#### 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 Used in ADC 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 Analog Devices AD558 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