EE 319K Introduction to Embedded Systems Lecture 11: Data Acquisition, Numerical Fixed-Point Calculations, Lab 8 Bard, Tiwari, Telang, Janapa Reddi, Gerstlauer, Valvano, Yerraballi

Agenda Recap Agenda Sampling, Nyquist Analog to Digital Conversion Data acquisition Numerical fixed-point calculations Lab 8 Bard, Tiwari, Telang, Janapa Reddi, Gerstlauer, Valvano, Yerraballi

Data Acquisition System (Lab 8) Hardware Transducer Electronics ADC Software ADC device driver Timer routines Output compare interrupts LCD driver Measurement system How fast to update Fixed-point number system Algorithm to convert ADC into position Bard, Tiwari, Telang, Janapa Reddi, Gerstlauer, Valvano, Yerraballi

Analog Input Device Transducer – A device actuated by power from one system that supplies power in the same or other form to another system. Bard, Tiwari, Telang, Janapa Reddi, Gerstlauer, Valvano, Yerraballi

Transducer Circuit Position to voltage Bard, Tiwari, Telang, Janapa Reddi, Gerstlauer, Valvano, Yerraballi

Data Acquisition System Data flow graph ST7735 P o s i t n S e r V l a g + 3.3V A D C h d w v m p 4 9 5 y T c k I R L F x - 2 . M b Bard, Tiwari, Telang, Janapa Reddi, Gerstlauer, Valvano, Yerraballi

Data Acquisition System Call graph ST7735 Bard, Tiwari, Telang, Janapa Reddi, Gerstlauer, Valvano, Yerraballi

Thread Synchronization in Lab 8 Background thread Foreground thread SysTick ISR Sample ADC Store in ADCmail Set ADCstatus Main loop Wait for ADCstatus Read ADCmail Clear ADCstatus Convert to distance Display on LCD Bard, Tiwari, Telang, Janapa Reddi, Gerstlauer, Valvano, Yerraballi

Sampling Jitter Definition of time-jitter, δt: Let nΔt be the time a task is scheduled to be run and tn the time the task is actually run Then δtn= tn – nΔt Real time systems with periodic tasks, must have an upper bound, k, on the time-jitter -k ≤ δtn ≤ +k for all n Bard, Tiwari, Telang, Janapa Reddi, Gerstlauer, Valvano, Yerraballi

Measurement Resolution: Limiting factors Accuracy: Limiting factors Transducer noise Electrical noise ADC precision Software errors Accuracy: Limiting factors Resolution Calibration Transducer stability Average accuracy (with units of x) = Bard, Tiwari, Telang, Janapa Reddi, Gerstlauer, Valvano, Yerraballi

Fixed-Point Revisited Why: express non-integer values no floating point hardware support (want it to run fast) When: range of values is known range of values is small How: 1) variable integer, called I. may be signed or unsigned may be 8, 16 or 32 bits (precision) 2) fixed constant, called  (resolution) value is fixed, and can not be changed not stored in memory specify this fixed content using comments value  integer •  Bard, Tiwari, Telang, Janapa Reddi, Gerstlauer, Valvano, Yerraballi

Fixed-Point Numbers The value of the fixed-point number: Fixed-point number  I• Smallest value = Imin • D, where Imin is the smallest integer Largest value = Imax • D, where Imax is the largest integer Decimal fixed-point, =10m Decimal fixed-point number = I • 10m Nice for human input/output Binary fixed-point, =2m Binary fixed-point number = I • 2m Easier for computers to perform calculations Bard, Tiwari, Telang, Janapa Reddi, Gerstlauer, Valvano, Yerraballi

Fixed-Point Math Example Consider the following calculation. C = 2**R The variables C, and R are integers 2p ≈ 6.283 C = (6283*R)/1000 Bard, Tiwari, Telang, Janapa Reddi, Gerstlauer, Valvano, Yerraballi

Fixed-Point Math Example Calculate the volume of a cylinder V = *R2 * L The variables are binary fixed-point R = I*2-4 cm L = J*2-4 cm V = K*2-8 cm3 2p ≈ 201*2-5 K = (201*I*I*J)>>9 Bard, Tiwari, Telang, Janapa Reddi, Gerstlauer, Valvano, Yerraballi

Make a Voltmeter with ADC Vin (V) Analog in N Digital out I (1 mV) Variable part LCD 0.000 0.75 1024 750 0.750 1.5 2048 1500 1.500 2.25 3072 2250 2.250 3 4096 3000 3.000 =0.001 V Vin = 3•N/4096 how ADC works Vin = I • 0.001 definition of fixed point I = (3000*N)/4096 substitution I = (m•N+b)/ 4096 calibrate to get m and b Bard, Tiwari, Telang, Janapa Reddi, Gerstlauer, Valvano, Yerraballi

Lab 8 Calibration Bard, Tiwari, Telang, Janapa Reddi, Gerstlauer, Valvano, Yerraballi