In this lab exercise you will gain a working knowledge of how to use an oscilloscope by measuring the amplitude of a square wave and the frequency of a sine wave.

Note that the goal of this experiment (from a learning perspective) is largely to give you an understanding of this (somewhat complicated) instrument, so that we can use it in future experiments without requiring further explanation. As such, there are questions in the procedure that you don't need to formally answer in your report, but should make sure you understand (for your own sake).^{Hoveroverthese!}

• 1 Oscilloscope (2 Banana/BNC Adaptor)
• 2 Function Generator (2 Banana/BNC Adaptor, 1 each)
• 4 Banana cables, 1 Alligator Clip
• Record data in this Google Sheets data table

A description of how the oscilloscope works can be found here: Oscilloscope Description ¹

A description of how the function generators work can be found here: Function Generator Description

In short, the oscilloscope is going to measure the voltage difference between the red and black wires plugged into it and plots this voltage (y-axis) as a function of time (x-axis). This is what appears on the oscilloscope screen.

In more detail: the oscilloscope starts by outputting a dot at the left-hand side of the screen, and moves up and down with the voltage input as it moves to the right. Then, it jumps back to the left, and draws it again. If it moves fast enough (which it will, given how we'll be using it), this will look like a curve as it moves across the screen. Each of these "screen crossings" is called a horizontal sweeep.

The physical mechanism by which the dot is made on the screen is similar to a CRT TV in that an electron beam (emitted from an electron gun at the back of the device towards the front) hits a phosphor-coated glass screen. The location of the dot is determined by a pair of vertical and horizontal deflection plates which use electric fields to deflect the electrons in the vertical and horizontal directions, respectively, to have the electron eventually collide with the correct point on the screen.

Now: if the oscilloscope really just restarted the moment it reached the end, then it might not have traced out an integer number of waves as it crossed the screen. This means it would start the next trace at a different point on the wave than it started the first trace, and you wouldn't see a coherent trace - just a bunch of sine waves with different phases piled on top of each other.

Accordingly, our instrument has to ensure that it starts at the same point on the wave each time. The way it does this is using what we call a trigger - it only starts a sweep when the voltage crosses some fixed (specified, by a particular knob) value. (It will also start a trace if it's been a "long time" since it last triggered - i.e., if your trigger is basically never going off.)

The oscilloscope can actually analyze two signals at the same time, input via two different channels. Later in this course, we'll use this to compare an "input signal" and a "system response" (of various sorts). In this lab, though, we'll just be comparing two separate input signals, both by putting them on the screen at the same time and using "XY mode" to make a plot of one voltage vs. the other (without time information).

Basic Oscilloscope Setup

Begin by unplugging any red or black cables from the front of all devices, before you turn anything on. (Always a good first step!)

Let's first get the oscilloscope to a good "default" position for getting some basics down:

• Press in the power button (just to the right of the screen, usually red).
• Ensure that all other buttons (the ones below the screen, the "Storage/Analog" button, and the "XY" button) are unpressed (i.e., pushed out).
• Ensure that all knobs that can be pulled out/pushed in, are pushed in.
• Set VAR SWEEP and the two red VAR knobs (on the front of the big white ones) to CAL'D (rightmost position - for the red knobs, they should "click" into place)
• Set HOLDOFF (top-right corner, second knob to the left) to the leftmost position. Set TRIG LEVEL to the center (vertical) position.
• Set COUPLING to AC and SOURCE to CH1. Set the VERT MODE switch to CH1 as well.
• Set the switch on the left-hand side to GND (ground.
• Turn TIME/DIV (the big knob on the bottom right) to an upwards-facing position (note there's a groove to indicate where it is pointing).
• Turn the left POS knob (just to the right of the red power button) until you see a line across your screen.

So, at this point you should just see a steady green line across your oscilloscope. If you can't get this to appear, double-check all your knobs (also try setting your INTENSITY knob all the way to the right), then consult your TA.

Once you have that on your screen, what you are measuring (physically) is just "zero," hence why we get a steady line: voltage isn't changing over time.

Intensity and Focus

The first knobs we will tweak are the two in the upper-right corner of your screen: INTENSITY and FOCUS.

Turn the INTENSITY knob first. As you can see, it makes the screen brighter and dimmer. Usually halfway turned (pointed up) will work here: you want it to be easy to see, but if you set it too bright then your line will be unnecessarily thick, which will increase your uncertainty (and could also damage the oscilloscope, in the long run).

Next, the FOCUS knob. You should see that turning this knob focuses and defocuses your line. You want your line as focused as possible - a narrower line is a more precise measurement!

Whenver you set up your oscilloscope, these should be the first things you check.

Setting Up a Square Wave

Turn the TIME/DIV knob up to 1ms (take note of the units there - the knob has several units to pick from!). Set the left-hand VOLTS/DIV knob to 0.2V.

Clamp an alligator clip onto the little metal clip in the bottom-center of the device (where it says CAL, along with a few numbers).

Wire a banana cable from this spot to the red port of CH1 (the left-hand wire input, which should hopefully already have an adaptor).¹²

Now, set the left-hand switch from GND to DC. You should now see a nice square wave that we can play with.

Adjusting Positions

Let's begin with the POSITION knobs. If you turn the knob in the upper-right hand corner of the device, the wave will shift left and right. If you turn the POSITION knob corresponding to channel 1 (to the right of the power button), it should move up and down.

This might sound strange: if we can freely move it up and down, how does that result in a "measurement"? We can set it to anything we want!

This is partially true, but usually for this kind of signal, we only care about the variations in voltage, or we know that they average out to zero (like a sine wave). The variations are directly measureable, so that works fine.

Moreover: if we want to measure the voltage on an absolute scale, we can measure zero by flicking the left-hand switch to GND briefly, so we could measure absolutely if we wanted to - perhaps even set GND to the middle of the screen. (In this class, though, we won't ever need to to this - we'll only ever be interested in the variations, for which we won't need to know what "zero" actually is.)

The ability to move stuff around is primarily so you can put it into a nice part of the screen to look at. (For one signal, this might seem esoteric, but when you have two signals on the screen at the same time, it can be useful.)

Adjusting Scales

The other knobs that do "interesting" (i.e., "useful to us") things here are the big gray ones: the VOLTS/DIV and TIME/DIV knobs.

The TIME/DIV knob measures the length of time that one horizontal box describes. (Note: one box, not one tick mark.)

Right now, you should observe that one period of the wave is one box. According to the knob setting we chose, one box is one millisecond. Therefore, the period of the wave is one millisecond.

Since \(f=1/T\), we can calculate the frequency. Since 1/(1ms)=1kHz, the frequency of our square wave is therefore 1kHz.

Look now at the numbers right by the little metal clip we attached the alligator clip to. One of these numbers says "1kHz" - the frequency of this square wave is 1kHz. So it matches what we expect!

Turn the knob by a click or two downwards. Check real quick: does the result still make sense on this new setting?

(Calculate the frequency and see if it is still the expected 1kHz. This isn't to hand in, just to get settled with the idea of the measurement.)

Now, look at the vertical setting: VOLTS/DIV. This is the same idea on a different axis. As our first measurement, we'll check whether the amplitude of the square wave is what we expect.

Part I: Square Wave Amplitude

Adjust the square wave with the POS settings and the VOLTS/DIV setting until your screen is almost entirely filled with a few periods of the square wave. Record the VOLTS/DIV and TIME/DIV on your data sheet for later reference.

On the paper provided, sketch a copy of what you see on the oscilloscope screen.³

Now: count the number of boxes vertically from the bottom of the grid on the screen to the bottom of the square wave, and record this on your data sheet as your "low reading." (Count the big boxes, not the little tick marks.) Round to the nearest half-tick-mark. Estimate your uncertainty in this reading based on how precise you think your measurement is (generally at least 0.5 tick marks).

Repeat this measurement, except this time counting from the bottom of the grid to the top of the square wave, and record this as your high reading.

Using your VOLTS/DIV, convert these to the physical upper and lower voltages for the square wave. The difference between these will be the "peak-to-peak" amplitude of the square wave.¹

We will compare this amplitude to the expected amplitude recorded by the little metal clip on the oscilloscope. Record this expected amplitude on your data sheet.

Part II: Sine Wave Frequency

Refer to the Reference Guide for Function Generators for this part. You will need to identify what sort of function generator you have in order to know how to use it correctly.

Turn on your function generator and wire it to CH 1 (red to red and black to black).⁴

Set your function generator to output a sine wave at a frequency of approximately 3kHz.⁵

If you tweak your position and scale knobs as necessary, you should now be observing a sine wave.

Adjust this sine wave until it takes up most of the screen vertically and you have ~5 periods of the wave on screen. Record the VOLTS/DIV and TIME/DIV on your data sheet for later reference.

Sketch the sine wave you see on the paper provided as you did for the first measurement.⁶

We'll now measure the time it takes to complete the periods you have on screen. Choose some point on the first oscillation you see to measure from (say, the top of the peak). Count the number of waves between that point and the corresponding point on the last wave on your screen. Record this as the number of waves. (Be careful not to get an off-by-one error!)

Now, record the number of boxes from the left edge of the grid on the screen to the point where you started counting waves as your start reading. Similarly, record the number of boxes from the left edge of the grid to the point where you stopped counting waves as your end reading. Note unlike before, we're counting horizontal boxes this time, not vertical boxes.

Understanding Triggering

Begin set up with the sine wave (per the previous part). Then, turn the horizontal position knob to the right - we want to see where our wave begins (i.e., what voltage the oscilloscope reads when it starts its trace).

Now, adjust your TRIG LEVEL knob up and down a little bit. What happens to the starting point on the wave? What happens when you turn the trigger level up too high (or down to low), above the top (or below the bottom) of the wave?

Now, set it back to a "reasonable" level, and try "pulling out" that knob. What happens to the starting point now?

Finally, what happens if you try a triangle or square wave (and vary the TRIG LEVEL knob, etc.)?

Analyzing Two Signals

Plug one of your function generators into CH1 and one into CH2 (not the rightmost port, the one to the left of that). Set your CH2 settings to the same as CH1 (DC on the lever, same VOLTS/DIV, etc.). Set the VERT MODE switch to DUAL.

Have both your function generators set to similar frequency sine waves (but not exactly the same). Now, look at your screen: you should see two sine waves. (If you don't see two signals but did set VERT MODE to DUAL, try adjusting your vertical POS knobs. One of them should be moving.

Look at both; by adjusting the vertical POS knobs, see which is the CH1 input and which is the CH2 input. (Which one moves when you turn each POS knob?) Which one is "stable" and which one is "moving"? What if you change the SOURCE from CH1 to CH2?

Finally, vary each VOLTS/DIV knob. What does each knob do to each signal? What about TIME/DIV and horizontal position? (Which knobs alter both curves, and which knobs alter them separately?)

Lissajous Figures

Now for one last feature of the oscilloscope (which we won't be using again in this class, but is still pretty neat): press in the X-Y button.

This plots the two voltages against each other (time is no longer an axis) - the dot now has its (x,y) position determined by the (CH1,CH2) voltages.

What happens when the are similar - what curve appears (and does it change)? What if you set one to a constant multiple of the other? What if they're in, say, a 3:2 ratio?

Understanding this is mostly just the math of parametric curves, but it's still pretty to see.

Take note of the shapes you see (draw on oscilloscope sketch paper, take pictures, whichever), along with what frequencies made that shape.

Understanding The Rest (Optional; No Procedure)

Finally, please turn off all the electronic equipment before you leave the lab. Do this for all labs in this course.

Oscilloscope Sketches

In this lab, you will make two oscilloscope sketches. Each of them should have the following:

• A title for the plot.
• Labelled axes, with units: "Voltage (V)" for the y-axis and "Time (s)" for the x-axis (with the units changed if you use mV, ms, or μs instead of V and/or s - choose appropriately for your Volts/Div and Time/Div settings).
• Numbered axes: choose an (arbitrary) origin for your plot, and put numbers on your axes, where the numbers correspond to physical quantities. That means you should use your Volts/Div setting to determine the y values and the Time/Div setting to determine the x values.
• A sketch of the curve that is visible on your screen (of course), drawn to the best of your ability.

You should ignore the little 0/10/90/100 numbers on the left side of the screen: none of those are relevant.

On the Data Sheet

You should show the following calculations, with error propagation for each:

• Part I:
  • Convert your vertical "box" measurements into physical voltages.
  • Take the difference of your physical voltages to measure the "peak-to-peak" amplitude of the square wave.
• Part II:
  • Convert your horizontal "box" measurements into physical times.
  • Take the difference of these times to calculate the total time for multiple waves.
  • Divide by the number of waves that occur in that time to get the period.
  • Take one over the period to get the frequency.

Based on the data you extract in this part, answer the questions in the data table about the compatibility of your results with expectation.

Your TA will ask you to discuss some of the following points (they will tell you which ones):

• Functions of the Oscilloscope: Describe, in your own words, what the following components of the oscilloscope do and how to use them:
  • Screen controls (INTENSITY, FOCUS)
  • Plot visual controls (POS, VOLTS/DIV & TIME/DIV)
  • Triggering (basic idea of what it does, TRIG LEVEL, SOURCE)
  • Two inputs (CH1 vs. CH2 controls [what they share, what differs], VERT MODE, XY)
• Analyzing Lissajous Figures: Answer these questions about the last part assuming the function generators are always outputting sine waves.
  • Same Frequency, special cases: What do you expect to see if the two function generators are at exactly the same frequency and in-phase? What if they are out of phase (by 180 degrees)? What if they are 90 degrees out of phase?
  • Same Frequency, general case: In general, what do you expect to see if the two function generators are at exactly the same frequency with arbitrary phase?
  • Perfect n:m ratio: Suppose the two frequencies were exactly in an integer ratio (2:1, so one is twice the other; 3:2, so one is 3/2 of the other; etc.). What do you expect to see (as a static image) in this case? (Again, you may consider phase shift as well.)
  • Frequency Difference: Now suppose they are at almost the same frequency, but slightly different. What do you expect to see here? (Hint: note that \(\sin(\omega_2 t)=\sin(\omega_1 t+(\omega_2-\omega_1)t)\); hence, if your two frequencies are similar, the second input looks kind of like the first with a slowly-varying phase shift.) Does this align with what you actually saw?
• Triggering for Other Purposes: One important use of an oscilloscope is as a sort of particle detector for phenomena like radioactive decay. A radioactive decay response generally looks flat, except that at random times there's a "bump" (of some more-or-less-fixed shape) from a particle detection from time to time.
  • Triggering Usefulness: Unlike our inputs in this experiment, which are periodic, radioactive decay occurs at random times. If we didn't use triggering in any way, we would see a mess on our oscilloscope screen. How can triggering be used to "organize" the radioactive decays into a single more-or-less stable waveform?
  • Limitations: There's a key limitation to our oscilloscope in such a circumstance, based on the fact that our trigger starts the scan. What is this limitation, and what does it prevent us from doing? (Hint: consider a modern, digital oscilloscope for contrast. Such an oscilloscope stores data for a short time, so can see "before" the trigger goes off. Our scope cannot do that. What does that mean if the "recognizable" part of the bump, for a trigger, occurs at the end of the event?)⁵

Guide to Uncertainty Propagation & Error Analysis (Quick Reference)

Notes on the Oscilloscope

Notes on the Function Generators

Spare Oscilloscope Sketch Paper