired/Approximate Output

Approximate output

Analog Output Voltage

Analog Output Voltage

Digital Input

Digital Input

Miss-alignment

Perfect Agreement

Specification – Linearity
  • Ideally, a DAC should produce a linear relationship between a digital input and the analog output, this is not always the case.
specification reference voltage
Specification – Reference Voltage
  • A specified voltage used to determine how each digital input will be assigned to each voltage division.
  • Types:
    • Non-multiplier DAC: Vref is fixed (specified by the manufacturer)
    • Multiplier DAC: Vref is provided via an external source
specification reference voltage26
Specification – Reference Voltage
  • Full Scale Voltage
    • Defined as the output when digital input is all 1’s.
errors
Errors

There are a multiple sources of error associated with DAC

Common DAC Errors:

  • Gain Error
  • Offset Error
  • Full Scale Error
  • Non Linearity
  • Non-Monotonic
  • Resolution Errors
  • Settling Time and Overshoot
gain error

High Gain

Desired/Ideal Output

Analog Output Voltage

Low Gain

Digital Input

Gain Error

Gain Error: Deviation in the slope of the ideal curve and with respect to the actual DAC output.

High Gain Error: Step amplitude is higher than the desired output

Low Gain Error: Step amplitude is lower than the desired output

offset error
Offset Error

Offset Error: Occurs when there is an offset in the output voltage in reference to the ideal output.

Output Voltage

Desired/Ideal Output

  • This error may be detected when all input bits are low (i.e. 0).

Positive Offset

Digital Input

NegativeOffset

full scale error
Full Scale Error

Full Scale Error: occurs when there is an offset in voltage form the ideal output and a deviation in slope from the ideal gain.

differential non linearity

Ideal Output

Analog Output Voltage

Diff. Non-Linearity = 2VLSB

2VLSB

VLSB

Digital Input

Differential Non-Linearity

Differential Non-Linearity: Voltage step size changes vary with as digital input increases. Ideally each step should be equivalent.

integral non linearity
Integral Non-Linearity

Integral Non-Linearity: Occurs when the output voltage is non linear. Basically an inability to adhere to the ideal slope.

Ideal Output

Analog Output Voltage

Int. Non-Linearity = 1VLSB

1VLSB

Digital Input

non monotonic output error
Non-Monotonic Output Error

Non-Monotonic Output Error: Occurs when the an increase in digital input results in a lower output voltage.

Desired Output

Non-Monotonic

Monotonic

Analog Output Voltage

Digital Input

resolution errors

Poor Resolution(1 bit)

Vout

Desired Analog signal

1

2 Volt. Levels

0

0

Digital Input

Approximate output

Resolution Errors

Does not accurately approximate the desired output due large voltage divisions.

resolution errors35

Better Resolution(3 bit)

Vout

Desired Analog signal

111

110

110

8 Volt. Levels

101

101

100

100

011

011

010

010

001

001

000

000

Digital Input

Approximate output

Resolution Errors

Better approximation of the of the desired output signal due to the smaller voltage divisions.

settling time and overshoot

Analog Output Voltage

+VLSB

Expected Voltage

-VLSB

Time

Settling time

Settling Time and Overshoot

Settling Time: The time required for the voltage to settle within +/- the voltage associated with the VLSB. Any change in the input time will not be reflected immediately due to the lag time.

Overshoot: occurs when the output voltage overshoots the desired analog output voltage.

common applications
Common 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
  • Video:Video signals from a digital source, such as a computer, must be converted to analog form if they are to be displayed on an analog monitor.

http://en.wikipedia.org/wiki/Digital-to-analog_converter

references
References
  • Alciatore, “Introduction to Mechatronics and Measurement Systems,” McGraw-Hill, 2003
  • Horowitz and Hill, “The Art of Electronics,” Cambridge University Press, 2nd Ed. 1995
  • http://products.analog.com/products/info.asp?product=AD7224
  • http://courses.washington.edu/jbcallis/lectures/C464_Lec5_Sp-02.pdf
  • http://www.eecg.toronto.edu/~kphang/ece1371/chap11_slides.pdf
  • Previous students’ lectures on DAC