数字电子技术(课件)lec27.ppt

1、2020/7/27,Chapter 11 Introduction to Digital Signal Processing,1,Chapter 11 Outline,11-1Digital Signal Processing Basics 11-2Digital-to-Analog Conversion Methods 11-3Converting Analog Signals to Digital 11-4Analog-to-Digital Conversion Methods,Lecture 27: Digital-to-Analog Conversion,Lecture 27,Lect

2、ure 28,2020/7/27,Chapter 11 Introduction to Digital Signal Processing,2,Key Knowledge in Lecture 27,Principles of DAC: the conversion formula. Binary-weighted-input DAC working principle. The working principle of R/2R ladder DAC. Performance characteristics of DACs DAC conversion error analysis.,Dif

3、ficult Topics: The DAC conversion formula and its analysis. Various DAC conversion circuits analysis. DAC conversion error analysis.,Lecture 27: Digital-to-Analog Conversion,2020/7/27,Chapter 11 Introduction to Digital Signal Processing,3,“Stairstep” Approximation of Analog Signal,Lecture 27: Digita

4、l-to-Analog Conversion,2020/7/27,Chapter 11 Introduction to Digital Signal Processing,4,A Typical Digital Signal Processing System,Lecture 27: Digital-to-Analog Conversion,2020/7/27,Chapter 11 Introduction to Digital Signal Processing,5,Principles of D/A Conversion,Lecture 27: Digital-to-Analog Conv

5、ersion,The conversion formula is:,Which is similar to binary-to-decimal conversion formula.,Di is the input binary number, for example, for a four-bit binary number, Di will be D0D3. Look at the figure,The figure on the right uses 4 bits to represent a maximum of 15 volts. In this case,k determines

6、the voltage difference between two adjacent voltage levels.,2020/7/27,Chapter 11 Introduction to Digital Signal Processing,6,Test Your Understanding,Lecture 27: Digital-to-Analog Conversion,If we use 8-bit binary number to represent 10 volts, how many volts does an LSB represent?,Solution:,If we use

7、 4-bit binary number to represent 30 volts, how many volts does an LSB represent?,Solution:,Conclusion: the more binary bits we use, the better relative accuracy we can get.,2020/7/27,Chapter 11 Introduction to Digital Signal Processing,7,A Review on The Operational Amplifier (Op-Amp),Lecture 27: Di

8、gital-to-Analog Conversion,When used as an inverting amplifier, the input-output relationship is as follows:,When used as a comparator, the op-amp is driven into one of its two saturated output states: HIGH or LOW.,2020/7/27,Chapter 11 Introduction to Digital Signal Processing,8,General Construction

9、 of a DAC Device,Lecture 27: Digital-to-Analog Conversion,Digital register,Analog switch,Binary weight,Base power source,Summing op amp,Analog output,2020/7/27,Chapter 11 Introduction to Digital Signal Processing,9,Binary-Weighted-Input DAC,Lecture 27: Digital-to-Analog Conversion,register,2020/7/27

10、,Chapter 11 Introduction to Digital Signal Processing,10,Analysis of Converted Analog Voltage,Lecture 27: Digital-to-Analog Conversion,Usually, we take the value RF=R/2, so, coefficient,Please notice the value of k for the real circuit, k is a little different from the ideal value. For example, for

11、a 4-bit binary number, the ideal k value is VREF/15, but the circuit determined k= VREF/16.,Important note: This formula implies the following: all R in different branches must be made equal; RF must equal one-half of R; The analog switch is ideal, ie. no contact resistance.,So, in practice it is di

12、fficult to implement this circuit.,2020/7/27,Chapter 11 Introduction to Digital Signal Processing,11,DAC Illustration Example 1,Lecture 27: Digital-to-Analog Conversion,If VREF=-8V, 2RF=R, given D3D2D1D0=1101, determine the output vo, LSB and FSR (full scale range).,Solution:,D3D2D1D0=(1101)2=(13)10

13、,Obviously, the output voltage range is 07.5 V.,2020/7/27,Chapter 11 Introduction to Digital Signal Processing,12,Illustration of Sequence of Input Data,Lecture 27: Digital-to-Analog Conversion,Determine the output of the DAC in figure below. D0(LSB),Solution:,Input data changes from 00001111 sequen

14、tially.,Which means the output voltage starts from 0, each time the input increment by 1, the output drops 0.25 volt. The output voltage waveform is shown on the next page.,2020/7/27,Chapter 11 Introduction to Digital Signal Processing,13,Output of the DAC in Preceding Figure,Lecture 27: Digital-to-

15、Analog Conversion,Only need to calculate the output when the input data is 1111(15).,VOUT=kx15= -3.75V,2020/7/27,Chapter 11 Introduction to Digital Signal Processing,14,DAC with Dual Polarity Output,Lecture 27: Digital-to-Analog Conversion,In figure below, VREF=-8 V, VB=-VREF=8 V; RF=R/2. Require vo

16、=0 when D2D1D0=100, determine RB.,i,iB,iF,Solve for RB RB=R,The general expression for vo,See demo,2020/7/27,Chapter 11 Introduction to Digital Signal Processing,15,The R/2R Ladder DAC,Lecture 27: Digital-to-Analog Conversion,The equivalent resistance of point D are: R,The total current,I is distrib

17、uted as shown above.,2020/7/27,Chapter 11 Introduction to Digital Signal Processing,16,The R/2R Ladder DAC,Lecture 27: Digital-to-Analog Conversion,Output:,2020/7/27,Chapter 11 Introduction to Digital Signal Processing,17,Another Example of R/2R Ladder DAC,Lecture 27: Digital-to-Analog Conversion,Th

18、e circuit structure is a little different, so the analysis will also be different.,Use superposition theorem and Thevenins theorem to analyze the above circuit.,2020/7/27,Chapter 11 Introduction to Digital Signal Processing,18,Analysis of the R/2R Ladder DAC,Lecture 27: Digital-to-Analog Conversion,

19、When D0D1D2D3=0001,When D0D1D2D3=0010,When D0D1D2D3=0100,When D0D1D2D3=1000,2020/7/27,Chapter 11 Introduction to Digital Signal Processing,19,Analysis of the R/2R Ladder DAC,Lecture 27: Digital-to-Analog Conversion,When D3=D2=D1=D0=1, the output is:,If we use the general formula:,2020/7/27,Chapter 1

20、1 Introduction to Digital Signal Processing,20,R/2R DAC Product Introduction (AD7524),Lecture 27: Digital-to-Analog Conversion,This chip has a lot of applications. We will discuss some of them in the following lecture.,2020/7/27,Chapter 11 Introduction to Digital Signal Processing,21,AD7524 Used As

21、D/A Converter,Lecture 27: Digital-to-Analog Conversion,These two potentiometer are used for circuit calibration (gain adjustment).,When input is 0, output should also be 0.,vo,2020/7/27,Chapter 11 Introduction to Digital Signal Processing,22,AD7524 Used As Digital Attenuator,Lecture 27: Digital-to-A

22、nalog Conversion,Reference terminal becomes input.,【Example】 00000000 衰减 00000001 衰减256倍 00000100 衰减64倍 10000000 衰减2倍,2020/7/27,Chapter 11 Introduction to Digital Signal Processing,23,Singular Value Current Source R/2R DAC,Lecture 27: Digital-to-Analog Conversion,Use superposition theorem and Theven

23、ins theorem to analyze the above circuit.,When S1S3 is on separately,2020/7/27,Chapter 11 Introduction to Digital Signal Processing,24,Performance Characteristics of DACs,Lecture 27: Digital-to-Analog Conversion,Resolution: The number of bits that are converted.,The resolution of an n-bit DAC can al

24、so be expressed as,2.Accuracy: The ratio of maximum error to FSR.,For a 10 V FSR, if the maximum error is 10 mV, then,Ideally, the accuracy should be no worse than 1/2 LSB. For an 8-bit converter, the least significant bit is 0.392% of full scale, the accuracy should be approximately 0.2%.,2020/7/27

25、,Chapter 11 Introduction to Digital Signal Processing,25,Performance Characteristics of DACs,Lecture 27: Digital-to-Analog Conversion,3.Linearity: A linear error is a deviation from the ideal straight-line output of a DAC.,4.Offset error: The amount of output voltage when the input bits are all zero

26、s.,5.Monotonicity: A DAC is monotonic if it does not take any reverse steps when it is sequenced over its entire range of input bits.,6.Settling time: The time it takes a DAC to settle within 1/2 LSB of its final value when a change occurs in the input code.,The error analysis will be covered in the

27、 following lecture.,2020/7/27,Chapter 11 Introduction to Digital Signal Processing,26,Digital-to-Analog Conversion Errors,Lecture 27: Digital-to-Analog Conversion,Usually caused by some input bits stuck LOW or HIGH,Usually caused by insufficient resistor weight,Usually caused by a faulty feedback re

28、sistor,Usually caused by a faulty op-amp,2020/7/27,Chapter 11 Introduction to Digital Signal Processing,27,Testing Digital-to-Analog Converters,Lecture 27: Digital-to-Analog Conversion,A sequence of binary code is applied to the inputs, and the resulting output is observed.,The ideal output is a str

29、aight-line stairstep. As the number of bits in the binary code increases, the output approaches a straight-line linear ramp.,See demo,2020/7/27,Chapter 11 Introduction to Digital Signal Processing,28,DAC Error Analysis Example,Lecture 27: Digital-to-Analog Conversion,A straight 4-bit binary sequence

30、 is applied to the DAC input, the observed output is shown on the right. Identify the type of error, and give a suggestion to correct the fault.,Solution:,The error type is nonmonotonic.,Analysis of the output reveals that the device is converting the following sequence, rather than the actual binar

31、y sequence,0010, 0011, 0010, 0011, 0110, 0111, 0110, 0111, 1010, 1011, 1010, 1011, 1110, 1111, 1110, 1111,Apparently, the 21 bit is stuck in the HIGH (1) state.,2020/7/27,Chapter 11 Introduction to Digital Signal Processing,29,The Reconstruction Filter,Lecture 27: Digital-to-Analog Conversion,2020/7/27,Chapter 11 Introduction to Digital Signal Processing,30,Test Your Understanding,2.In an R/2R DAC, there are a) four values of resistors; b) one resistor value; c) two resistor values; d) A number of resistor values equal to the number of inputs;,Answer: c),In a binary-wei