The nature of the Experiment
We will shift gears now. We will learn how a digital storage oscilloscope, DSO, works and how to use it. This experiment will take two weeks to complete.
We will start out working as a group to become familiar with how to use the DSO. You will then do a series of mini-experiments as independent groups and finish up with an experiment in which we will take data as a class and then analyze these data individually to determine the speed of sound. One of the major goals of this series of exercises and mini-experiments is to enable you to become familiar with the DSO and how to use it, as well as other equipment.
There is a lot of information I must communicate to you. I can’t present it all at the start and expect you to make sense of all the mini-experiments. The learning curve on using the DSO is steep. I will cover the first couple of mini-experiments and let you begin. I will work with each group individually when you begin a new mini-experiment.
There are four aspects to this experiment:
- Learning about the basics of electronic instrumentation and measurement, particularly the digital storage oscilloscope (DSO).
- Learning the concept of a transducer—something that converts one thing (a physical process or electrical signal) into another (an electrical signal or a physical process respectively).
- Doing some physics, running experiments, learning from instructor tips
- Doing the formal report.
(Figure 1 is a copy of overhead (Electronics))
Electronics: extension of one’s senses for control and/or observation. Used for:
- Measurement of signals
o We have used DMMs, the VOM, and the potentiometer to measure direct current and voltage values.
o We will use the DSO to measure alternating voltages
§ Many signals we measure will be from the Function Generator
- Control of something
o When you press the buttons on the remote control for your television or stereo, you are using electrical signals generated in the remote that are converted, typically to infrared, for transmission to the TV. The TV, in turn, uses electronics to select the station, adjust the sound, etc. A mechanical action (pressing a button) is converted by a transducer into an electrical signal. When the temperature in a room goes up, a sensor detects the change and sends an electrical signal to the air conditioning unit which starts up and lowers the temperature. The conversion of a temperature reading to an electrical signal is done by a transducer. When the room temperature is low enough, the thermostat sends another signal and the air conditioning unit turns off.
- Processing of signals for:
o Human use or
o Automation and control
§ Heating and cooling in the Science Complex are controlled by a contractor in Cleveland, Ohio. Sensors in the building are monitored by computer in Cleveland. In response to inputs from these sensors, heating and cooling equipment, and hence the temperature, in the Science Center, are controlled.
We will begin with a discussion of how the DSO works and how we use it. An oscilloscope is a device for writing a time-varying signal to a screen where we can observe the strength (maximum and minimum values) and time-dependant behavior of the signal. Signals studied using a DSO are usually periodic. The first issue is: How does the DSO write on the screen? The DSO writes on the screen the same way a CRT TV or a CRT computer monitor writes on the screen. The DSO generates a very narrow beam of electrons. On the inner surface of the screen is a phosphorescent material that glows when exposed to radiation and continues to glow for a certain time after the radiation is removed. What we actually see is the glow of the phosphors in response to stimulation by electron irradiation. We typically use an oscilloscope to look at periodic signals such as a sine wave. For a sine wave of steady amplitude and frequency, each period looks the same. We typically display one or a few periods of the sine wave on the screen for study. The electron beam traces out the pattern of the sine wave on the phosphors on the inside of the screen. It writes from one side to the other then shuts off and returns to the starting side of the screen and begins writing across the screen again. As long as the signal we are studying is periodic (repeats over and over in time) and the phosphors glow longer than it takes the beam to return and irradiate them a second time, the picture of the sine wave we see on the screen appears steady and unmoving. There are a lot of processes going on to make all this work and we will examine them in some detail, but this is essentially what is going on. The beam generates on the screen a trace of glowing phosphors in the shape of the input periodic signal (e.g., sine wave) and then retraces the picture before the phosphors cease to glow.
We have an electron gun that generates an electron beam, in an evacuated (vacuum-filled—an oxymoron) tube (called a cathode ray tube) by heating an oxide-coated cathode. The oxide coating is selected to have a high thermionic emission coefficient. That is a fancy way of saying that when it gets hot it emits a lot of electrons. Electrodes accelerate the electrons emitted by the cathode and focus them into a very narrow beam. This beam is steered by two sets of deflection plate electrodes at right angles to each other. These deflection electrodes respond to input signals from some signal source and cause the electron beam to trace out a path on the phosphors on the inner surface of the cathode ray tube, CRT. The phosphors continue to glow longer than the time it takes the electron beam to complete one full pass across the tube face from left to right (as you see the screen), shut off and return to its starting point at the left side of the screen, and then retrace its path exciting the same phosphors again. Clearly this works only for continuous, periodic signals. This does not work for single events or transients, electronic delta-functions as it were. It is possible to capture transient, one-of-a-kind signals, and we will do so in mini-experiment 8 in which we measure the speed of sound in air.
In television picture tubes and computer CRT monitors, we also have an electron gun and phosphors on the inside of the tube face that glow in response to excitation by the electron beam. However, televisions and computer monitors do not use electrodes to steer the electron beam. They use electromagnets. The reason an oscilloscope uses electrodes is that the frequency of the signals we wish to measure using an oscilloscope is often far higher than the frequencies at which the CRT television or computer monitor must stear the beam to refresh the excitation of the phosphors. There are GHz scopes. These are marvelous devices that will display signals with frequencies in the GHz range. 1GHz is 109Hz. To see the behavior of signals that have a very high frequency (that oscillate very fast) we must have a beam-steering mechanism that is as fast as the signals. For GHz signals, electric deflection is fast enough but magnetic deflection is not.
There are two inputs to the scope labeled vertical (sometimes indicated by “Y”) and horizontal (sometimes indicated by “X”). The vertical (or Y) input feeds a time-varying signal to the plates at the top and bottom of the CRT that cause the electron beam to trace a vertical path up and down on the screen. Similarly, the horizontal (or X) input causes the electron beam to trace out a horizontal path left and right on the screen. If there were no input to either the vertical or horizontal input, then the electron beam would strike the phosphors at the center of the screen and all we would see is an unchanging dot.
Consider just the vertical input. If we introduce a periodic, time-varying, signal to the vertical beam-steering plates, the electron beam will trace out a single vertical line on the screen and all we would see is an unchanging vertical line. This is because the phosphors on the inside of the screen glow longer than the time it takes the electron beam to complete one cycle along this up-down path and return and excite the same phosphors a second time. We could use the grid on the screen-face to measure the length of the line and this would give us information about the peak-to-peak voltage of our signal. That is the voltage difference between the negative peak voltage and the positive peak voltage. (I will explain peak-to-peak voltage later in more detail.) But we would have no information on the behavior over time, e.g., the period or frequency, of the signal. The information the vertical input alone can give us is very limited.
There are two possible sources of a vertical signal in an oscilloscope. One is the BNC input on the front of the oscilloscope cabinet marked CH1 or “X.” The other is CH2 or "Y." Both vertical inputs will be used in one of our mini-experiments to drive the vertical electrodes and display two signals, each from a different source, on the screen simultaneously. The horizontal beam-steering plates are controlled by a sweep generator that is internal to the DSO. The sweep generator is also called a “Saw-tooth Generator.” A saw-tooth signal is a voltage signal in which the amplitude rises linearly to a maximum then falls linearly to a minimum. If you display this signal on an oscilloscope, you would see a series of triangles strung together that resemble the teeth on a hand-saw viewed from the flat side of the saw. Recall the comment above that if we put a periodic signal into the vertical input we would see a single vertical trace on the screen. Visualize for a moment what would happen if we input to the horizontal plates a signal that started at zero and rose linearly. What do you think this linear horizontal signal would do to the electron beam? It would cause the beam to move in a straight line across the screen in a horizontal direction. If we now combine the linear horizontal trace with the periodic vertical trace, AND if we synchronize the two signals, we would see the vertical trace (for example a sine wave) rise and fall between its maximum value and its minimum value as it moves across the screen. (We will see what synchronization means shortly.) We would, for a sine-wave signal delivered to the vertical input (synchronized with the saw-tooth wave on the horizontal input), see a sine wave traced out on the screen. We would see the kinds of pictures of sine waves we are used to seeing in textbooks.
The key to getting the sine wave to stay steady on our scope screen is to synchronize the saw-tooth generator sweep with the period of the sine wave input to the vertical electrodes. The DSO “triggers” the sweep generator to supply a linearly rising voltage to the horizontal beam-steering plates. This “trigger” is given in response to characteristics (that you select) of the signal being supplied to the vertical beam-steering plates. Periodic functions oscillate (conventionally up and down as we look from left to right because we read from left to right). Thus a sinusoidal signal has the same voltage twice in every half-period—once when the voltage is going up and once when it is going down. During one half-period, both voltages are positive. During the other half-period, both voltages are negative. You must specify the voltage (positive or negative) at which you want to trigger the sweep signal. In addition, you must specify whether to start when the voltage is going up (positive slope—positive or negative voltage) or when it is going down (negative slope—positive or negative voltage). We must decide if we want to trigger on a positive slope or a negative slope in the voltage-versus-time graph. We set the DSO to trigger at a particular voltage (positive or negative) applied to the vertical beam-steering plates. In addition, since periodic pulses move from a minimum through an average (frequently zero) to a maximum, we can find the same voltage (positive or negative) either on a rising voltage trace or on a falling voltage trace.
One problem, as we will see later, is that in many cases we will be measuring signals when there is a lot of noise (electrical signals not related to the signal we want to measure) being picked up by our equipment and displayed on the scope. Thus, as we will see, the voltage at which we trigger must be high enough to actually trigger on the signal and not on the noise. If we do not trigger at the same point on the signal every cycle, and at the same slope at every cycle (positive or negative), then the picture of the signal will not be frozen on the scope screen and we can’t make measurements of its parameters. There will be times when we look at signal that is so complex that it has more than one rising (or falling) voltage of the same magnitude in each cycle. We must be careful to select a unique trigger voltage. When you have a signal on the screen that is not steady, you need to adjust the trigger. We will see how to do that in class. This discussion is intended to familiarize you with the concepts.
There are two basic types of oscilloscopes.
- Analog—there is a one-to-one relationship between what is on the screen and what is coming into the horizontal and vertical inputs.
- Digital—the signal is digitized and input to a computer that then controls the deflection electrodes. In addition, the signal can be stored and a snapshot of the input signal frozen on the screen. In a digital oscilloscope, digital circuitry comes between the pre-amplifier and the vertical and horizontal amplifiers. (See Figure 2.) The vertical and horizontal amplifiers still steer the beam.
The following will not be complete until I can place a photograph of the front of the scope on my website. In the meantime, if you read this at home and bring it with you to class, you can refer to it when you get stuck on which controls do what on the scope. I will walk you through this description of the scope in class to help familiarize you with it.
The scope screen has, permanently inscribed on it, a line-grid pattern. The vertical scale is given in volts per division; a vertical division is the space between horizontal lines. The horizontal scale is given in time per division; a horizontal division is the space between vertical lines. The particular scales, both time and voltage, the scope is using are displayed on the screen immediately above the line-grid pattern. In taking your data, be sure to record the horizontal scale in seconds per major division, or pair of grid lines, and the vertical scale in volts per division, or pair of grid lines.
When you print using the print function on the scope, the output records the image on the screen, including the vertical and horizontal scales, and key settings of the controls described below.
The controls on the front of your scope are arranged in blocks and the blocks are labeled. In the following discussion, we will explore each block and its function. Before we begin, note that in the bottom of the frame around the DSO display there are six push-buttons. As we press buttons on the face of the DSO, a set of “softkey” (software-controlled key) options will be displayed at the bottom of the DSO display that correspond to the physical buttons (keys). The function of each button will be determined by software (hence the term “softkey”) in response to each button pressed on the face of the DSO.
- At the bottom of this block, there are two coaxial cable connectors labeled 1X and 2Y respectively. These are for connecting two separate inputs to the DSO simultaneously. They can be used to place two signals on the screen simultaneously. That is, one can drive the vertical deflection plates while the other drives the horizontal deflection plates. In this case, the images on the screen are called Lissajous figures.
- Position knobs. Moving up, you next see the position knobs that allow you to change the vertical screen position of the trace you are observing. That is, each knob allows you to raise or lower the position of one trace on the screen.
- 1. Selects a set of softkeys at the bottom of the display for control of inputs to channel 1. The softkeys we will use in class are:
o Off/on. Permits you to turn channel 1 off or on.
o Coupling. Selects AC, DC, or ground coupling—explained later.
o Probe. 1, 10, 100. Permits you to select appropriate attenuation for the probe being used—explained later.
- 2. Selects a set of softkeys at the bottom of the display for control of inputs to channel 2.
o Softkeys are the same as channel 1 keys above.
- Volts/Division knobs. At the top of this block, are two knobs that allow you to separately control the vertical scale for each input (channels 1 and 2) in volts/division. Each division is the space between two horizontal gridlines on the scope face. The vertical scale in volts per division (shown for each input, if both inputs are in use) is shown at the top left of the screen.
- Delay knob. Allows you to set delays for the horizontal time sweep. This has the effect of moving the signal left or right on the screen, depending on whether you reduce or increase the time delay. As you change the time delay, the tiny triangle at the top of the screen moves to indicate the point on horizontal or time scale on the scope face where the scope is triggering.
- Main/Delayed. Generates a softkey menu at the bottom of the display that permits you to display, in the lower half of the screen, an expanded portion of the main signal (the input signal). We will use this in mini-experiment 5.
- Time/div knob allows you to adjust the horizontal scale. The actual horizontal scale setting is displayed at the top center of the screen.
- Level knob
o This sets the vertical input signal voltage at which the horizontal time-sweep generator triggers. As you turn this knob, a horizontal line moves up or down on the screen and the changing trigger voltage level is displayed briefly at the bottom left of the display.
o You can select an external trigger. We will use this capability in mini-experiment 8 to measure the speed of sound.
- Mode. Generates a softkey menu.
o Permits a selection of trigger modes.
- Slope/Coupling. Generates a softkey menu. Two of the keys are:
o Slope. Permits you to trigger the horizontal sweep on a rising voltage or falling voltage (positive slope or negative slope).
o Coupling. You may select AC or DC coupling. Earlier I said that a periodic signal such as a sine wave oscillates about a mean value which is frequently zero. The oscillating portion that moves up and down around this average value is the AC or alternating current signal. If the average is not zero, we say that there is a “DC bias” or “DC offset.” This just means that the average value of the signal is not zero—it is “offset” from zero. The average may be positive or negative. We will select the DC offset for the signal we display on the screen when we use the Function Generator to produce time-varying signals for study on the DSO. The DC bias, or offset, can be visualized as a platform on which the AC signal rides. This platform may be elevated above the voltage value of zero (a positive DC offset voltage) or depressed below the voltage value of zero (a negative DC offset voltage).
- This block essentially controls the computer functions of the DSO. The functions are:
o Run. You are viewing a “live” input signal
o Stop. You are viewing a stop-frame or frozen piece of the input signal
o Auto store. Stores the input signal
o Erase. Erases the stored input signal
- Voltage. Generates a softkey menu.
o Enables the automatic measurement of Vpeak-peak, Vaverage, and Vrms—explained later—on channels 1 or 2.
- Time. Generates a softkey menu.
o Enables the automatic measurement of frequency, period, or duty cycle on channels 1 or 2.
- Cursors. Generates a softkey menu.
o Enables measurement of two different voltages or two different times on channel 1 or 2 using cursors that you set at different voltage-values or time-values of interest. We will use these in mini-experiment 5.
- Setup. Generates a softkey menu.
o Enables you to save the current softkey settings for the DSO or retrieve a previously saved combination of settings. There are two ways to retrieve previously saved settings for the scope.
§ Beneath the screen there are 6 buttons. At the left, you will see a number in a highlighted background. Press the button beneath this number until the number you want is displayed.
· Alternatively, turn the knob to the right of the Setup button until the desired number appears.
§ Now press the button at the bottom of the screen under “Recall.” This changes the DSO settings to correspond to those stored under the chosen number in memory.
Auto-scale. This is your “panic button.” You press it when you cannot find the signal. The DSO locates the signal, determines the appropriate volts/div and seconds/div, and displays the signal on the screen. Auto-scale does not always find the signal, but almost always.
Print Utility. Generates a softkey menu. One option is:
o Print screen. Enables printing a copy of the current display. The printed output will also display many of the softkey settings to enable you to understand fully what is communicated in the graphical display.
Beneath the display. On the face of the case beneath the display, there are two items of interest.
- One is a flat metal tab with a sketch of a square wave with 0 and 5V and »1.2kHz. This provides a 1.2kHz, 5V peak-voltage square wave output. We will use this to adjust the capacitive compensation on the 10:1 probe (compensation and the probe will be discussed in detail later).
- The second is a rectangular white button marked 0, 1. This is the power switch. The DSO is on when the button is pressed in.
Let’s begin working with the scope. Press Setup, place the number 7 in the far left position under “Setup Memory.” Press Recall. Setting 7 is a stored-version of the set-up conditions for the scope that I have pre-set so that everyone starts out the same for this first exercise.
Let’s observe some things about the scope.
- Look at the top left corner of the screen just above the gridlines. You will see: 1.00V. This means there is a 1.00V/division vertical scale. This is the vertical scale to which the scope is set. This means that each large pair of horizontal lines on the screen is 1.00 volt apart. There are 9 horizontal lines, but eight vertical divisions (spaces between horizontal lines) on the display.
- Look of the screen just above the grid lines and to the right of the center of the screen. You will see 1.00ms. This means that the horizontal scale is 1.00ms/division.
- At the center of the far right side of the display, just outside the gridlines, is a tiny arrowhead attached to a ground symbol. This is the zero voltage point of your display. You can adjust it using the position knob for channel 1 in the Vertical block. Try it. When you are done, return the zero point to the middle of the screen. You can also adjust the zero point for channel 2 using the other arrowhead with ground symbol. REMEMBER THIS: When you do not see this ground symbol on the right of the screen, you will see an arrow to the right of the display at the top of the screen pointing up or an arrow at the bottom of the screen pointing down. This will occur when there is a DC-offset or DC bias, you are looking at a time-varying signal on the screen, and you have selected AC coupling. This means that the DSO displays only the AC portion of the signal, and not the DC offset. The arrows to the right of the display are showing you that the zero voltage point is off-screen above (for a negative DC offset) or off-screen below (for a positive DC offset).
I will go through the eight mini-experiments one at a time. I will both elaborate on the procedures in the manual and give you some theory. I will make no attempt to repeat every step from the manual. The manual is very complete and detailed.
Part 1. Analysis of hand-induced signal
- Take the gray probe from your lab bench and connect the coaxial cable to channel 1 at the bottom of your scope control panel.
- Press the Ch 1 button in the Vertical block. At the bottom of the screen on the right, you will see Probe with, 1, 10, and 100, beneath it. The number 1 will be highlighted. Press the button beneath Probe until the number 10 is highlighted. We will discuss the reason for doing this when using the probe later. Remember to set Probe to 10 when using the gray 10:1 probe.
- Remove the plastic tip from your probe. When you remove the plastic tip, you will expose a sharp metal tip. Place your finger gently on this tip it is fairly sharp. You will see the dark line across the center of your scope screen sort of wiggle a bit, but it doesn’t look like much. This is because the vertical and horizontal scales are set incorrectly. Keep your finger on the metal probe tip. CAUTION: Press gently, only on the sharp point. If you press on the sharp point AND at the same time touch the metal collar, you will ground the input signal and see nothing useful on the screen.
- Press the Auto-scale button just to the right of the screen.
- Adjust the volts/div knob for channel 1 until you can see a sine wave. The period of the wave is too long to display a whole cycle on the screen. Adjust the Time/Div knob in the Horizontal block until you can display one full cycle in the width of the screen.
- Adjust the Volts/div knob again. As you make the scale too sensitive, the trace disappears off the screen at both top and bottom. Always select the vertical scale that allows you to see the largest possible amplitude without the trace going off-screen at either the top or the bottom. This gives you the largest amplitude you can display and still measure. If you think about uncertainties, your ability to read the scope screen is limited by how well you can interpolate the distances between gridlines. Your ability to interpolate these distances should be the same for any voltage or time scale. The percent uncertainty in your measurement is the uncertainty divided by the measurement and the quotient multiplied by 100. The larger the measurement, the smaller the percent uncertainty. Thus the larger the amplitude of the signal on the screen, the smaller the percentage uncertainty in your measurements.
- With your finger still on the metal tip of the probe, press Stop in the Storage block. This takes a freeze-frame photograph of the signal and continually displays that frame on the scope screen to permit you to make measurements.
- Figure 8, top, shows the peak-to-peak voltage and the peak voltage of a sine wave. It also shows the period of the wave. While you could measure the period between peaks by lining up a vertical gridline with a peak and then interpolating the time at the next peak, it is more precise to use two points where the wave crosses the zero volts line because you have vertical hash marks on this line and it is far easier to precisely determine the second crossing point.
- Using the gridlines and the horizontal time scale at the top right of the screen, determine the period of the sine wave. From the period, calculate the frequency of the wave. USE TWO PERIODS and divide by 2. For the same reason as making the vertical dimension of the wave as large as possible, measuring the time for more than one period and dividing by the number of periods decreases the percent uncertainty of the measurement. Record your values for period and frequency on page LR8-1 in your manual.
- Now use the horizontal gridlines and the scale at the upper left-hand corner of the screen above the gridlines to determine the peak-to-peak voltage of your signal. Record this information on page LR8-1.
- Why is the frequency you measured the value it is?
There is a small spike on the wave form that occurs twice in each period. Thus the frequency of this spike is at 120Hz. Do you know why?
Part 2. Sine wave measurements
Disconnect the probe. Do Steps 5 and 6 in the manual.
I will guide you through the following steps in class. In the Trigger block, press Mode. Press the button under Normal at the bottom of the screen so that Normal is highlighted. Turn the Level knob in the Trigger block left and right and see how the trace moves left or right as you change the voltage level at which the horizontal sweep triggers. When you move the trigger level too far up or down it goes beyond the signal and the trace freezes. Try it.
Place the trigger level back within the sine wave. In the Trigger block, press Mode/Coupling. At the bottom left of the screen you will see Slope and beneath it, two symbols. One has an arrow pointing up that corresponds to triggering on a positive slope (rising voltage—hence the upward-pointing arrow) and the other has an arrow pointing down and corresponds to triggering on a negative slope. Change back and forth between positive and negative trigger slope and see what happens. Return the trigger slope to positive and leave it there.
Turn the Delay knob in the Horizontal block. Watch what happens to the position of the trace on the screen. Watch carefully to see what happens to the tiny arrowheads at the top and bottom of the screen that indicate the trigger point. Look at the read-out above the center of the top of the screen as you turn the Delay knob and move the trace. Return the trigger point to the center of the display.
Move the small light gray knob in the Vertical block. Watch the tiny arrowhead with the ground symbol at the right of the gridlines. This is the zero-voltage point. Also observe the read-out at the bottom of the screen as you move the zero voltage point.
Follow the directions in your manual starting with Step 7.
Step 7. Vpeak-to-peak, Vp-p, is the difference between the highest voltage in the sine wave trace on the screen and the lowest. It is the vertical distance, in voltage, between the top of the trace and the bottom of the trace. Recall, from Physics 210L, that a periodic function is one that repeats in a fixed period of time. One cycle, or one period, is the time it takes the function starting at a particular value or location on the display, to return to that same value or location. The period is given in seconds per cycle. The inverse of this number, cycles per second, is the frequency. For a sine wave, always measure Vpeak-to-peak. Then if you need Vpeak divide by 2. This increases precision of measurements.
The reason for measuring the root-mean-square voltage, Vrms, is as follows. For DC, power is calculated based on
P = IV (1)
Where 1A (ampere) dissipates 1W (watt) when flowing through a resistance of 1Ω (Ohm). AC power is calculated based on the values of AC current and AC voltage needed to dissipate 1W in a resistance of 1Ω. The RMS or root-mean-square values of voltage and current give the equivalent AC heating of a 1Ω resistor.
For a sine wave only,
Vrms = Vpeak/√2 (2)
The 120V power in your house is 120Vrms. Vpeak is ~170V. Vpeak-to-peak is 340V. The RMS value for a square wave is the peak voltage of the square wave.
Step 8: Measuring Vrms with the gray bench-type DMM.
Move the coaxial cable from the DSO to the gray bench-type DMM using the coax-to-dual-banana adaptor on the DMM inputs.
TIP: The coax-to-banana adaptors have a black tab above one banana prong. This is the negative or ground side of the adaptor. It is electrically connected to the ground sheath or outside conductor of the coaxial cable. If you do not keep the side with the black tab on the ground side of the circuits you construct using the solderless breadboard, you will not get the anticipated results. Similarly, if you plug the banana prong with the black tab into the red (positive) receptacle of the DMM, you will also get strange results.
TIP: Read the front of your equipment. When measuring AC signals with the DMM, the switch marked AC/DC must be pushed in.
Step 9, DC offset. The average voltage of a pure sine wave is zero, because half the time the signal is positive and half it is negative. However, when you have a combined AC and DC signal, the average value of the combined signal is not zero. If there is a DC value, and the average of the pure AC value is zero, then the average of the combined AC and DC voltages is just the DC voltage. Think of the DC offset as a platform, elevated or depressed, on which the AC signal rides. If it is a positive DC offset, the platform is elevated, or the average of the signal is elevated above zero or is positive. If it is a negative DC offset, then the average of the signal is depressed below zero or is negative.
Steps 10 and 11: Determine the effect of the DC, AC, and GND setting on the softkeys after you press the CH1 button. The DC setting provides a direct current path between the source and the pre-amplifier in the DSO. This direct path passes both AC and DC components of the signal equally. The GND setting shunts the entire signal to ground and there is no input to the DSO pre-amplifier. The AC setting inserts a capacitor in series with the input to the DSO pre-amplifier. Think for a moment what this means. When you have a series circuit composed of a DC voltage source, a switch, and a capacitor, what happens when you close the switch? The charge begins to build up on the plates of the capacitor and the voltage drop across the capacitor builds up until it equals the voltage drop across the voltage source and no further charge can flow. From this point on, the capacitor appears to the DC voltage source as an open circuit. That is, after the initial current that results in the charge and voltage build-up on the capacitor no current flows. If the signal input to the DSO has a DC component, this DC component does not get to the DSO pre-amplifier and is not displayed on the scope trace. Now consider what happens if, instead of a switch that you throw once, you have an alternating voltage source such as a sinusoidal voltage function. Now every half-cycle the voltage reverses. Charge flows into the capacitor on one half cycle and out on the next then in on the next half-cycle then out on the next, and so on. Thus there is an oscillating current and voltage on both sides of the capacitor. The bottom line is: An AC signal (of high enough frequency—we will explore what “high enough” means later) goes right through the capacitor while a DC voltage does not.
If there is a signal input to the DSO that has both an AC component and a DC offset, you can choose DC coupling and display both components on the DSO screen. If you choose AC-coupling, only the AC portion of the signal is displayed. The DC component never gets to the DSO amplifier. The DC component is blocked by the capacitor and since the capacitor is inside the scope, it is said that the DC signal is “blocked in the scope.”
We use the AC and DC coupling settings to measure the DC offset of a signal. Think about what is happening. The average value of a pure sine wave is zero. The average value of an AC signal with a DC offset is just the DC offset. If I select DC coupling and observe the position of the average value of the signal and then switch to AC coupling and observe the average value of the signal, the difference between these two values is the magnitude of the DC offset. If, when I switch from AC to DC, the signal moves up on the display then the offset is positive. Conversely, if the signal moves down on the display when I switch from AC to DC coupling then the DC offset is negative. Observing the average of the wave is not as easy as observing the position of a peak on the wave for each coupling mode. You want to choose a vertical scale (volts/division) so that you can get the same point on the wave to show on the screen in both AC and DC coupling modes. You need not see the entire signal on the screen when measuring the DC offset. All you need is one point that stays on screen when you switch between AC and DC offset. You are just measuring how much that single point moves when you change coupling modes.
The number of volts between the same point on the wave when switching form AC to DC coupling is the value of the DC offset. If the wave moves up when you go from AC to DC coupling, the offset is positive. If the wave moves down, the offset is negative.
Items 14, 15, and 16, measurement of Vp-p and Vrms and calculation of Vrms. Review the discussion above for Step 8 on why we measure Vrms if necessary.
The DMM should give you the same value as the oscilloscope. If not, you need to re-do the measurement. When reading the DMM, you want a scale that gives at least three digits. Remember: The DMM gives four digits for numbers less than or equal to 1999, regardless of where the decimal occurs. The DMM gives three digits for numbers greater than 1999, regardless of where the decimal occurs. Choose a scale for which you do not have any left-hand zeroes. Remember: Right-hand zeroes are significant. Left-hand zeroes are not.
The DC offset shifts the sine wave up or down depending on whether the offset voltage is positive or negative. The little arrowhead at the right edge of the gridlines indicates where the zero voltage point is. When you get a situation where you are using a DC offset and the AC signal disappears, increase the vertical scale to ~1-2V/div (or greater if needed) until both the AC signal and the voltage zero point show up on the screen. When measuring the height of the AC signal, use the full height of the display to increase precision in your reading of the voltages.
When you change from AC to DC offset, the trace moves if the signal has both an AC and a DC component. Expand the signal as much as possible.
Part 3. A. Adjustment of probe compensation; B. Rise time measurements.
A. Adjustment of probe compensation.
A key characteristic of the DSO is that it amplifies a wide range of signal frequencies uniformly. A square wave is generated by the signal generator by superimposing a large (theoretically infinite) series of sine waves with odd wave numbers because only odd wave numbers will superimpose to fill in the corners of the square wave. I will discuss this in lecture. The point I want you to take away from this is that a square wave can be decomposed into a series of waves with a very large range of frequencies. We will use a square wave to adjust the frequency compensation on the 10:1 probe to assure that the DSO is amplifying a very wide range of frequencies uniformly. We will do this with a square test wave because the uniformity (or non-uniformity) of amplification can be easily seen in the flatness (or non-flatness) of the top of a square wave. The reason for using the 10:1 probe is that the probe has a resistance of 9MW while the scope has an input impedance of 1MW. Together they have an input resistance of 10MW. As we have seen before, the higher the input resistance of a measuring instrument (such as the DSO) the less current the instrument draws from the measured circuit, therefore the less change is induced in the measured circuit, and therefore the more accurate are the measurements.
How does the compensation circuit work? A capacitor provides an effective resistance to current flow in a time-varying circuit called the reactance, given by 1/(wC); w is the frequency of the time-varying signal and C is the capacitance. The capacitor in the probe is in parallel with a 9MW resistor. To an AC signal, the parallel combination of a resistance and a capacitive reactance looks just like the parallel combination of two resistors so the parallel combination is
Where Z is the reactance of the circuit. As the frequency, w, goes to zero (the DC case) the value of Z reduces to R. This is because (as discussed above in Steps 10 and 11 on AC versus DC coupling to the scope) after an initial (brief) transient voltage the capacitor appears to DC voltages as an open circuit. As w gets very large, Z becomes purely reactive, rather than resistive, and Z approaches zero. As you adjust the capacitor in the probe using the tiny screwdriver at your lab station, you are adjusting Z (the capacitance) to assure that the DSO is, in fact, amplifying the signals uniformly across the frequency range of interest.
The parallel combination of a 1MW resistor and a 13pF capacitor, between the positive input to the DSO pre-amplifier and system ground, perform exactly the same function in the DSO. In this case, however, the DSO is measuring the voltage drop across this parallel combination. At DC, the parallel combination looks exactly like a resistive load of 1MW and the DSO detects, amplifies, and displays the voltage difference across the 1MW resistor. At high frequencies, the capacitor looks like a dead short to the alternating voltage in comparison to the 1MW resistor. Thus the alternating input voltage appears across the capacitor and the DSO detects, amplifies, and displays the voltage difference across the capacitor.
Step 19. Read the front of the DSO. Beneath the display is a tiny metal tip sticking out of a small depression. Next to it there is a picture of a square wave with “0, 5V, and »1.2kHz.” You will clip the probe to this tiny metal tip using the spring-loaded hook in the end of the probe.
Step 20. The point here is that you are only interested in the top of the square wave. If, the left (leading) edge of the flat top of the square wave has a peak in it, the probe is over compensated. This means that the DSO is amplifying higher frequencies more than lower. If the leading edge of the top of the square wave is rounded, the probe is under compensated and the DSO is amplifying lower frequencies more than higher ones. When you have adjusted the capacitor in the probe until the top of the square wave is as straight as you can make it, the probe is properly compensated.
Step 21. When you press Main/Delayed, an expanded portion of the square wave will appear on the display below the original square wave. When you look above the grid lines, you will see the time scale for the delayed trace and you can see that it is a finer time scale. The point is to practice doing an eyeball (your best estimate by eye) measurement of the rise-time of the signal.
Steps 22 and 23. The point here is to use the internal measurement functions in the DSO to determine fall-time and rise-time and compare them to your eyeball value for rise-time.
Part 4, Dual trace operation.
The point of this part is purely to give you some experience with some additional functions of the DSO. When you get your print-out of the screen, note that it contains a lot of the softkey settings for the scope to help you understand the information conveyed by the printed signal trace. IN YOUR REPORT, CLEARLY EXPLAIN WHAT YOU DID AND WHAT YOU OBSERVED. SHOW EXAMPLES OF THE SCREENS USING PRINT-SCREEN.
Part 5. Response of an RC circuit to sine and square waves.
In this part, we introduce the concept of a filter circuit that we will deal with much more extensively in Experiment 11. Take a look at Figure 1 in the manual. The function generator provides the input to a circuit consisting of two resistors and one capacitor. The function generator output is also recorded on channel 1 of the DSO. The output voltage across one of the resistors is recorded on channel 2 of the DSO. We use the DSO to compare the input to the circuit to the output. The 100W resistor prevents signals generated in the circuit from getting back into the function generator. It also lets the Function Generator “see” a primarily resistive load. The filter circuit consists of the 0.1mF capacitor and the 33kW resistor. This is called a high-pass filter circuit. What that means is that it will pass high frequency AC signals, but not DC signals. Look at the circuit. A DC voltage introduced at the input would, after the capacitor was fully charged, see the capacitor as an open circuit. An AC signal of sufficiently high frequency (more on how high is high enough later), on the other hand, would appear across the capacitor as an alternating voltage that would propagate on through the circuit. The time for the capacitor to charge or discharge is determined by the “time-constant” of the circuit. The time constant for a circuit containing a resistor and a capacitor (called an RC circuit) is just the product of the resistance and the capacitance, RC. We use a square wave output from the signal generator and examine both the square wave input to our filter circuit and the output recorded across the 33kW resistor.
In AC circuits, there are two perspectives that are used. One is to look at how the circuits behave as frequency is changed—this is called the frequency-dependent behavior. The other is to see how the voltage and current change with time—this is called time-dependent behavior. We will look at both behaviors for our high-pass filter circuit. This serves as an introduction to the much more extensive treatment in Experiment 11 of both high-pass and low pass resistive-capacitive and resistive-inductive filter circuits.
5a. Frequency-dependent behavior.
Step 28. The key to using the solderless breadboard is to understand how the connections within the board work. The board is designed to let you insert wires into holes so that wires can be electrically connected to each other without having to solder, clamp, or twist the wires. The easiest way to understand how the board works is to turn it over and look at the underside. If you turn the board over and set it on the bench with the long axis of the board oriented left to right, you will see a series of metal bars imbedded in plastic. Study the bars for a moment. In the middle of the board are two rows, extending from left to right, of short, vertical metal bars. NOTE THAT NONE OF THESE BARS IS CONNECTED TO ANY OTHER BAR. Now turn the board back over, still oriented with the long axis from left to right. There are two horizontal rows of five-hole vertical columns, one row above the other, each column is five holes high and each row is sixty-four columns long. There is a horizontal groove in the plastic between the two rows of holes. Each five-high column of holes corresponds to one of the metal bars you saw on the back of the board. A wire inserted in one hole in any five-high column of holes is electrically connected to a wire inserted in any other of the five holes IN THAT COLUMN ONLY. One thing students struggle with is: NO VERTICAL COLUMN OF FIVE HOLES IS ELECTRICALLY CONNECTED TO ANY OTHER COLUMN OR HOLE ON THE BOARD.
Turn the board over again so you can see the underside. Keep the long axis of the board oriented from left to right. At the top of the board are two pairs of horizontal metal bars. Look carefully to convince yourself that there are two pairs, one horizontal pair on the left half of the board and one horizontal pair on the right half of the board. NOTE THAT EACH OF THE FOUR BARS IS ELECTRICALLY ISOLATED FROM ALL THE OTHERS. Note that there is a small vertical gap in the middle of the board between the pairs of bars. Notice that at the bottom of the board, the same pattern of bars exists. Turn the board back over so you are looking at the top of the board and the long axis is again oriented from left to right. Near the top and bottom of the board, near the center of the board are two screws. To the left of the screws are two horizontal rows each consisting of five sets of five holes. ALL the holes in each row to the left are connected to all other holes IN THAT ROW ONLY. The two rows are not electrically connected to each other. Each row to the left corresponds to one of the horizontal metal bars you observed when looking at the back of the board. Similarly, there are two rows of five sets of five holes on the right of the screw. ALL the holes in each row to the right are connected to all other holes IN THAT ROW ONLY. The same pattern is repeated at the bottom of the board. When wiring circuits using the solderless breadboard, whenever you are in doubt about how the connections on the breadboard work turn it over and look at the back.
At the top and at each end of the board there are female receptacles for male banana plugs. You will use these receptacles to connect the breadboard to the function generator and the DSO. You will use a coaxial cable to connect to the function generator and the DSO. To connect these coaxial cables to the breadboard you will use a coax-to-banana adaptor. It is a small black plastic connector with a coaxial connection on one side and two male banana jacks on the other side. VERY IMPORTANT: THE ADAPTOR HAS A BLACK PLASTIC TAB STICKING OUT ON ONE SIDE. THAT SIDE IS GROUND. This is the side that is connected to the outer conducting sheath of the coaxial cable and this sheath is connected to earth ground at the function generator and the DSO. If you are not careful to keep this tab on the ground side of your circuit, you will not get the expected results.
Step 31. You will determine the “corner” frequency, fcor, by finding the frequency at which eout is 0.707 times ein. The “corner” frequency is the frequency at which the phase of the output leads that of the input by 45° or ¼ cycle.
We have now explored how the output of the signal differs from the input as frequency changes. Now let’s see how output differs from input as time changes.
5b. Time-dependent behavior.
The theory section in the manual for Part 5b is quite complete and I will confine my comments to clarifications of various steps.
Step 34. You will move the signal on channel 1 by pressing the CH1 button and using the position knob for that channel to move the signal to where you want it. Press the CH2 button and do the same for the signal on that channel.
Step 35. To access the cursors, press the Cursors button. You can select, one at a time, voltage cursors (v1 or v2) or time cursors (t1 or t2). Practice using the knob next to the Cursors button to move the currently selected cursor. (Remember, only one cursor—the one you selected—is adjustable at a time. Practice with the cursors is the best way to learn how they work. Raise your hand if you need help.
Step 37. Follow the directions carefully and raise your hand if you have trouble. Think about what you are doing and what the various functions on the scope are doing.
Part 6. Induced EMF in a coil
6a. A magnet moving in a coil.
The theory is quite complete. The only thing I find students have difficulty with in this part is determining which end of the coil is positive.
Step 42. Think about what is implied by equation (14) in the manual. Equation (14) says that when the magnetic flux through a coil changes there is an EMF induced in the coil. If the coil is part of a closed circuit, this EMF results in a current flowing in the coil.
- The direction of the induced current is such that the magnetic field generated by the induced current is in a direction to oppose the original change in flux.
- One face of the plastic frame holding the coil has two female banana connectors on it. As you look at this face of the magnet, the coil is wound from the right-hand banana connector toward the left-hand banana connector. I.e., it is wound counter-clockwise.
- Recall that if the fingers of your right hand curl in the direction the current flows in a coil then the induced magnetic field is in the direction in which your right-thumb points.
- By convention, the direction of the lines of magnetic flux is out of the north pole and into the south pole.
- The coil experiencing a change in magnetic flux is a source of EMF, similar to a battery. The point of this is that the terminal out of which the current in the coil (source of EMF) flows is positive. This is exactly analogous to the situation in a battery, or other source of EMF, where by convention the current flows out of the positive terminal.
- If you have the north pole of a magnet inserted in the coil and pull it out, you cause the magnetic flux flowing into the coil to decrease. (By convention, field lines flow out of the north pole and into the south pole.) Thus the EMF in the coil acts in such a way that the current flowing in response to that EMF generates magnetic flux lines that are into the coil. Thus the induced magnetic flux acts to oppose the change in flux from withdrawing the magnet.
From these six pieces of information, you can determine which end of your test magnet is the north pole and which the south. After you have made your assessment, ask me for the magnet with marked poles so you can check your result. If you were wrong, don’t worry about it; just learn where you went wrong and be sure you thoroughly understand what is going on. If you made a mistake, explain in your formal report what mistake in reasoning or understanding resulted in the mistake.
6b. A speaker as a sound transducer.
The speaker we will use consists of a paper diaphragm, a conducting coil of wire, and a permanent magnet. The paper diaphragm is connected to the coil. A microphone can act as a transducer to convert sound waves to variations in current that are amplified and used to excite the coil in the speaker. When the coil experiences a time-varying current, it generates a time-varying magnetic field. This time-varying magnetic field interacts with the field of the permanent magnet and the coil moves at a rate determined by the changes in current input to the coil. Since the coil is connected to the paper diaphragm, the diaphragm moves at the same rate and as it moves it creates regions of compression and rarefaction in the air that propagate outward and that we hear as sound. The speaker will also work in reverse. That is, the diaphragm will vibrate in response to sound input and force the coil to move in the magnetic field. Movement of the coil in the magnetic field results in a time-varying magnetic flux experienced by the coil. This time-varying magnetic flux results in the generation of a time-varying EMF in the coil. This time-varying EMF can be amplified and transmitted through wires to excite another speaker that will emit an approximation of the sound input to the first speaker. The first speaker is acting as a microphone.
We will excite mechanical vibrations in the coil. The coil will move in the field of the permanent magnet and generate a time-varying EMF that we will display and analyze using the DSO.
Step 44. Whistle and see on the DSO display the time-varying EMF generated in the coil by the mechanical movements of the paper diaphragm excited by your whistle.
Step 45. Here you will use a tuning fork and measure the frequency of the wave displayed on the DSO screen. You will compare the measured frequency to the frequency stamped on the tuning fork. Be careful to press the base of the tuning fork FIRMLY against the back of the speaker box in order to get good coupling of the vibrations of the fork to vibrations of the box and speaker coil. Do not let your hand touch the wooden speaker box.
Step 46. Here you will start two tuning forks, with similar but not identical frequencies, vibrating and press both simultaneously against the back of your speaker box. Do not let your hand touch the wooden speaker box. The two tuning forks will generate two frequencies in the speaker and on the DSO display. One will be the average of the two frequencies of the tuning forks. The other will be one-half the difference between the fork frequencies. This requires a little explanation. Let’s represent the wave generated by one fork as a sine wave with a particularly frequency, wA. Let’s represent the wave generated by the second fork as a sine wave with a particularly frequency, wB. Our two waves generated by the two forks are then
f1(t) = Asin(wAt) (4)
f2(t) = Bsin(wBt) (5)
The two tuning forks are going to be vibrating the speaker at the same time so we can expect their frequencies to combine in some way. We need to determine how to combine equations (4) and (5). We will use the following trigonometric identity.
Thus you will see an “envelope” with a frequency of ½(wA - wB) and a “carrier” with frequency ½(wA + wB). We will not measure the amplitude of either of these waves. We will measure only the frequencies.
Part 7. A semiconductor solar cell – A light transducer
Step 47. Connect a solar cell to CH1 with the coax-to-banana-connector cable. Expose the cell to only the ceiling lights in the room. Place the solar cell in a position where outside light cannot fall on it. Press Setup, select setup 7, and press Recall. The volts per division will be set for 1.00V. The time scale will be set to 1ms/division. You will see a nearly linear signal between +2 and +3 volts. Adjust the Time/Div knob until you see a periodic wave with several cycles. Switch to AC coupling. Adjust the Volts/Div knob until the signal nearly fills the display from top to bottom. Press Stop. Measure and record Vpeak-to-peak. Press Setup, select setup 7, and press Recall. You will see a nearly linear signal between +2 and +3 volts. Press Voltage, select Vaverage. Record Vaverage. Cover the solar cell and observe what happens to Vaverage.
Step 48. Turn off the room lights and repeat Step 47 using only outside (sun) light. There is not much outside light anymore since they walled us in, but there is enough to get a reading for Vaverage that will be of the order of 500mV. You may need to tilt the solar cell array a bit so it has a more direct “view” of the light from the windows.
The point of this part is to give you practice in working with a signal with an AC ripple that is far smaller than the DC offset.
Part 8. Measurement of the speed of sound.
This part will be done as a class exercise. A single experiment will be set up in which the external trigger function of the DSO is used to measure the speed of sound. If you will look at the figure below, you will see that two things happen when the metal hammer strikes a thick aluminum plate. The first thing that happens is: Sound waves are emitted, move outward from the strike point, and cause the paper diaphragm of a speaker to vibrate. This is the same speaker we used in Part 6b, “A speaker as a sound transducer.” The moving diaphragm causes a coil to move in the field of the permanent magnet in the speaker. The resulting EMF in the coil is conducted by a coaxial cable to Channel 1 of the DSO. The second thing that happens is: An electrical signal is generated as a result of the conducting hammer striking the aluminum plate and is delivered to the DSO external trigger input. The negative side of a battery pack is connected to the aluminum plate. The positive side of the battery pack is connected to the inner, positive conductor of the coaxial cable connected to the DSO external trigger input. The metal hammer is connected to the grounded sheath of the coaxial cable which is connected to the external trigger input of the DSO. The electrical signal generated by the hammer triggers the scope to start its horizontal sweep. On successive experiments, you will record the total distance of the speaker from the strike point and the time between the corresponding points on successive waves displayed on the DSO. We assume that the delay in conducting the signal from the speaker to the DSO is negligible compared to the time to propagate the sound wave from the strike point to the speaker. This is a pretty good assumption since the electrical signal travels at the speed of light in the copper coaxial cable.Figure 1. Setup for mini-experiment 8, Experiment 8, 211L.
Step 49. Use Excel to do your regression analysis and your plot of distance (from the strike point to the speaker) versus time. The slope from your regression (with its uncertainty) is your first-order estimate of the speed of sound. In Step 50, you will refine this estimate.
Step 50. The speed of sound in air is a function of temperature. Use the given formula for refining your estimate of the speed of sound from Step 49.
Step 51. You are to compute the simple sum of the percent uncertainties of temperature (given in the manual) and the slope from your regression analysis. You will compute the percent difference between the experimentally measured and theoretical speed of sound. By comparing the sum of the percent differences to the absolute value of the percent difference, you will determine if your experimental speed of sound agrees with the theoretical value.
The formal report.
Abstract: This can be very brief. You may simply point out that a series of experiments were conducted to enable you to become familiar with the operation and use of the digital storage oscilloscope (DSO).
Introduction: Introduce the report in a way you would find helpful if you were someone reading the introduction with no knowledge of this experiment.
- Table of equipment used.
Descriptions of the experiments: Break these out as mini-experiments one through eight. That is: Each mini-experiment should stand on its own in the report with a technical introduction, a description of the mini-experiment, a data and analysis section, and a results and conclusions section. Provide the following information:
- A brief introduction and theory section. State the purpose of the experiment. All are designed to familiarize you with some function or functions of the DSO and how to use the DSO to perform these functions.
- A brief description of the mini-experiment. Assume the audience is familiar with a DSO and with physics in general, but not with your particular experiment.
- Describe completely the data collected.
- Describe the analyses performed.
- Describe the results obtained.
o If it was a qualitative experiment, what did you learn from the process?
o If it was a quantitative experiment, such as mini-experiment 6a where you determined which end of your test magnet was north and which was south and then confirmed (or not) the results using a known magnet, you should state whether the results agreed with theory and what you learned. If there are experimental and theoretical (or accepted) values, state whether the experimental and theoretical values agreed within experimental uncertainty. SHOW QUANTITATIVELY HOW YOU KNOW—SHOW THE NUMBERS AND THE CALCULATIONS, PARTICULARLY CALCULATIONS OF UNCERTAINTY.
- Summary and conclusion: Wrap it up. State briefly what you learned and whether the quantitative mini-experiments agreed with accepted values or not.
- Make frequent use of sketches and graphs.
- Integrate all tables and graphs into the text.
- Use correct format for equation—see the manual for the format.
- Use Microsoft Equation Editor to do the equations. If you need help in getting started with equation editor, come see me.
- DOUBLE SPACE ALL TEXT.
- Place the LR-pages from the manual containing your raw data in an Appendix.