MASSACHUSETTS INSTITUTE OF TECHNOLOGY 22 071 6 071 Introduction to Electronics Signals and Measurement Spring 2006 Lab4 Protoboarding Techniques Sampling and Aliasing Experiment 1 For this exercise you will build the following circuit on the protoboard Connect the 5 Volts and Ground as indicated and then measure the signal at the points indicated by A B and C A 5 Volts 10k B 10k 10k 5k C 10k Ground The goal of the exercise is to become more familiar with the prototyping board and how it is wired The guidelines to follow are 1 Make sure the system power is off while you are building your circuits 2 Establish power traces and test them For example if you will be building a circuit that needs 5V and ground then first establish the 5V as one of the red traces and the ground as the adjacent blue by connecting them to the power supply Test the actual value of the voltage at the power traces with the multimeter or the oscilloscope 3 Turn the system back off and start building your circuit 4 Keep your wires short and do not run wires over components 5 Build your circuit is sections and test each section before proceeding First measure the Voltages at A B and C and record the values below Next change the input voltage from 5V to 15 V Assume that the system you have just constructed is linear what do you expect the voltages at A B and C to be and why Do your measurements agree with your expectations Input Voltage Voltage at A Voltage at B Voltage at C 6 071 22 071 Spring 2006 5V 15V 1 Experiment 2 Building a device to power a speaker In the following experiments we will need to send a signal to our speaker from the computer For our speaker to work properly we must provide to it more current than the computer can output We will build a device called a buffer that will sit between the output of the computer and the speaker This device will provide the necessary power to the speaker but without affecting the signal that comes from the computer output We will thus have the opportunity to see and hear the exact form of the original signal In any event this is going to help us further understand how to build circuits on the protoboard The circuit we are going to build is based on a device called the operational amplifier We will learn a lot more about this very useful device later on For now we will just use it without consideration of its properties and operational characteristics The schematic of the circuit is to ACH5 signal from DAC0 15 V 1 8 2 7 3 6 4 5 15 V to speaker Place the device as indicated in the schematic below and make the connections shown 15V 15V Output signal Input signal Test your circuit by connecting the power as indicated and use a 1 kHz sine wave with an amplitude of 5 Volts as the input signal View the output with your scope and test to make sure that everything works Now you have built a very useful device that can be used for various experiments Save it 6 071 22 071 Spring 2006 2 Experiment 3 Sampling a signal Here we will investigate sampling and the phenomenon of aliasing In class we learned that in order to be able to reproduce a signal from a sample the sampling frequency has to be greater than twice the bandwidth of the signal under investigation With this experiment we will investigate the sampling process in a visual way The first instrument to use is called SamplingAliasing and may be downloaded from your class web site Run the instrument and investigate the results as you change the signal frequency and the sapling rate The green trace represents the original signal and the red dots indicate the sampled values On the right side of your instrument interface you see the Fourier transform of the original signal and the sampled signal Courtesy of National Instruments Used with permission Construct a signal with a frequency of 500 Hz Now change the sampling frequency and observe the results What happens when the sampling frequency is 1000 Hz What do you observe when the sampling frequency is less than 1000 Hz What do you observe when the sampling frequency is 1000 Hz 6 071 22 071 Spring 2006 3 What do you observe when the sampling frequency is 1000 Hz Let s now continue with the sampling problem by using yet another instrument which is also available for download from the class web site It is called Aliasing Courtesy of National Instruments Used with permission The system diagram of the instrument is shown below ACH5 Generate Signal Sampled Signal DAC0 View output sampled signal Buffer The output from the computer comes at DAC0 Connect the output signal to ACH5 The sampled output signal appears in the lower graphs of the instrument Notice you have to use the Start Play and Stop Play buttons in order to hear the results of your sampling selection Run the instrument and observe the phenomenon of aliasing i e what happens when sampling frequency is less than twice the signal frequency Select a signal frequency of 800 Hz Listen to the sampled signal with the highest possible sampling rate Now decrease the sampling rate until you begin to notice a difference in the sound What is the sampling rate below which you begin to notice a change in the signal pitch 6 071 22 071 Spring 2006 4