Signals Case

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Memorandum

Date:        12 July 2014

To:        Dr. Charles

From:        Jacob Locke

Subject:        Signals

Introduction

        The first laboratory of the Measurements Lab course at Lamar University was the Signal and Data Analysis Laboratory which consisted of three experiments. The experiments included (1) Signal Analysis, (2) Capturing and analyzing a strain gage’s response, and (3) Determination of the values of spring constants. The primary objective of this lab was to become more familiar with different types of signals as well as accurately obtain desired data and adequately analyze such data. Chapter two of the course textbook, Measurements Lab, defines a signal as “the transmission of information” (Figlioa, 55). Physical parameters of signals are referred to as waveforms which contain information about the signal’s amplitude, magnitude, and frequency. Engineers deal with inspecting multiple waveforms as the signals follow a process path from the input of a mechanical device or thermal system to the output of the system. Automobile suspension systems, heat engines, and hydraulic pumps are but a few instances where engineers apply signals and data analysis. Furthermore, another key goal of this lab was to attain hands-on experience with various electronic test instruments. These electronic instruments present a quicker and more efficient procedure for collecting and analyzing data.

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Theory

        The laboratory instruments operated in this first lab was an oscilloscope, a function generator, a frequency counter, and signal conditioner. An oscilloscope is conducted to display waveforms of time varying, electronic signals. A signal is applied to the input terminal of the device from probes connected to scientific equipment or an electrical circuit. Once the oscilloscope receives this signal it generates a graph of the waveform on its CRT (or cathode-ray tube) screen. Frequency, amplitude, period, and other data from the signal are exhibited on this screen. Oscilloscopes can collect data from both electrical signals as well as non-electrical signals. Some non-electrical signals may include the deflection and oscillatory motion of springs, vibrations, and sound. Also, some oscilloscopes are equipped to receive more than one input signal and formulate data based on these signals. A figure of a standard oscilloscope, along with its controls and functions, is displayed below.

[pic 1]

Figure 1. The Oscilloscope

        Function generators are signal sources which provide a specifiable voltage applied over a specifiable time (“The Oscilloscope and the Function Generator”). Experiment (1), Signal Analysis,

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implemented a Simpson function generator, model FG-8002, to send sine, square, and triangle signals to the oscilloscope at different specified frequencies. Figure 2 shown below is the exact function generator used for this experiment. It provides a means to select a waveform frequency and/or waveform amplitude to be sent to the oscilloscope for further data analysis. The controls of a generator control the frequency range of the signal sent to the oscilloscope and the wave type of the signal.

[pic 2]

Figure 2. The Function Generator

        A frequency counter is precisely what its title portrays. It measures the frequency of a signal sent from electronic devices, such as a function generator, and displays its readings on a visible screen. Again, for experiment (1) of the first lab, a frequency counter was applied to record the actual frequency being sent from the function generator to the oscilloscope. Figure 3 shown on the next page gives a visualization of the Simpson frequency counter, model 710, employed for this portion of the lab. As shown in the figure, this particular frequency counter can read frequencies anywhere from 10 Hz to 60 MHz.

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[pic 3]

Figure 3. The Frequency Counter

        Spring-mass systems require the knowledge of how much force is required to displace a spring at rest from its equilibrium position. To determine this, one must know a physical property of the spring called the spring constant (k). Hooke’s Law can be described as…

F spring = -kx     ( N or lbs )                             (1)

F spring is the force exerted on the spring, x is the amount that the spring stretches relative to its equilibrium position, and k is the proportionality constant, often referred to as the spring constant (physics classroom).

Results

        Experiment (1), Signal Analysis, was completed by generating a sine wave, a triangle wave, and a square wave on an oscilloscope. The signal’s frequency, amplitude, and period were recorded for each waveform at different frequencies. A function generator was employed to send these signals to the oscilloscope for data readings. Furthermore, a frequency counter was connected in between these two devices to measure the frequency leaving the function generator. The results computed using these electronic measuring devices are presented in the table on the next page.

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Table 1. Frequency, Amplitude, and Period Readings from Oscilloscope and Frequency Counter

        Below are a few pictures of the oscilloscope readings for the three different waveforms.