12-1 EE 319K Introduction to Microcontrollers Lecture 12: A/D Conversion and Lab 8 Read Book Sections 10.2 and 11.4

12-2 Ramesh Yerraballi A/D and D/A Conversion Basics Digitization:Amplitude and time quantizing

12-3 Ramesh Yerraballi Nyquist Theory  If a signal is sampled at f s then the digital samples only contain frequency components from 0 to (1/2)f s  Conversely, if the analog signal does contain frequency components larger than (1/2)f s, then there will be an aliasing error.  Aliasing is when the digital signal appears to have a different frequency than the original analog signal.  Say, V(t) = A sin(2πft + )  Nyquist theory says that if f s is strictly greater than twice f, then one can determine A f and  from the digital samples.  But if f s is less than or equal to 2f, then the apparent frequency, as predicted by analyzing the digital samples, will be shifted to a frequency between 0 and (1/2)f s

12-4 Ramesh Yerraballi.. Nyquist Theory

12-5 Ramesh Yerraballi A/D and D/A Conversion Basics  Range of the system is the maximum minus the minimum values  Precision of the system defines the number of values from which the amplitude of the digital signal is selected. (Alternatives)  Resolution is the smallest change in value that is significant. Range = Precision x Resolution

12-6 Ramesh Yerraballi A/D Converter Example Analog to digital Converter  Analog input 0 ≤ V in ≤ +5  Digital output 0 ≤ ATD0DR0 ≤ 255 oDigital Output is about 256*V in /5 oOr Digital Output is about 255*V in / Analog Digital V in cm Analog D

12-7 Ramesh Yerraballi 9S12 has 16 Analog Inputs AD1 AD0 One Control Register per ADC module: ATD0CTL2 and ATD1CTL2

12-8 Ramesh Yerraballi Port AD0 ATD0CTL2=$80 ; set bit 7 to 1 to enable ADC ATD0CTL3=$08 ; sequence length = 1 SRES8 ; 1 for 8-bit values, 0 for 10-bit values

12-9 Ramesh Yerraballi ADC Clock  The ADC has an internal clock that controls how fast the ADC runs  Not how many samples it takes but how fast the conversion (A/D) works.  Speed controlled by 5-bit value in the lower 5- bits (PRS5-PRS1) of ATD0CTL4  Say this value is m (e.g., => m=4)  The ATD internal clock speed is given by: (1/2)E/(m+1) where E is the E clock speed  Say we want this speed to be 1 MHz, So for: oE-clock speed of 4 MHz m is set to 1 oE-clock speed of 8 MHz m is set to 3 oE-clock speed of 24 MHz m is set to 11  Internal clock speed can range from 500 kHz to 2 MHz

12-10 Ramesh Yerraballi Other settings  ATD0CTL5 write channel number (analog input) to start ADC  channel number $80 to $87 (CC:CB:CA)  ATD0STAT bit 7 SCF  cleared by write to ATD0CTL5 (i.e., starting a new conversion) or just write 1 to it  set when ADC finished  ATD0DR0 first 8/10-bit ADC result  precision 8/10-bit, 256/1024 alternatives  range 0 to +5V  resolution (5-0)/255  0.02 V ; (5-0)/1023  V 1.5/255  cm; 1.5/1023  cm

12-11 Ramesh Yerraballi 8-bit Conversion Example Digital o/p = 255 * V in /5 Ex1: V in = 1.50 => Dig out = Integer approx (255 * 1.50/5) = 76 = $4C = % Ex2: V in = 3.75 => Dig out = Integer approx (255 * 3.75/5) = 191 = $BF = %

12-12 Ramesh Yerraballi 10-bit Conversion Example Digital o/p = 1023 * V in /5 Ex1: V in = => Dig out = Integer approx (1023 * 0.005/5) = 1 = $001 = % Ex2: V in = => Dig out = Integer approx (1023 * 3.750/5) = 768 = $300 = %

12-13 Ramesh Yerraballi Complete ADC Example  Tut3 in TExaS is an ADC example  See ADC Driver  ADC_Init oTurns it on oSets it to 10-bit mode  ADC_In owrite channel number to ATD0CTL5 owait for SCF flag in ATD0STAT oread 10-bit result from ATD0DR0  SCI_OutDec

12-14 Ramesh Yerraballi Lab 8: Design a Position Meter  Hardware  Transducer  Electronics  ADC  Software  ADC device driver  Timer routines oOutput compare interrupts  LCD driver  Measurement system oHow fast to update oFixed-point number system oAlgorithm to convert ADC into position

12-15 Ramesh Yerraballi Lab8: Data Flow Graph 1.50 cm

12-16 Ramesh Yerraballi Lab8: Transducer  A transducer converts some observable phenomena (temperature, pressure, opening, position, speed etc. to a analog form that can then be digitized.  A potentiometer converts position to a resistance  Solder wires to pins 1,2,3  Glue potentiometer to a solid base  Position metric ruler (for calibration and testing)  Create a hair-line cursor

12-17 Ramesh Yerraballi Lab8: Circuit  What is R 12 + R 23 at all times?  What are R 12 and R 23 when cursor is at 1 cm?  What is V in when cursor is at 1 cm?  What is ATD0DR0 when cursor is at 1 cm?  What do you want to display on the LCD when cursor is at 1 cm?

12-18 Ramesh Yerraballi Lab8: Call Graph

12-19 Ramesh Yerraballi Convert ADC data into integer part of fixed-point Three possibilities  The relationship between the ADC data and what it represents is expressible as an equation  The relationship is expressible as a partially complete table and we use interpolation to infer the missing  The relationship is expressible as a complete table and we perform explicit table lookup

12-20 Ramesh Yerraballi Equation for Temperature Example Complex Equation let n be ADC (0 to 1023) V = 5.0*n/1023 (in volts) R = *V (in k) T = 1/(H 0 +H 1 ln(R)) (in o C) (H 0 = , H 1 = ) I = 100*T (in 0.01 o C) Simple Equation I = 3971 – *n

12-21 Ramesh Yerraballi Muls and Divs mulunsigned A*B into D emulunsigned D*Y into 32-bit Y:D emulssigned D*Y into Y:D idivunsigned D/X into X, D remainder idivssigned D/X into X, D remainder fdivunsigned (D:0)/X into X, D remainder edivunsigned (Y:D)/X into Y, D remainder edivssigned (Y:D)/X into Y, D remainder

12-22 Ramesh Yerraballi Examples 1. Count (0 to 199) = (5/9) * Angle (0 to 359) * Count =(5*Angle)/9 ldd Angle ldy #5 emul ;(Y:D)= 5*Angle ldx #9 ediv ;Y=(5*Angle)/9 sty Count 2. Angle (0 to 359) = (9/5) * Count(0 to 199) * Angle =(9*Count)/5 ≈ (65536*Count)/36409 ldd Count ldx #36409 fdiv stx Angle 3. Column (0 to 6) = (7/256) * Xpos (0 to 255) * Column =(7*Xpos)/256 ldaa Xpos ldab #7 mul ;RegD=7*Xpos staa Column ;RegA=(7*Xpos)/256

12-23 Ramesh Yerraballi Promotion/Demotion Unsigned 8 to 16-bit promotion ;to promote RegB into RegD clra ; to promote RegA into RegX tfr A,B clra tfr D,X Signed 8 to 16-bit promotion sex A,D (same as tfr A,D ) sex B,D (same as tfr B,D ) sex A,X (same as tfr A,X ) sex B,X (same as tfr B,X ) sex A,Y (same as tfr A,Y ) sex B,Y (same as tfr B,Y ) 16 to 8-bit demotion (signed or unsigned) tfr D,A tfr D,B tfr X,A tfr X,B tfr Y,A tfr Y,B

12-24 Ramesh Yerraballi Equation for Temperature Example Complex Equation let n be ADC (0 to 1023) V = 5.0*n/1023 (in volts) R = *V (in k) T = 1/(H 0 +H 1 ln(R)) (in o C) (H 0 = , H 1 = ) I = 100*T (in 0.01 o C) Simple Equation I = 3971 – *n Using fdiv, find m such that 65536/m = m = 65536/ = ≈ * Reg D has ADC result, 0 to 1023 ldx #33153 fdiv pshx ; *n ldd #3971 subd 2,SP+ std I ; 0.01 C

12-25 Ramesh Yerraballi Simple Equation

12-26 Ramesh Yerraballi Interpolation  We will look at examples in TExaS help system  8-bit table access on the 6812  16-bit table access on the 6812  Basic idea Y L - Y 1 Y 2 - Y 1 X L - X 1 X 2 - X 1 Y L = Y 1 + B *(Y 2 - Y 1 ) = B The TBL Instruction does this

12-27 Ramesh Yerraballi Back to Lab 8  Sample ADC every 0.2s  Map (Data: 0 to 255) into (Position: 0000 to +1500)  Option A: Use a linear function  Position = 1500*(Sample)/255 (NOT THIS ONE)  Option B : Use a paired calibration table (S[i],P[i])  S[i] are ADC samples measured at corresponding positions P[i]  Given sample, find i such that S[i]<=sample<S[i+1]  Use linear interpolation (look up etbl in TExaS help)  position = P[i]+((sample-S[i])*(P[i+1]-P[i]))/(S[i+1]-S[i])  Option C : Create a 255-entry calibration table (P[ATD0DR0L])  Fixed-Point output  1234 is displayed as “1.234 cm”