1 / 44

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

gus
Download Presentation

Digital to Analog Converters

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  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

More Related