Electronic instrumentation Digitization of Analog Signal in TD Lecturer: Dr. Samuel Kosolapov

Items to be discussed Digitization (or digitizing) of Analog Signal Sampling and Quantization Storage of Digital signal as array of counts Nyquist Frequency Alias Serial Monitor and Serial Plotter Arduino Examples

ADC ADC Clock Quantization. Result: Digitized signal stored as a sequence of numbers  array Analog Signal : AI V(t) = F(t) Clock (Pulse Wave signal) Sampling interval, Sampling Frequency

ADC: Sampling and Quantization (simplified operation as a two stage process) Quantization. Result: Digitized signal stored as a sequence of numbers  array Analog Signal : AI S/H Sample and Hold circuit Quantizer

Stage 1. Sample and Hold Sample and Hold circuit AI : Analog Input AO : Analog Output C : control signal (Clock) Analog Signal : AI Analog Signal : AO The output level of the S/H is updated on every rising edge of the ADC’s clock input AI not equal to AO !!!

Stage 2. Quantization Quantizer Circuit Clock Analog Signal : AO (Pulse Wave signal) Sampling interval, Sampling Frequency Quantization. Result: Digitized signal stored as a sequence of numbers  array

Stage 2. Quantization: Number of Quantization Levels Quantizer Circuit Quantizer circuit “searchs” for the best “approximation” To finish the process in the reasonable time one must LIMIT a number of quantization levels.  Speed versus Accuracy

Sampling Frequency. Nyquist Frequency Nyquist sampling theorem: The sampling frequency should be at least twice the highest frequency contained in the signal. Example: signal is sinewave at a frequency 1 Hz According to Nyquist theorem, if we sample this waveform at 2 Hz , this is sufficient to capture every peak of the signal  We can reconstruct this signal

Oversampling and Undersampling Oversampling (at a frequency, say 3 Hz) is OK. We have more than enough samples to reconstruct the signal Undersampling (at a frequency, say 1.5 Hz) is BAD. The problem is that with undersampling we get wrong information about the signal. The person receiving these samples reconstruct different signal

Nyquist Frequency Real signal is a complex signal composed of many frequency components. By Fourier theorem we know, that any continuous signal can be decomposed in terms of a sum of sines and cosines at different frequencies. Example: sum of sinewaves at frequencies 1 Hz, 2 Hz and 3 Hz We know, that highest frequency in this signal is 3 Hz. This signal must be sampled at least at 2*3 Hz = 6 Hz. One can see that then we can exactly reconstruct the signal

Nyquist Frequency and Nyquist Rate Strictly speaking, the Nyquist frequency should not be confused with the Nyquist rate, which is the minimum sampling rate that satisfies the Nyquist sampling criterion for a given signal  Thus, Nyquist rate is a property of a continuous-time signal, whereas Nyquist frequency is a property of a discrete-time system.

Restoring Analog Signal by “samples”

Arduino: Presenting Digitized Signal with Serial Monitor and Serial Plotter Version 1.6.6. Reinstall !!! Arduino has a class “Serial” Arduino communicates with PC by using USB cable. However communication is executed by using RS232 protocol Arduino IDE has “Serial Monitor” and “Serial Plotter”. “Serial Monitor” can accept bytes from Arduino and send bytes to Arduino. Class Serial has a number of “methods” (functions) enabling to work with bytes, int, strings, etc.

Arduino: Generating Synthetic Signal and Presenting it with Serial Monitor and Serial Plotter int digitalSignal[100]; void setup() { Serial.begin(9600); for (int i=0; i<100; i++) { digitalSignal[i] = i; } void loop() { for (int i=0; i<100; i++) { Serial.println( digitalSignal[i] ); delay(1); }

Arduino: Presenting Digitized Signal with Serial Monitor and Serial Plotter

Arduino: Analog Input. Potentiometer Potentiometer used as a “Angle Sensor”. Potentiometer connected as Voltage Divider. One (say, left) pin of the potentiometer is connected to +5V Then right pin of the potentiometer is connected to GND Middle pin of the potentiometer is connected to A0 : Analog Input Pin Rotating the handle changes the voltage on the middle pin from 0 V to +5V

Arduino: Analog Input. Potentiometer. Code. int analogPin = 0; // A0 int val; void setup() { // put your setup code here, to run once: Serial.begin(9600); } void loop() { // put your main code here, to run repeatedly: val = analogRead( analogPin); Serial.println(val); delay(50); Reads an analog input on pin 0, converts it to voltage, and prints the result to the serial monitor.  Graphical representation is available using serial plotter (Tools > Serial Plotter menu)   Attach the center pin of a potentiometer to pin A0, and the outside pins to +5V and ground. // initialize serial communication at 9600 bits per second:   Serial.begin(9600); Serial.println(val);

Arduino: Analog Input. “Simple Voltmeter”. void loop() {   // read the input on analog pin 0:   int sensorValue = analogRead(A0);   // Convert the analog reading // (which goes from 0 - 1023) to a voltage (0 - 5V):   float voltage = sensorValue * (5.0 / 1023.0);   // print out the value you read:   Serial.println(voltage); } Reads an analog input on pin 0, converts it to voltage, and prints the result to the serial monitor.  Graphical representation is available using serial plotter (Tools > Serial Plotter menu)   Attach the center pin of a potentiometer to pin A0, and the outside pins to +5V and ground.

Arduino: Analog Input. Voltage range The Arduino UNO board contains a 6 channel 10-bit analog to digital converter (Pins A0 .. A5) This means that it will map input voltages between 0 and 5 volts into integer values between 0 and 1023. This yields a resolution between readings of: 5 volts / 1024 units or, 0.0049 volts (4.9 mV) per unit. * Some authors uses 5 V / 1023 !!!! The input range and resolution can be changed using analogReference(). Do not do this until full understanding

Arduino: Analog Input. Sampling Rate For a 16 MHz Arduino the ADC clock is set to 16 MHz/128 = 125 KHz. Each conversion in AVR takes 13 ADC clocks so 125 KHz /13 = 9615 Hz. That is the maximum possible sampling rate, but the actual sampling rate in your application depends on the interval between successive conversions calls Practically: Much less. Something must be done with samples. Sending data to PC takes time PC must response But Windows is not real-time system  one may get jitter Professionals using direct access to processor’ registers can increase Sampling Rate but on the price of the precision (less bits)