Sonoma State University Department of Engineering Science Spring 2017

Transcription

1 EE 110 Introduction to Engineering & Laboratory Experience Saeid Rahimi, Ph.D. Lab 4 Introduction to AC Measurements (I) AC signals, Function Generators and Oscilloscopes Function Generator (AC) Battery (DC) The purpose of this experiment is to become more familiar with AC voltage measurements using (a) standard oscilloscope and (b) the Discovery Scope (DS). You have already seen the AC concepts in the previous labs. However, the purpose of today s lab is to perform quantitative measurements and carefully record the results in your lab book. You will carry out the measurements first with the Keysight scope and then with the DS, and then compare the results. In the event that you run out of time, the remaining DS portion of the experiments should be done at home. Your instructor will demonstrate the AC operation of both the standard laboratory equipment and the Discovery Scope in the beginning of the lab. Students are required to carefully record their observations in their lab books. Diagrams should include the label and tick marks of the vertical axis (volts) and the horizontal axis (seconds, ms or µs). To ensure completion of the work, lab books will be reviewed and signed by the instructors before the end of the lab. 1

2 Review and Introduction: Unlike a DC signal in which charges flow only in one direction, the direction of motion of electric charges in an alternating current (AC) signal varies with time. A DC current is characterized by its magnitude and direction. For an AC current the magnitude of current in each direction changes with time, but the current reaches a maximum or minimum (amplitude) in each direction. In addition to the magnitude of the maximum value of current, we also need to know how fast the current goes through a complete cycle and changes direction (frequency f, period T). The manner in which the current changes with time defines the type of the AC current. Sinusoidal, saw-tooth, triangular square and pulsed signals are among the most common types of AC signals. The voltage across a resistor through which an AC current flows is an AC voltage. Figure below illustrates the variations of a sinusoidal AV voltage with time. 2

3 This voltage is characterized by its amplitude (1/2 peak-to-peak voltage) and its period (the distance in time between two consecutive peaks). This sinusoidal signal is mathematically defined by the following equation: V(t) = V 0 Sin (ωt + ϕ) Where, V 0 is the amplitude, ω = 2 π f, f = frequency, and ϕ is the phase. For the above figure ϕ = 0. Note that the wave's frequency f is the inverse of its period T. Two identical sine waves with different phases are shown below. Square Wave Duty Cycle A pulse or square wave is a signal that is "off" (low) for a length of time and "on" (high) for another length of time. The graph below indicates a repetitive pulse with period T that is "on" for time τ. The signal's duty cycle is defined to be 100(τ/T). For example, a signal with a 50% duty cycle is on for 50% of time, whereas a 20% duty cycle means that the signal is "high" only 20% of time. 3

4 1. Monitoring AC Signals Using Standard Laboratory Equipment The goal of this section of the lab is to monitor a time-varying signal generated by a function generator using an oscilloscope. The Keysight 2002 series includes both a function generator and a dual input oscilloscope. You will connect the output of the function generator directly to one of the inputs of the oscilloscope to monitor the following signals. For the FG, use a BNC cable that has a BNC connector at one end and a black alligator clip and a red grabber at the other end. You will find the BNC output of the function generator at the bottom left of the scope. For the oscilloscope use the special BNC cable attached to the scope. Choose a sinusoidal signal of 1.2 V peak-to-peak amplitude and frequency of 4.8 khz. The task is to display two full cycles of the signal and to use the scope's cursors to determine the period of each signal. Your instructor will demonstrate how to adjust the frequency and amplitude of the signal output of the function generator, and how to use the cursors to measure signal amplitude and frequency. Keysight 2002 Series Oscilloscope Step 1: Select the following waveforms: A. Sine wave; B. Saw tooth; C. Square wave with 50% duty cycle; D. Square wave with 20% duty cycle Carefully draw two cycles of these waves with appropriate scale and tick marks. Reminder: The oscilloscope display is a two-dimensional screen that measures "voltage, V" on its vertical axis and "time, t" on its horizontal axis. To display a time-varying signal, we should be able to monitor and record the height (voltage) of the signal as time progresses. The advantage of using a repetitive (periodic) signal is that shape of the signal during a certain period can be displayed. In order to analyze a signal, one can freeze the waveform 4

5 and use the mathematical functions of the scope to alter the signal if needed. We will not use these functions in the present course. The units of the axes are displayed in volts/division and time/division, respectively. The oscilloscope also has a triggering mechanism that locks onto the waveform that it receives at its input. By adjusting the values of volts/div and time/div, you can zoom in or zoom out the waveform. You can measure the frequency of the AC signal by counting the length of time of one full cycle, called period. The signal's frequency is simply the inverse of its period (f=1/t). Also note that you will need special cables to connect the output of the function generator to the input of the oscilloscope. Step 2: Display the sine wave again. Try zooming in and out so you can see a full cycle on the screen. You can do this by changing the horizontal time scale (sec/div) and the vertical voltage scale (V/div). Now, activate the time cursors, X 1 and X 2. Move the cursors and locate them at the end points of the full cycle. Read X and record the value. This is the period T of the signal. Now switch the cursors to Y 1 and Y 2, and place the horizontal dotted lines at the top and bottom points of the sine signal. Read and record Y. This is the peakto-peak amplitude of the signal V pp. Determine the frequency by inverting the period (f=1/t) and the amplitude of the signal (V A =V pp /2). Compare the measured f and V A with the expected values provided by the function generator. 2. Monitoring AC signals Using Discovery Scope Step 3: Now duplicate the above measurements using your Discovery Scope. The DS pin diagram is shown below. The color coded wires clearly indicate the output wires of the signal (waveform) generator (yellow wires) and the input wires of the oscilloscope. Note that there are two sets of inputs for the oscilloscope. Each set represents one of the two available channels. Choose channel 1 represented by orange wires. 5

6 Blinking LED: In order to visually observe the effects of the AC signal, connect the output of the DS wave generator to the circuit below and observe light emitted by the LED. Step 3: Set the wave generator frequency to 1 Hz and observe the blinking LED. Steadily increase the wave generator frequency and note the frequency at which the LED appears to stop blinking. Note that in order to protect the LED from excessive current, you need to place a current-limiting resistor in series with it. Record the circuit and explain the result in your lab book. R1 V1 5Vrms 2Hz 0 330Ω LED1 3. More on Function Generators and Oscilloscopes Let us now use the function generator and oscilloscope in making AC voltage measurements across series and parallel resistors. In addition to using the standard laboratory oscilloscope and the portable Discovery Scope, the goal of this part of the experiment is to verify the voltage divider concept for AC circuits. Last week we tested the principle of voltage dividers in DC circuits. Today we will apply the same concepts to circuits driven by AC signals. In case you do not have sufficient time to finish this part in the lab, use your DS device at home to complete the laboratory. So far we have seen that we can adjust FG's frequency, select the shape or function (sine, triangle and rectangle functions), and change the amplitude level. We can also adjust the DC offset of the wave. The DC offset function superimposes a positive or negative DC voltage (called bias) to the AC signal. The entire AC waveform is lifted or lowered by the DC bias value (offset) with respect to the ground. Without an offset, the AC signal is vertically symmetric with respect to Zero (ground level). The goal of this part of the experiment is to show that the signal output of the function generator is equal to the sum of the voltages across the three resistors shown in the diagram below. Separately measure the voltages using your laboratory scope. Record the waveform and amplitudes in your lab book. Record the amplitudes in a table and verify that the sum of voltage drops across the resistors to be equal to the amplitude of the output of the function generator. Be careful to connect the main pin of the oscilloscope probe to the high side of the resistor and the black alligator clip end of the probe to the low side of the scope. The figure below only shows the high connections of the probes of the two channels. Ask your instructor to clarify the concept of high and low if you are not sure about their meaning. 6

7 Step 4: For simplicity, make sure you turn off the offset voltage for the following measurements. Ask your instructor if you are not sure how to do that. Series Resistors with Function Generator and Oscilloscope Select the following resistance values: R 1 =300 Ω, R 2 = 1 kω, R 3 =4.7 kω. Set the frequency of FG to 240 Hz sine wave with1.0 V peak-to-peak amplitude and zero offset. Using the Keysight scope, carefully record the waveforms with appropriate scales on a graph in your lab book. Calculation and Comparison: Record the amplitude of the voltages across the three resistors R 1 and R 2 and R 3, and compare their sum to the amplitude of the output signal of the FG. Higher Frequencies Your Keysight 2000 series laboratory function generator and oscilloscope are capable of handling signals with high frequencies as high as 200 Mhz. However, the high frequency limits of 200 KHz for the DS is much lower (by a factor of a thousand). The low frequency range of the DS drastically limits its applications. As you will see in the future experiments, inexpensive electronic components are severely limited in their frequency response. 4. RMS Value of a Sinusoidal Signal (optional) RMS stand for Root Mean Squared. Consider a sine wave that is vertically symmetric about the x-axis (time axis). Since the voltage value of the signal varies with time, we will need to characterize the value of the signal using an average value. For a simple sine wave centered about zero, half of the cycles are positive and half are negative. The sum of all values cycles amount to zero. Therefore, regardless of its amplitude, the simple average of all sine wave signals is zero. Therefore a simple averaging technique is not suitable for AC signals. Instead, one can first square the wave by raising all values of the wave (positive and negative) to power 2. The square root of the sum of the squared values is called the "Root Mean Square" or RMS value. The magnitude of a sine wave is therefore identified by 7

8 its rms value. It turns out that the V rms = V 0 /2 1/2, where V 0 is the signal amplitude. When we say that the voltage of the signal from the wall power outlet is said to be 120 volts, we mean that its rms value is 120 volts. This is what your multimeter measures when its knob is set on V. Calculate the rms value of the sine wave of part A above. Calculate the amplitude of the 120 V AC voltage provided by PG&E. Show your work to your instructor before leaving the lab. 8