1 Basic Signal Conversion 센서 및 계측 공학 (Sensor and Instrumentation Engineering) 2016 년 1 학기 충북대학교 전기전자반도체공학과 박 찬식 교육관 325 호, T. 3259

목차 Binary Code Sampling Concepts Digital To Analog Converters 2

3 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

4 Binary Code n Numbers in Base 10 u = 4     n Numbers in Base 2 u 1101 = 1     2 0 = 13 (Decimal) n n bits Binary Number u Unipolar: 0 ~ 2 n –1 u Bipolar: - 2 n-1 ~ 2 n-1 –1 n Binary Strings as a fraction of full scale u Used in ADC u 0 ~ 1 – 2 -n u 1101 = 1     2 -4 = 13/16 (Decimal) u See Figure 4.2, for 4 bits Natural Binary Code

5 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 Full Scale of 10V, 4-bit Encoding F MRV = 10/16 = 625mV F Impossible to represent a voltage lower than 625mV u To improve accuracy of conversion, Increase n F Example: n = 8 F MRV = 10 / 28 = 39mV

6 BCD and Gray Code n Binary Coded Decimal u 4 bit is used to represent 0 ~ 9 F 2 4 = 16 (6 개는 버림 ) u Example F 283 Decimal F Binary F BCD n Gray Code u Useful when angle is measured u Change by only one bit as it proceed from one bit pattern to the next

7 Bipolar Codes

8 Code Conversion

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10 Sampling Concepts n Sampling n Fourier Transform

11 Sampling Theorem 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 n The use of low pass filter before sampling u To band limit signal u To Avoid Aliasing u Loss of high frequency information F Error of omission

12 Aliasing n When sampling frequency is less than twice the highest frequency of the signal, Signal is no longer recoverable by low pass filtering n Homework #4-1 u 1 초에 30 번 돌아가는 바퀴를 1/30 초 단위로 촬영한 영화를 보면 ? u 바퀴가 뒤로 돌아가는 것처럼 보인다면 실제 바퀴의 회전속도는 ? F 가능한 최소값을 구할 것 n Cosine wave Example Spectrum of cosine wave Low pass Filter reconstruct cosine wave Of lower frequency (fs – fo)

13 Interpolation n The process of reconstructing a signal from its values at discrete instants of time u Zero order hold or One Point u Linear or Two Point u Band limited or Low pass Filtering

14 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)

15 Implementing DAC n Usually Single Chip n A Realistic Value of R in IC is 5K  u 4 bit DAC F 2 4 R = 80K  u 8 bit DAC F 2 8 R = 1.28M  u 12 bit DAC F 2 12 R = 20.48M  n Large R is hard to implement in IC u Needs very large area n Hope to design a DAC with Small, Equal-Value Resistors u Easy to implement with IC technology

16 Practical DAC based on R-2R ladder network n Resistive Ladder Network n Require twice R n But small value u 5K  and 10K  n Homework #4-2 u Show that Eout = Eref x (bit3/2 + bit2/4 + bit1/8 + bit0/16) 2R||2R=R R+R=2R

17 Actual 8-bit DAC n Analog Devices AD558 n DAC for PC prototype board Separate Analog and Digital Ground To reduce noise

18 C Program for DAC Generating Sawtooth waveform  Only the LS 8 bits of 16-bit integer are used since this is 8-bit DAC