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# Analog-to-Digital Conversion

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1. Analog-to-Digital Conversion Terminology analog: continuously valued signal, such as temperature or speed, with infinite possible values in between digital: discretely valued signal, such as integers, encoded in binary analog-to-digital converter: ADC, A/D, A2D; converts an analog signal to a digital signal digital-to-analog converter: DAC, D/A, D2A An embedded system’s surroundings typically involve many analog signals.

2. Vmax = 7.5V 4 4 1111 7.0V 1110 6.5V 1101 3 3 6.0V 1100 5.5V 1011 2 2 analog input (V) analog output (V) 5.0V 1010 4.5V 1001 1 1 4.0V 1000 3.5V 0111 time time 0110 3.0V t1 t2 t3 t4 t1 t2 t3 t4 2.5V 0101 0100 0110 0110 0101 0100 1000 0110 0101 2.0V 0100 Digital input Digital output 1.5V 0011 1.0V 0010 0.5V 0001 0V 0000 analog to digital digital to analog proportionality Analog-to-digital converters Embedded Systems Design: A Unified Hardware/Software Introduction,(c) 2000 Vahid/Givargis

3. Proportional Signals Simple Equation Assume minimum voltage of 0 V. Vmax = maximum voltage of the analog signal a = analog value n = number of bits for digital encoding 2n = number of digital codes M = number of steps, either 2nor 2n – 1 d = digital encoding a / Vmax = d / M

4. Resolution Let n = 2 M = 2n – 1 3 steps on the digital scale d0 = 0 = 0b00 dVmax = 3 = 0b11 M = 2n 4 steps on the digital scale d0 = 0 = 0b00 dVmax - r = 3 = 0b11 (no dVmax ) r, resolution: smallest analog change resulting from changing one bit

6. ADC: Digital Encoding Guessing the encoding is similar to finding an item in a list. • Sequential search – counting up: start with an encoding of 0, then 1, then 2, etc. until find a match. • 2n comparisons: Slow! • Binary search – successive approximation: start with an encoding for half of maximum; then compare analog result with original analog input; if result is greater (less) than the original, set the new encoding to halfway between this one and the minimum (maximum); continue dividing encoding range in half until the compared voltages are equal • n comparisons: Faster, but more complex converter  Takes time to guess the encoding: start conversion input, conversion complete output

7. ADC using successive approximation • Given an analog input signal whose voltage should range from 0 to 15 volts, and an 8-bit digital encoding, calculate the correct encoding for 5 volts. Then trace the successive-approximation approach to find the correct encoding. • Assume M = 2n – 1 a / Vmax = d / M 5 / 15 = d / (256 - 1) d = 85 or binary 01010101

8. 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 ADC using successive approximation Step 1-4: determine bits 0-3 ½(Vmax – Vmin) = 7.5 volts Vmax = 7.5 volts. ½(7.5 + 0) = 3.75 volts Vmin = 3.75 volts. ½(7.5 + 3.75) = 5.63 volts Vmax = 5.63 volts ½(5.63 + 3.75) = 4.69 volts Vmin = 4.69 volts. Embedded Systems Design: A Unified Hardware/Software Introduction,(c) 2000 Vahid/Givargis

9. 0 1 0 1 0 0 0 0 0 1 0 1 0 1 0 0 0 1 0 1 0 1 0 0 0 1 0 1 0 1 0 1 ADC using successive approximation Step 5-8: Determine bits 4-7 ½(5.63 + 4.69) = 5.16 volts Vmax = 5.16 volts. ½(5.16 + 4.69) = 4.93 volts Vmin = 4.93 volts. ½(5.16 + 4.93) = 5.05 volts Vmax = 5.05 volts. ½(5.05 + 4.93) = 4.99 volts Embedded Systems Design: A Unified Hardware/Software Introduction,(c) 2000 Vahid/Givargis

10. Constructing ADC Statemachine Analoginput Timingcontrol SAR BUF Vmax DAC Digitaloutput Vmin SAR Comparator SAR: Successiveapproximation register

11. Bit Weight Notice the concept of bit weight in the last example: bit 7 = 7.5 V = 15/2 bit 6 = 3.75 V = 15/4 Each bit is weighted with an analog value, such that a 1 in that bit position adds its analog value to the total analog value represented by the digital encoding. Example: -5 V to +5 V analog range, n=8

12. Bit Weight Example (continued): -5 V to +5 V analog range, n=8 Digital numbers for a few analog values • Values shown increment by 6 bits (weight for bit position 5 is 1.25 V) • Maximum digital number only approximates the maximum analog value in the range • Try (-5) + sum of all bit weights

13. Terms & Equations Offset: minimum analog value Span (or Range): difference between maximum and minimum analog values Max - Min n: number of bits in digital code (sometimes referred to as n-bit resolution) Bit Weight: analog value corresponding to a bit in the digital number Step Size (or Resolution): smallest analog change resulting from changing one bit in the digital number, or the analog difference between two consecutive digital numbers; also the bit weight of the Span / 2n(Assume M = 2n) Let AV be Analog Value; DN be Digital Number: AV = DN * Step Size + Offset = (DN / 2n)* Span + Offset DN = (AV - Offset) / Step Size = (AV - Offset) * 2n / Span

14. MPC555 QADC64 QADC64 - Queued Analog to Digital Converter Module-64 • 16 analog channels via internal multiplexing • 10-bit ADC resolution • Converts voltage to an integer value (0-1023) • Polling or interrupt driven • Programmable channels AN0-ANx

16. MPC555 QADC64 CCW Table CCW0 CCW1 … CCW63 A CCW tells the ADC which channel to scan and how long to sample the signal. AN0 AN1 AN2 AN3 ADC QACR1: start a scan by setting SSE bit QASR0: CF flag is set after conv is done Result Table Result0 Result1 … Result63 A Result is stored for each scan of a channel when the conversion is complete.

17. Scan Sequence and Conversion • After the ADC is initialized, a sequence of scans is set up as a “queue” in the CCW Table. • Each channel to be scanned is added to the queue at successive positions 0, 1, 2, etc. For example: CCW0, CCW1, CCW2, CCW3. • An end-of-queue marker should be added at the next position. • The ADC starts the scan and conversion when it is triggered by the enable bit. • The ADC reads the CCWs, one after another until end-of-queue is reached, and for each CCW, it converts the signal on the specified channel. • A conversion on a channel stores a result in the respective position of the Result Table, e.g., the result for CCW0 is stored at Result0, etc. • When the scan and conversion is complete for all CCWs, then the ADC sets the completion flag to 1. Now all digital results are available to be read from the Result Table.

18. QADC Interface • Programmability using a queue • Scan a few channels quickly • Scan a channel multiple times • Scan large number of channels • QACR1 – QADC64 Control Register 1 • 16 bit register at 0x30480C • SSE1 – bit 2 – Single Scan enable (bit 0 is MSb) • MQ1 – bits 3-7 • Set to binary 00001 to identify Queue 1 • QASR0 – QADC64 Status Register 0 • 16 bit register at 0x304810 • ADC sets a flag when the conversion is done • CF1 – bit 0 – Conversion Complete flag (bit 0 is MSb)

19. QADC Interface • CCW Table • table of Conversion Command Words, where each command word specifies how to perform a scan/conversion operation for an input channel • CCW: 16 bit command word, starting at address 0x304A00 • A queue is a scan sequence of one or more input channels. • A queue is started by a trigger event, which is a way to cause the QADC64 to begin executing the command words. • Each CCW requests the conversion of an analog channel to a digital result. The CCW specifies the analog channel number, the input sample time, and whether the queue is to pause after the current CCW.

20. QADC Interface • Total conversion time: initial sample time, final sample time, and resolution time • Initial sample time – time during which the selected input channel is driven by the buffer amplifier onto the sample capacitor (disabled by means of the BYP bit in the CCW) • Final sampling period – time to set up DAC array • Resolution period – time to convert voltage in the DAC array to a digital value

22. QADC64 Memory-mapping Layout 0x30 4A00 Bit 0 Bit 15 0x30 4800 Module Config. Reg. 64-entry 16-bit Conversion Command Word Table(Configurable: one queueor two queues) 0x30 4802 Test Reg. 0x30 4804 Interrupt Reg. 0x30 4806 Port A Data Port B Data 0x30 4A7E 0x30 4808 Port A Direction Reg. 0x30 480A 0x30 4A80 Control Reg. 0 64-entry 16-bit Result Word Table 64-entry, 16-bit 0x30 480C Control Reg. 1 0x30 480E Control Reg. 2 0x30 4810 Status Reg. 0 0x30 4812 0x30 4AFE Status Reg. 1 The above is the memory-mapping for the 1st QADC64.The 2nd QADC64 using different starting addresses.

23. Programming QADC64 6 7 8 9 10 11 12 12 14 15 CCW Format: P BYP IST CHAN • Example: Write a CCW into CCW table to scan channel nChannel with no amplifier bypassing and 4-cycle initial sample time (16 cycles in total). • nQueueVal = nChannel;nQueueVal = nQueueVal & 0xFF3F; nQueueVal = nQueueVal | 0x0040;*(pCCWTable + nQueue) = nQueueVal;

24. The Control Registers

25. The Status Registers

26. Programming the ADC • Initialize the QADC: reset queue to be empty; set up interrupt driven mode, interrupt levels, clock rate. • Write into the command word queue (a sequence of A to D conversion commands). • In software triggered mode, initiate the conversion by writing into QACR[SSE] bit. • Monitor the conversion finished flag (CF). • Read the results, and reset CF and PF flags.

27. Programming QADC64 Example: Reset QADC64 by writing END-OF-QUEUE (63 in decimal) as the first word of CCW table. void QADCR64_Reset() { g_nNumChannels = 0; QADCR64_SetQueue(0, QADCR64_END_QUEUE, QADCR64_QCKL_MAX); } QADCR64_SetQueue: Given CCW entry index, CCW channel/end-of-queue command, and final sample setting, write the corresponding CCW.

28. Programming QADC64 Example: Start scanning in polling mode (interrupt disabled) • Set up control register 1 void QADCR64_Start_Convert_Poll () { unsigned short * pQACR1; pQACR1 = (unsigned short *) 0x30480C; // Bit 0 CIE1 Conversion Interrupt Enable 0 // Bit 1 PIE1 Pause Interrupt Enable 0 // Bit 2 SSE1 Single Scan Enable 1 // MQ=00001; software triggered single scan mode *pQACR1 = 0x2100; }

29. Programming QADC64 Example: Determine if all conversions has finished • Checking status register 0 unsigned short QADCR64_Is_Done() { unsigned short * pQASR0; unsigned short nResult; pQASR0 = (unsigned short *) 0x304810; nResult = (*pQASR0 & 0x8000); return nResult; }