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Digital to Analog Converters

Digital to Analog Converters. Alexander Gurney Alexander Pitt Gautam Puri. Digital to Analog Converters. Alexander Gurney What is a DAC? Applications of DACs Alexander Pitt Types of DACs Binary Weighted Resistor R-2R Ladder Gautam Puri Specifications Resolution

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Digital to Analog Converters

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  1. Digital to Analog Converters Alexander Gurney Alexander Pitt GautamPuri

  2. Digital to Analog Converters • Alexander Gurney What is a DAC? Applications of DACs • Alexander Pitt Types of DACs Binary Weighted Resistor R-2R Ladder • GautamPuri Specifications Resolution Speed Linearity Settling Time Reference Voltages Errors

  3. What is a DAC? – Alexander Gurney 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 1001 0101 0011 0111 1001 1010 1011 DAC

  4. Reference Voltage • What is a DAC? – Alexander Gurney • DACs rely on an input Reference Voltage to calculate the Output Signal

  5. What is a DAC? – Alexander Gurney Analog Output Signal 0100 0101 0110 0111 1000 1001 1010 0000 0001 0010 0011 1011 Digital Input Signal Binary to Analog Conversion • Each sample is converted from binary to analog, between 0 and Vref for Unipolar, or Vref and –Vref for Bipolar

  6. What is a DAC? – Alexander Gurney 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

  7. What is a DAC? – Alexander Gurney Ideally Sampled Signal Output typical of a real, practical DAC due to sample & hold 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 DAC

  8. What is a DAC? – Alexander Gurney 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

  9. What is a DAC? – Alexander Gurney 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 Piece-wise Continuous Output Analog Continuous Output Digital Input n bit DAC 0 bit 011010010101010100101 101010101011111100101 000010101010111110011 010101010101010101010 111010101011110011000 100101010101010001111 Filter nth bit

  10. What is a DAC? – Alexander Gurney DACs in Audio DigitalAnalog MP3s ->3.5mm Audio Out HD Radio ->Signal received by speaker CDs ->RCA Audio Out

  11. What is a DAC? – Alexander Gurney DACs in Video DigitalAnalog DVDs ->Composite Output OTA Broadcast ->Converter Box Output Youtube ->Analog Monitor Input

  12. DAC Types – Alex Pitt Types of Digital to Analog Converters • Binary Weighted • Explanation • Advantages and disadvantages • R-2R Ladder • Explanation • Example • Advantages and disadvantages

  13. DAC Types – Alex Pitt Binary Weighted DAC • Use transistors to switch between open and close • Adds resistors in parallel scaled by two to divide voltage on each branch by a power of two Vout = Analog Out • Use a summing op-amp circuit with gain

  14. DAC Types – Alex Pitt 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.

  15. DAC Types – Alex Pitt Binary Weighted DAC • General equation B0 B1 B2 B3 MSB LSB

  16. DAC Types – Alex Pitt 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

  17. DAC Types – Alex Pitt R-2R Ladder DAC • Requires only two resistance values (R and 2R) • 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. Vref RF 4 bit converter

  18. DAC Types – Alex Pitt R-2R Ladder Example • Convert 0001 to analog V2 V1 V0 V3 Vref V1 V0 RF

  19. DAC Types – Alex Pitt R-2R Ladder Example • Convert 0001 to analog RF R 2R Vref V0 RF

  20. DAC Types – Alex Pitt R-2R Ladder By adding resistance in series and in parallel we can derive an equation for the R-2R ladder.

  21. DAC Types – Alex Pitt 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

  22. DAC Types – Alex Pitt R-2R Ladder • 4-Bit Equation • Substituting • General Equation Rf

  23. DAC Types – Alex Pitt R-2R Ladder DAC • Advantages • Only two resistor values • Can use lower precision resistors

  24. Specifications - GautamPuri Specifications of DAC Lets discuss some terms you’ll hear when dealing with DACs • Reference Voltage • Resolution • Speed • Linearity • Settling Time • Some types of Errors

  25. Specifications - GautamPuri 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).

  26. Specifications - GautamPuri 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

  27. Specifications - GautamPuri Resolution • 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

  28. Specifications - GautamPuri 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

  29. Specifications - GautamPuri tsettle 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

  30. Specifications - GautamPuri 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 Linear Non-linear

  31. Specifications - GautamPuri 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

  32. Specifications - GautamPuri 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.

  33. Specifications - GautamPuri 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

  34. Specifications - GautamPuri 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.

  35. Specifications - GautamPuri 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.

  36. Specifications - GautamPuri 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.

  37. Specifications - GautamPuri 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

  38. Specifications - GautamPuri 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 code • 2 Types of Gain Error • Low Gain: Step Amplitude Less than Ideal • High Gain: Step Amplitude Greater than Ideal Gain Error can be adjusted to zero by using an external potentiometer

  39. Specifications - GautamPuri 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

  40. Specifications - GautamPuri Full Scale Error • It is a combination of gain and offset error • It is measured at the full scale input

  41. Specifications - GautamPuri 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)

  42. Specifications - GautamPuri 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.

  43. References • Previous semester lecture slides • http://www.hitequest.com/Hardware/a_dac.htm http://www.national.com/appinfo/adc/files/ms101157.pdf • http://www.noise.physx.u-szeged.hu/DigitalMeasurements/ADConversion/ADSpecs.pdf • Scherz, Paul. PracticalElectronicsforInventors. 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/

  44. Questions ? Alexander Gurney What is a DAC? Alexander Pitt Types of DACs GuatamPuri Specifications

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