2 AC and RMS. To pass this lab you must solve tasks 1-2. Tasks 3 and 4 are included in the grading of the course.

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1 2 AC and RMS Purpose of the lab: to familiarize yourself with the oscilloscope to familiarize yourself with AC voltages and different waveforms to study RMS and average values In this lab, you have the opportunity to learn how to use an oscilloscope. You can prepare by reading about this in the course literature. You also have the chance to once and for all understand "effective values" and "average values". You should be able to solve the integrals of the sine wave and triangular wave asked for in the lab instructions. Marking: Answer the questions in the lab instructions, and solve the integrals. Hand in a written report with your solutions. Make sure that your lab instructor verifies that you have completed your tasks. o pass this lab you must solve tasks 1-2. asks 3 and 4 are included in the grading of the course.

2 Oscilloscope he oscilloscope is used to study voltage as a function of time. he voltage is connected to the oscilloscope input, and is continuously plotted on a screen. Measuring two signals allows the user to not only be able to see the period time and peak values of an alternating voltage, but also to see any phase shift and amplification of signals that are for instance sent through an amplifier. With the oscilloscope you can magnify signals, and see variations and disturbances that could not be detected with a voltmeter. A short description of an oscilloscope can be found at the end of these lab instructions. For further information, refer to the manual for your oscilloscope. 2.1 Connect the oscilloscope and the function generator he function generator is our AC voltage source. You can locate a manual for the function generator at your lab place. It is possible to adjust the frequency and the amplitude of the AC voltage. You can choose between different waveforms (sine, triangle or square wave). You can also select a DC voltage contribution as offset or bias to the signal, but it should normally be zero. he amplitude of the signal from the function generator should generally be checked with the oscilloscope, since the reported amplitude might not be reliable for all types of function generators. Connect the function generator output directly to channel 1 on the oscilloscope. ry different settings for the two instruments until you understand how they work. Set the frequency of the function generator to 500 Hz, and the amplitude to 5 V. he time scale of the oscilloscope has to be changed so that at least one full period of the signal is visible. he voltage scale must be similarly adjusted (Autoset can often give you a good starting point for both these settings). Function generator OSCILLOSCOPE CH1 CH2 time Sine wave Output Figure 2.1 * What period time corresponds to 500 Hz?. ry using different waveforms on the function generator; sine-, triangle- and square-waves. Vary the oscilloscope settings for focus and trigger. Add an offset voltage by adjusting the signal generator bias level. What is the impact on the oscilloscope screen when you change the settings DC, AC and GND? * Show the supervisor when you think you've mastered the signal generator and oscilloscope, and can adjust the oscilloscope so that one full period of the signal can be seen on the screen. Supervisor's signature

3 Voltage [Volt] 2.2 Measurement of sinusoidal alternating voltage Function generator OSCILLOSCOPE CH1 CH2 time Sine wave u out u in Figure 2.2 Before you start making any connections, it is wise to read through the whole task! Connect the signal and ground from the signal generator to the lab board. Connect the oscilloscope probe to the same points on the lab board. Connect a 5 V light bulb between the measuring points. Adjust the oscilloscope scales, as well as the amplitude and frequency of the function generator, until your measured signal is identical to curve A in Figure 2.3. Be careful when adjusting the output signal, since the light bulb could be destroyed if the signal s amplitude or bias becomes too high. Calculate the theoretical average and RMS voltage for curves A, B and C. he mathematical definitions can be found at the end of these instructions. 4 3 A B C time [ms] Figure 2.3

4 Connect the multimeter across the light bulb on the breadboard. Measure U dc and U ac with the multimeter. Is the RMS the same as the U ac reading on the multimeter? * Explain how to obtain a measured RMS value. Fill in the measured and calculated voltages in the table, including the signal's peak-to-peak value, from the oscilloscope. Also try to estimate (remember) how strong the light is for each waveform. You should rank the lamp brightness for the three curves A, B and C. (1 = strongest, 2 = in between, 3 = weakest) Curve U ac U dc U RMS U peak-to-peak Brightness (1,2,3) A B C Move the scope's curve by changing the bias on the function generator until the signal is identical to curve B. In order to measure the change in offset, the oscilloscope must be set to DC mode. Fill in the table above for curve B. Replace the signal generator with the variable DC voltage from the lab board. Adjust the output until you obtain curve C. Complete the table with the same measurements for this curve as well. Compare your measurements for curves A, B and C. For which of the three waveforms did you get the strongest intensity on the light bulb? Explain why this waveform gives the strongest intensity, and why the various waveforms produce different results. * Show your measurement results to your supervisor. Explain your conclusions, and how you intend to derive the average and RMS values. Supervisor's signature

5 V o lta g e [V o lt] 2.3 Measuring triangular AC voltage Change the signal generator output to a triangular wave. Generate the two waveforms in Figure 2.4 below. Use the multimeter to measure both average- and RMS voltage. Use the same measurement methodology as when you measured the sinusoidal voltage. Calculate the theoretical average and RMS values for curves A and B. he mathematical definitions can be found at the end of these instructions. 5 A B tim e [m s ] Figure 2.4 Fill out the theoretical and measured values in the table. Calculate U ac with the traditional formula U ac Uˆ 2, and compare with the measured value for the five curves. Is this formula valid for a triangular signal? When is the formula is valid?. Curve Measured U dc Measured U ac Measured U RMS A B Compare your measurements with the theoretical values based on integral calculations for a triangular wave. Discuss the results in your report. Are the measured values consistent with your calculations? Supervisor's signature

6 2.4 square wave Change the input signal waveform to a square wave, and set the oscilloscope to DC mode. Set the amplitude to 2.5 V, and the frequency to 1 khz. Measure the new signal with the multimeter. * Compare the multimeter s amplitude readings to those for a sine wave, and comment on your observations: Rise time measurement A square wave may at first glance look rather ideal, but the truth is that you can never get an infinitely fast voltage jump. he definition of the rise- and fall- time of a voltage jump / step / square wave is shown below. 100% 90% 10% Stigtid Falltid You should now measure the rise time and fall time of your input signal using the oscilloscope. ry to get as flat a curve as possible by reducing the time scale on the oscilloscope. Preferably you should only see one edge of the square wave (e.g. the rise). When you have found a positive flank, you can use the help lines ( %) to help you read the rise time. Show your supervisor. * Rise time = Now try to find a falling edge, and measure the fall time. * Fall time = Supervisor's signature

7 Formulas Ohm's Law Sinusoidal voltage Angular Frequency "Ohm's Law for AC" U = R I u(t) = û sin(t + U ) U = û e ju = 2f U = Z I, with Z = Û / Î and arg Z = U - I Definitions of mean and RMS U U RMS avg 1 U U P U I 1 U 0 0 eff u t u 2 I dt t eff dt U ac is U RMS without any DC contribution U dc = U avg ip: o simplify the integrals, the period time can be chosen as: Sine waves: Use the period 2 Ramps: Use the period 1 his simplifies the calculations without affecting the outcome.

8 he oscilloscope - some general instructions. he oscilloscope on you lab place might have different names on inputs and knobs. One voltage as a function of time 1. Select channel A or B as vertical axis input by pressing the selection button. 2. Make sure that the channel amplifier is in calibrated mode. 3. Select a proper amplification, Volts/div 4. Decide, if using channel B, if the inversion function is to be used or not. Make sure that the selection is made on the scope as desired. 5. If the DC component of the signal is to be observed, you must select DC-mode on the channel input. ACmode is passing the signal through a high pass filter with a few Hertz as cut-off-frequency, that way eliminating the DC-component. AC-mode can be useful when observing a waveform with very small amplitude, overloaded on a DC-voltage. 6. If you are about to measure a DC voltage, make sure to know where the zero-level is located on the screen. Grounding the channel input will easily visualise the zero-level, which then can be adjusted with the y- position rotary knob. Don't forget to deselect the grounding after adjustment! 7. Select the time base of the sweep generator, make sure it is in calibrated mode. With the time base you'll adjust the speed of the electron beam in the horizontal direction, thus defining the scale of the time axis. 8. Select a proper trigger mode - read in the instrument manual about different modes. he start point of each sweep must be selected by adjusting the trigger level. With the hold off rotary knob the time between each sweep is adjusted, this can be useful to achieve a stable picture. Positive or negative slope can be selected on most oscilloscopes. Don't forget to select the desired source for the triggering circuit, either channel input or the dedicated trigger input can usually be selected. wo voltages as functions of time Make adjustments and selections for both input channels as point 1 to 6 above. Adjust the time base to fit both input channels. Only one of the two sources can be selected as trigger source. With two input voltages, the sum or difference between them can be measured. For difference measurement, press INVER on channel B and ADD. For sum measurements, press just SUM. he phase shift between two voltages can be measured. What is possible to measure with the instrument is time, so if the phase shift read in time is t and the period time is, then the phase shift will be: 2 t X-Y graph mode It is possible to graph one voltage as a function of the other: Y = F(X) where X is the horizontal amplifier input and Y is the vertical amplifier input. Which channel is connected to which axis can for some versatile oscilloscopes (Philips) be selected. Don't forget to adjust the origo position by first grounding (press the button) both channels, then use the two X- and Y-position rotary knobs. Deselect input grounding! he scales of the axis can be adjusted by changing the channel amplification. Be careful about which channel is connected to which axis! he probe and ground. 1. Select a proper probe for your oscilloscope. Probe connectors sometimes have different mechanical solutions for telling the scope if it's a x10 or x1 attenuation attached. 2. he probe ground wire is connected directly to the protective ground, so be aware of your grounding when connecting several probes and instruments. Some instruments have a floating ground, some are connected to the protective ground. 3. A probe is usually equally to a 10 Mohms load. Keep in mind that the probe can thus affect circuits with high impedance!