ADC, Data Acquisition and Control (2024)

Chapter14: Analog to Digital Conversion, Data Acquisition and Control
Modified to be compatible with EE319K Lab 8

Jonathan Valvano andRameshYerraballi

Throughout this course we have seen that anembeddedsystem uses its input/output devices to interact with the externalworld. Inthis chapter we will focus on input devices that we use to gatherinformationabout the world. More specifically, we present a technique for thesystem to measureanalog inputs using an analog to digital converter (ADC). We will useperiodicinterrupts to sample the ADC at a fixed rate. We define the rate at which we sample as the sampling rate, and use the symbol fs.We will then combinesensors, theADC, software, PWM output and motor interfaces to implement intelligentcontrolon our robot car.

Video 14.1. Digitization Concepts.

The measurand is a real world signal ofinterestlike sound, distance, temperature, force, mass, pressure, flow, lightandacceleration. Figure 14.1 shows the data flow graph for a dataacquisitionsystem or control system. x(t) is the time-varying signal we are attempting to measure. The control system uses an actuatorto drive ameasurand in the real world to a desired value while the dataacquisitionsystem has no actuator because it simply measures the measurand inanonintrusive manner. Consider an entire system that collects data, not just the ADC. The following four limitations exist when sampling data.

• Amplitude resolution
• Amplitude range
• Time quantization
• Time interval

Amplitude resolution is the smallest change in input signal that can be distinguished.For example, we might specify the resolution as dX.Amplitude range is defined as the smallest to largest input value that can be measured. For example, we might specify the range as Xmin to Xmax.Amplitude precision is defined as the number of distinct values from which the measurement is selected. The units of precisionare given in alternative or bits. If a system has 12-bit precision, there are 2^12 or 4096 distinct alternatives. For example if we use a slide pot to measure distance, the range of that pot might be 0 to 1.5cm. If there is no electrical noise and we use a 12-bit ADC, then the theoretical resolution is 1.5cm/4095, or about 0.0004 cm. In most systems, the resolution of the measurement is determined by noise and not the number of bits in the ADC. Time quantization is the time difference between one sample and the next. Time interval is the smallest to largest time during which we collect samples. If we use a 10-Hz SysTick interruptto sample the ADC and calculate distance, the sampling rate, fs, is 10 Hz, and the time quantization is 1/fs=0.1 sec. If we use a memory buffer with 500 elements, thenthe time interval is 0 to 50 sec.

: Assume Xmin, Xmax, and dX are all given in the same units. Give a formula that relates the precision in bits as a function of Xmin, Xmax and dX.

: Assume the precision is n in bits, and Xmin, Xmax, and dX are all given in the same units. Give a formula that relates the resolution, dX as a function of Xmin, Xmax and n.

: Assume you have a 12-bit ADC and store data into an array of type uint16_t. Let fs be the sampling rate in Hz, and T be the total time interval required to collect samples in sec. Give a formula that relates needed memory in bytes as a function of fs and T.

: Assume you have an 8-bit ADC. Let the sampling rate be 100 Hz. Assume you allocate 20,000 out of the available 32,768 bytes of RAM to store the data. What is the corresponding time interval? I.e., how many seconds of data can you record?

: Assume you have a 4-bit DAC used to play sound. Let the sampling rate be 11 kHz. You can pack two DAC samples into one byte. Assume you allocate 128 kibibytes out of the available 256 kibibytes of ROM to store the data. What is the corresponding time interval? I.e., how many seconds of sound can you play?

Figure 14.1. Signal paths a data acquisitionsystem.

The input or measurand is x. The outputis y.A transducer converts x into y. A wide variety of inexpensive sensors can beseen at https://www.sparkfun.com/categories/23 Examples include

·SoundMicrophone

·Pressure, mass,force Strain gauge, forcesensitive resistor

·TemperatureThermistor,thermocouple, integrated circuits

·DistanceUltrasound,lasers, infrared light

·FlowDopplerultrasound, flow probe

·AccelerationAccelerometer

·LightCamera

·BiopotentialsSilver-SilverChloride electrode

A lineartransducer is aninput/outputfunction fits a straight line. In other words, the input/output response fits a linear equation:

y = m*x*b

where m and b are constants.Software will have an easy time with a lineartransducer. Forexample, the linear potentiometer, PTA20432015CPB10, hasa transfer function as shown in Figure 14.2, where the input x is distance in cm, and the output y is resistance in kΩ. You can use a simple circuit to convert resistance to voltage, the ADC to convert voltage to an integer, and simple softwareto convert an integer to distance.

Figure 14.2.The linear potentiometer distance sensor exhibits linear behavior.

: Consider the linear potentiometer in Figure 14.2. Let x be the distance in cm and let y be the resistance in kohm. Give an appropriate transfer function showing y as a function of x.

A nonmonotonictransducer is aninput/outputfunction that does not have a mathematical inverse. For example, if twoor moreinput values yield the same output value, then the transducer isnonmonotonic.Software will have a difficult time correcting a nonmonotonictransducer. Forexample, the Sharp GP2Y0A21YKIR distance sensorhasa transfer function as shown in Figure 14.3. If you read a transducervoltageof 2 V, you cannot tell if the object is 3 cm away or 12 cm away. However,if we assume the distance is always greater than 10cm, then this transducer can be used. Details about transducers and actuators can befound in EmbeddedSystems: Real-Time Interfacing to ARM Cortex-MMicrocontrollers, 2020,ISBN: 978-1463590154.

Figure 14.3.The Sharp IR distance sensor exhibits nonmonotonic behavior.

14.2. The Analog to Digital Converter

An analog to digitalconverter(ADC)converts an analog signal into digital form,shown in Figure 14.4. An embeddedsystem uses the ADC to collect information about the external world(dataacquisition system.) The input signal is usually an analog voltage, andtheoutput is a binary number. The ADC precisionis the number ofdistinguishableADC inputs (e.g., 4096 alternatives, 12 bits). The ADC rangeisthe maximum and minimum ADC input (e.g., 0 to +3.3V). The ADCresolutionis the smallestdistinguishable change in input (e.g.,3.3V/4095, which is about 0.81 mV). The resolutionis the change in input that causes the digital output to change by 1.

Range(volts) =Precision(alternatives) • Resolution(volts)

Figure 14.4. A 12-bit ADC converts 0 to 3.3V on its inputinto a digital number from 0 to 4095.

The most pervasive method for ADC conversion isthe successiveapproximationtechnique, as illustrated in Figure 14.5. A12-bit successiveapproximation ADC is clocked 12 times. At each clock another bit isdetermined,starting with the most significant bit. For each clock, the successiveapproximation hardware issues a new "guess" on V_dacby setting the bit under test to a "1". If V_dac isnow higher than the unknown input, V_in, then the bitundertest is cleared. If V_dac is less than V_in,then the bit under test is remains 1. In this description, bitis anunsigned integer that specifies the bit under test. For a 12-bit ADC, bitgoes 2048, 1024, 512, 256,...,1. D_out is the ADCdigitaloutput, and Z is the binary input that is true if V_dacis greater than V_in.

InteractiveTool 14.1

: With successive approximation, what is the strategy when making the first guess?For example, if you had a 10 bit ADC, what would be your first guess?

Observation: The speed of a successiveapproximationADC relates linearly with its precision in bits.

Normally we don’t specify accuracy forjust the ADC, butrather we give the accuracy of the entire system (including transducer,analogcircuit, ADC and software). An ADC is monotonicifit has no missing codes as the analog input slowly rises. This means ifthe analog signal is a slowlyrisingvoltage, then the digital output will hit all values one at a time, always going up, never going down. The figure ofmeritof an ADC involves three factors:

• precision (number of bits),
• speed (how fast can we sample), and
• power (how much energy does it take to operate).

How fastwe can sample involves both the ADC conversion time (how long it takestoconvert), and the bandwidth (what frequency components can berecognized by theADC). The ADC cost is a function of the number and quality of internalcomponents. Two 12-bit ADCs are built into the TM4C123microcontroller, called ADC0 and ADC1.You will use ADC0 to collect data and we will use ADC1 and the PD3 pintoimplement a voltmeter and oscilloscope using TExaSdisplay.

Table 14.1 shows the ADC0register bitsrequired to performsampling on a single channel. Any bits not specified will read 0. There are two ADCs; you will use ADC0 and TExaSdisplay uses ADC1. For more complex configurations refer tothespecific data sheet. The value in the ADC0_PC_R specifiesthe maximum sampling rate, see Table 14.2. This is not the actual sampling rate; it is the maximum possible.Setting ADC0_PC_R to 7, allows the TM4C123 to sample up to 1million samples per second. The example code in this section will set ADC0_PC_R to 1, because we will be sampling much slower than 125 kHz. It will be more accurate and require less power to run at 125 kHz maximum mode, as compared to 1 MHz maximum mode.In this chapter we will use software trigger mode, so the actual sampling rate is determined by the SysTick periodic interrupt rate; the SysTick ISR will take one ADC sample.On the TM4C123, we will need to set bits in the AMSELregister to activate the analog interface. Furthermore, we will clear bits DENregister to deactivate the digital interface.

Table 14.1. The TM4C ADC registers. Eachregister is 32bits wide. You will use ADC0 and we will use ADC1 for the grader and to implement theoscilloscopefeature.

Table 14.2. The maximum sampling rate specified in the ADC0_PC_R register.

Table 14.3 shows which I/O pins on the TM4C123can be usedfor ADC analog input channels.

Table 14.3. Twelvedifferentpins on the TM4C123 can be used to sample analog inputs. The example codewill use ADC0and PE4/Ch9 to sample analog input. TExaSdisplay uses ADC1 and PD3 to implement theoscilloscope feature.

The ADC has four sequencers, but you will useonlysequencer 3 in EE319K Labs 8,9,10 (edX MOOC Labs 14 and 15). We set the ADC0_SSPRI_R register to0x0123 tomake sequencer 3 the highest priority. Because we are using just onesequencer,we just need to make sure each sequencer has a unique priority. We setbits15–12 (EM3) in the ADC0_EMUX_Rregister tospecify how the ADCwill be triggered. Table 14.4 shows the various ways to trigger an ADCconversion. More advanced ADC triggering techniques are presented inthe book EmbeddedSystems: Real-Time Interfacing to ARM® Cortex™-MMicrocontrollers. Howeverin this chapter, we use software start (EM3=0x0). Thesoftwarewrites an 8 (SS3) to the ADC0_PSSI_R to initiate aconversion onsequencer 3. We can enable and disable the sequencers using the ADC0_ACTSS_Rregister. There are twelve ADC channels on the TM4C123. Whichchannelwe sample is configured by writing to the ADC0_SSMUX3_Rregister.The mapping between channel number and the port pin is shown in Table14.3. Forexample channel 9 is connected to the pin PE4. The ADC0_SSCTL3_Rregister specifies the mode of the ADC sample. We set TS0 tomeasuretemperature and clear it to measure the analog voltage on the ADC inputpin. Weset IE0 so that the INR3 bit is set when the ADC conversion is complete,and clearit when no flags are needed. When using sequencer 3, there is only onesample,so END0 will always be set, signifying this sample is the endof thesequence. In this class, the sequence will be just one ADC conversion. We set the D0 bit to activate differential sampling,such asmeasuring the analog difference between two ADC pins. In ourexample, weclear D0 to sample a single-ended analog input. Because we setthe IE0bit, the INR3 flag in the ADC0_RIS_R register will beset whenthe ADC conversion is complete, We clear the INR3 bit by writing an8 to the8 to theADC0_ISC_Rregister.

Table 14.4. The ADC EM3, EM2, EM1, and EM0 bitsin the ADC_EMUX_Rregister.

We perform the following steps to configure the ADC for software starton one channel. Program 14.1 shows a specific details for sampling PE4, which is channel 9. The function ADC0_InSeq3 will sample PE4 using software start and use busy-waitsynchronization to wait for completion.

Step 1. We enable the ADC clock bit 0 in SYSCTL_RCGCADC_R for ADC0.

Step 2. We enable the port clock for the pin that we will be using for the ADC input.

Step 3. We wait for the two clocks to stabilize (some people found extra delay prevented hard faults)

Step 4. Make that pin an input bywriting zero tothe DIR register.

Step 5. Enable the alternative functionon that pinby writing one to the AFSEL register.

Step 6. Disable the digital function onthat pin bywriting zero to the DEN register.

Step 7. Enable the analog function onthat pin bywriting one to the AMSEL register.

Step 8. We set the ADC0_PC_Rregister specify the maximum sampling rate of the ADC. In this example,we willsample slower than 125 kHz, so the maximum sampling rate is set at 125kHz.This will require less power and produce a longer sampling time,creating amore accurate conversion.

Step 9. We will set the priority of eachof thefour sequencers. In this case, we are using just one sequencer, so thepriorities are irrelevant, except for the fact that no two sequencersshouldhave the same priority.

Step 10. Before configuring thesequencer, we needto disable it. To disable sequencer 3, we write a 0 to bit 3 (ASEN3)inthe ADC0_ACTSS_R register. Disabling the sequencer duringprogrammingprevents erroneous execution if a trigger event were to occur duringtheconfiguration process.

Step 11. We configure the trigger eventfor thesample sequencer in the ADC0_EMUX_R register. For this example,we writea 0000 to bits 15–12 (EM3) specifying software start modefor sequencer3.

Step 12. Configure the correspondinginput sourcein the ADC0_SSMUX3 register. In this example, we write thechannel numberto bits 3–0 in the ADC0_SSMUX3_R register. In thisexample, we samplechannel 9, which is PE4.

Step 13. Configure the sample controlbits in thecorresponding nibble in the ADC0_SSCTL3 register. Whenprogramming thelast nibble, ensure that the END bit is set. Failure to set theENDbit causes unpredictable behavior. Sequencer 3 has only one sample, sowe writea 0110 to the ADC0_SSCTL3_R register. Bit 3 is the TS0bit, whichwe clear because we are not measuring temperature. Bit 2 is the IE0bit,which we set because we want to the RIS bit to be set when thesample iscomplete. Bit 1 is the END0 bit, which is set because this isthe last(and only) sample in the sequence. Bit 0 is the D0 bit, whichwe clearbecause we do not wish to use differential mode.

Step 14. Disable interrupts in ADC by clearing bits in the ADC0_IM_R register. Sincewe are using sequencer 3, we disable SS3 interrupts by clearing bit 3.

Step 15. We enable the sample sequencerlogic bywriting a 1 to the corresponding ASEN3. To enable sequencer 3,we writea 1 to bit 3 (ASEN3) in the ADC0_ACTSS_R register.

Program 14.2 gives a function that performs anADCconversion. There are four steps required to perform a software-startconversion.The range is 0 to 3.3V. If the analog input is 0, the digital output willbe 0,and if the analog input is 3.3V, the digital output will be 4095.

Digital Sample =(Analog Input (volts) • 4095) / 3.3V(volts)

Step 1. The ADC is started using thesoftwaretrigger. The channel to sample was specified earlier in theinitialization.

Step 2. The function waits for the ADC tocompleteby polling the RIS register bit 3.

Step 3. The 12-bit digital sample isread out ofsequencer 3.

Step 4. The RIS bit is cleared by writingto theISC register.

Figure 14.3. The four steps of analog to digitalconversion: 1) initiate conversion, 2) wait for the ADC to finish, 3)read thedigital result, and 4) clear the completion flag.

It is important to sample the ADC at a regular rate. One simple way to deploy periodic sampling is to perform the ADC conversion in a periodic ISR. In the following code,the sampling rate is determined by the rate of the periodic interrupt. The global variable, Flag iscalled a semaphore, which is set when new information is stored into the variable Data.We can connect PF1 to a logic analyzer or oscilloscope to verify the sampling rate.

uint32_t Data; // 0 to 4095
uint32_t Flag; // 1 means new data
void SysTick_Handler(void){
GPIO_PORTF_DATA_R ^= 0x02;// toggle PF1
Data = ADC0_InSeq3();// Sample ADC
Flag = 1;// Synchronize with other threads
}

There is software in the book EmbeddedSystems:Real-Time Interfacing to ARM® Cortex™-M Microcontrollersshowing you howto configure the ADC to samplea single channel at a periodic rateusing atimer trigger. The most time-accurate sampling method is timer-triggeredsampling (EM3=0x5).

: If the input voltage is1.65V, what value will the TM4C 12-bit ADC return?

: If the input voltage is 1.0V,what value will the TM4C 12-bit ADC return?

To collect information from the external worldinto thecomputer we must convert it from analog into digital form. Thisconversionprocess is called sampling and because the output of the conversion isonedigital number at one point in time, there must be a finite time inbetweenconversions, Δt. If we use SysTick periodic interrupts,then this Δtis the time between SysTick interrupts. We define the sampling rate as

f_s =1/Δt

If this information oscillates at frequency f,thenaccording to the Nyquist Theorem, we must sample that signal at

f_s> 2f

Furthermore, the Nyquist Theoremstatesthat if the signal is sampled with a frequency of f_s,thenthe digital samples only contain frequency components from 0 to½ f_s.Conversely, if the analog signal does contain frequency componentslarger than½ f_s, then there will be analiasingerror during thesampling process (performed with a frequency of f_s).Aliasingis when the digital signal appears to have a different frequency thantheoriginal analog signal.

InteractiveTool 14.2:

Discover theNyquist Theorem. In thisanimation, you control the analog signal by dragging the handle on theleft. Clickand drag the handle up and down to create the analog wave (the bluecontinuous wave). The signal is sampled at a fixed rate (f_s=1Hz) (the red wave). The digital samples are connected by straight redlines soyou can see the data as captured by the digital samples in the computer.

Exercise 1: Ifyou move the handle up anddown veryslowly you will notice the digital representation captures the essenceof theanalog wave you have created by moving the handle. If you wiggle thehandle ata rate slower than ½ f_s, the Nyquist Theoremis satisfied andthe digital samples faithfully capture the essence of the analog signal.

Exercise 2:However if you wiggle thehandlequickly, you will observe the digital representation does not capturetheanalog wave. More specifically, if you wiggle the handle at a ratefaster than½ f_s the Nyquist Theorem is violated causingthe digitalsamples to be fundamentally different from the analog wave. Trywiggling thehandle at a fast but constant rate, and you will notice the digitalwave alsowiggles but at an incorrect frequency. This incorrect frequency iscalled aliasing.

Figure 14.4 shows what happens when the NyquistTheorem isviolated. In both cases a signal was sampled at 2000 Hz (every 0.5 ms).In thefirst figure the 200 Hz signal is properly sampled, which means thedigitalsamples accurately describe the analog signal. However, in the secondfigure,the 2200 Hz signal is not sampled properly, which means the digitalsamples donot accurately describe the analog signal. This error is calledaliasing.Aliasing occurs when the input signal oscillates faster than thesampling rateand it characterized by the digital samples “looking like”it is oscillating ata different rate than the original analog signal. For these two sets ofsampleddata, notice the digital data are exactly the same.

Figure 14.4. Aliasing occurs when the inputanalog signaloscillates faster than the rate of the ADC sampling.

Video 14.5. Aliasing Demonstration: The Wagon Wheel Effect

: Assume you wish to represent sounds in digital form on the computer, either as inputs sampled from an ADC, or as outputs created with a DAC. The approximate range of canine hearing is 40 to 60 kHz. What sampling rate preverves all information for canine sound?

: The sounds in Lab 10 are sampled at 11 kHz. What range of frequencies can exist in the samples?

: Assume the input is a pure sine wave at 1 kHz, 1.65+1*sin(2*pi*1k*t), and the ADC is sampled at 2 kHz. Will the information be properly represented in the digital data?

Valvano Postulate: If f_max is the largest frequency componentof theanalog signal, then you must sample more than ten times f_maxinorder for the reconstructed digital samples to look like the originalsignalwhen plotted on a voltage versus time graph.

The resolution of a measurement system is the smallest change in input that can be reliably detected. The accuracy of a measurement system is the average difference between measured value and truth.For most systems, resolution and accuracy are dominated by noise, rather than the precision of the ADC. To improvesignal to noise ratio, we can sample the ADC multiple times and average the samples.

ADC0_SAC_R = 0;// take one sample
ADC0_SAC_R = 1;// take 2 samples, return average
ADC0_SAC_R = 2;// take 4 samples, return average
ADC0_SAC_R = 3;// take 8 samples, return average
ADC0_SAC_R = 4;// take 16 samples, return average
ADC0_SAC_R = 5;// take 32 samples, return average
ADC0_SAC_R = 6;// take 64 samples, return average

You will notice the signal to noise ratio will improve dramatically if you use hardware averaging.However, the disadvantage of hardware averaging is the time to convert. If taking one sample takes 8us, then activating 32-point hardware averaging will increase the time to sample to 32*8=128us. Similarly, it will take more electrical power to deploy hardware averaging.

Video . Central Limit Theorem

Because of noise, if we set the ADC input to a constant voltage, and sample it many times, we will get a distribution of digital outputs. We plot the number of times we got an output as a function of the output sample. The shape of this response is called a probability mass function (pmf) characterizing the noise processes. A pmf plots the number of occurrences versus the ADC sample value. To illustrate the CTL, 1.65V was connected to PE2 and the software in Section 14.3 was used to measure the ADC 1000 times. The experiment was performed at three values of ADC0_SAC_R: 0 (1 point), 2 (4-point average), and 4 (16-point average). Notice the shape becomes Gaussian and the standard deviation reduces. In particular, the data with 1 point (no averaging) has two or three humps (not normally distributed), but with 16-point average there is one symmetric hump (normally distributed)

Figure 14.5. Probability mass functions showing hardware averaging improves signal to noise ratio.

: Give an advantage of using hardware averaging.

: Give two disadvantages of using hardware averaging.

: The TM4C123 has hardware averaging. What would you do if you want to deploy averaging, but you are using a different microcontroller that does not support hardware averaging?

In most aspects, running C++ on the microcontroller is identical to running C++ on other machines. However, be aware of the memory limitations of the TM4C123. To run C++ we will create a small heap and continue to have a small stack, knowing that all globals, statics, locals, and heap must fit into the 32 kibibytes of RAM on the TM4C123. The following code exists in the startup file for Lab8_C++ project, creating 1024 bytes of stack and 512 bytes of heap.

Stack_Size EQU 0x00000400
AREA STACK, NOINIT, READWRITE, ALIGN=3
Stack_Mem SPACE Stack_Size
__initial_sp
; Heap Configuration
Heap_Size EQU 0x00000200
AREA HEAP, NOINIT, READWRITE, ALIGN=3
__heap_base
Heap_Mem SPACE Heap_Size
__heap_limit

Video . Running C++ on the TM4C123.

Video . Running a vector.cpp C++ example from EE312H on the TM4C123.