Transcript Digital to Analog Converters n

```Basic Signal Conversion
센서 및 계측 공학
(Sensor and Instrumentation Engineering)
2016년 1학기
충북대학교 전기전자반도체공학과
박 찬식
http://gnc.chungbuk.ac.kr
[email protected]
교육관 325호, T. 3259
1
목차
n
n
n
Binary Code
Sampling Concepts
Digital To Analog Converters
2
Signal Conversion System
n
Analog to Digital
u
Conversion of Sensor
Output to Binary Code
n
Digital to Analog
u
Conversion of Binary Code
to Analog Signal
3
Binary Code
n
Numbers in Base 10
u
n
461.8 = 4 102
+ 6 101
+ 1 100
+ 8 10-1
Numbers in Base 2
u
1101 = 1 23
+ 1 22
+ 0 21
+ 1 20
= 13 (Decimal)
n
n
n bits Binary Number
u Unipolar: 0 ~ 2n –1
u Bipolar: - 2n-1 ~ 2n-1 –1
Binary Strings as a fraction
of full scale
u 0 ~ 1 – 2-n
u 1101 = 1 2-1
+ 1 2-2
+ 0 2-3
+ 1 2-4
= 13/16 (Decimal)
u See Figure 4.2, for 4 bits
Natural Binary Code
4
Resolution and MRV
n
For n bits Binary
u
Resolution : 2-n
n
MRV (Minimum Representable
Voltage)
u MRV = Full Scale 
Resolution
u Example
F
F
F
u
Full Scale of 10V, 4-bit
Encoding
MRV = 10/16 = 625mV
Impossible to represent a
voltage lower than 625mV
To improve accuracy of
conversion, Increase n
F
F
Example: n = 8
MRV = 10 / 28 = 39mV
5
BCD and Gray Code
n
Binary Coded Decimal
u
4 bit is used to
represent 0 ~ 9
F
u
24 = 16 (6개는 버림)
Example
F
F
F
283 Decimal
000100011011 Binary
0010 1000 0011 BCD
n
Gray Code
u
u
Useful when angle is
measured
Change by only one bit
as it proceed from one
bit pattern to the next
6
Bipolar Codes
7
Code Conversion
8
Code Conversion
9
Sampling Concepts
n
Sampling
n
Fourier Transform
10
Sampling Theorem
n
n
The conditions for exact
representation and
recovery are: The
Signal must be band
limited, and the sampling
frequency must not be
lower than twice the
highest frequency
present in the signal
n
In real, Sensor output
has infinite harmonics
The use of low pass
filter before sampling
u
u
u
To band limit signal
To Avoid Aliasing
Loss of high frequency
information
F
Error of omission
11
Aliasing
n
n
n
When sampling frequency
is less than twice the
highest frequency of the
signal, Signal is no longer
recoverable by low pass
filtering
Homework #4-1
u 1초에 30번 돌아가는
바퀴를 1/30초 단위로
촬영한 영화를 보면 ?
u 바퀴가 뒤로 돌아가는
것처럼 보인다면 실제
바퀴의 회전속도는 ?
F 가능한 최소값을 구할
것
Cosine wave Example
Spectrum of cosine wave
Low pass Filter reconstruct cosine wave
Low pass Filter reconstruct cosine wave
Of lower frequency (fs – fo)
12
Interpolation
n
The process of
reconstructing a signal
from its values at
discrete instants of time
u
u
u
Zero order hold
One Point
Linear
Two Point
Band limited
Low pass Filtering
or
or
or
13
Digital to Analog Converters
n
n-bit DAC
u n Latches hold Binary
Number
u n transistor switch
Register network
u Voltage reference
controls the range of
output
u OP amp provides
summing function
n
Concept: 4-bit DAC
u 1010B  Eout ??
F
Bit 3 (1000B)
• Eout = R/2R x Eref
F
Bit 1 (0010B)
• Eout = R/8R x Eref
F
Total (1010B)
• Eout = Eref/2 + Eref/8
u
Eout: 0 ~ (15/16 x Eref)
14
Implementing DAC
n
n
Usually Single Chip
A Realistic Value of R in
IC is 5K
u
4 bit DAC
F
u
u
Easy to implement with IC
technology
28R = 1.28M
12 bit DAC
F
n
Hope to design a DAC
with Small, Equal-Value
Resistors
8 bit DAC
F
u
24R = 80K
n
212R = 20.48M
Large R is hard to
implement in IC
u
Needs very large area
15
Practical DAC based on R-2R ladder
network
n
Resistive Ladder Networkn Require twice R
n
But small value
u
n
5K and 10K
Homework #4-2
u
Show that
Eout = Eref x (bit3/2 +
bit2/4 + bit1/8 + bit0/16)
R+R=2R
2R||2R=R
16
Actual 8-bit DAC
n
n
DAC for PC prototype
board
Separate Analog and Digital Ground
To reduce noise
17
C Program for DAC
n
Generating Sawtooth waveform
u
Only the LS 8 bits of 16-bit integer are used since this
is 8-bit DAC
18
```