Physics 241 Lab: Oscilloscope Name:____________________________ Section 1: 1.1. The following picture shows the energy bands for a generic semiconductor, which must be calculated using quantum mechanics.

If the temperature is low so that each electron in the valence band of the semiconductor has an average kinetic energy much less than the band gap energy, explain whether the semiconductor acts as a conductor or insulator. Your explanation:

Imagine that an external voltage source is applied across the semiconductor so that each valence electron has more kinetic energy. Approximately what must the applied external voltage be in order for the semiconductor to transition from an insulator to a conductor? (Hint: energy equals charge times electric potential.) Your answer and explanation:

Diodes are layered semiconductors and in a simple circuit act as one-way components. Light emitting diodes (LEDs) have a myriad of practical uses. The photons emitted by an LED each have energy roughly equal to the band gap energy of the semiconductor. Laser diodes are conceptually similar to LEDs and have led directly to the “digitized age of music”. More and more electrical engineering programs requiring their majors to gain a firm understanding of quantum mechanics. (Not a question.)

Section 2: 2.1. Before actually using the oscilloscope, you need to be able to understand and predict what will appear on the oscilloscope screen. For the next few pages you will be asked predict what would appear on the oscilloscope screen, then later you will use the oscilloscope to make measurements. Feel free to experiment with your oscilloscope as you work through the prediction-making activities of this section. An oscilloscope is a device that measures voltage differences over time. It can be used to study rapidly oscillating voltages. For example, the voltage supplied by a wall outlet oscillates at the incredibly slow rate of 60 Hz. However, the oscilloscope can easily measure an oscillation of 1MHz or more. Most DMMs indicate that they can measure an oscillating voltage. However, a DMM can only make average measurements of sinusoidal 60 Hz voltages. In other words, a DMM is only useful for alternating current measurements (AC) on household circuits, not radios or other electronics. What is the period T of one oscillation for a linear frequency f = 5 MHz sinusoidal oscillating voltage? What is the angular frequency? Remember: T=1/f and ω=2πf. Your work and answers:

2.2. The simplest way to use an oscilloscope is as a DMM measuring a constant voltage. Imagine you have a 1.5 Volt battery and you measure the voltage every second for 5 seconds. Make an imaginary data table. Then use the data table to make a graph of what you would see on the oscilloscope screen. Your oscilloscope allows you to control the size of the tick marks on its screen. FOR THIS PROBLEM ONLY you are provided a choice of axis settings and selection of origin. For all other problems, you will need to select the appropriate axis settings yourself. Connect your data points on your graph to demonstrate what the oscilloscope would really show. Fill out the data table and make your graph directly in the oscilloscope screen below.

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2.3. Now imagine you have a 6 Volt sinusoidal power supply with a frequency of 60 Hz. What is VMAX and VMIN for this voltage? _____________ and ___________ . What is the period of one oscillation? _________________ Mathematically, this voltage is described as V (t) = 6sin(2" # 60 # t) where 2" # 60 is often referred to as the angular frequency, ω. Use this formula and a calculator to complete the given data table and make a graph on the oscilloscope. Be sure to label your axes and choose your units per ! all your data fits on the screen. division on the time axis wisely so that

2.4. Now imagine you have two sinusoidal voltage signals. Both have a frequency of 60 Hz, but V1 has an amplitude of 6 Volts while V2 has an amplitude of 12 Volts. Furthermore, V2 lags behind V1 out of phase by 90o. Without making a data table, sketch what would appear on the oscilloscope. Feel free to use a graphing calculator with the functions % "( V1 (t) = 6sin(2" # 60 # t) and V2 (t) = 12sin' 2" # 60 # t $ * . & 2) Be sure to label your axes and choose appropriate time and voltage units per division for your graph. !

2.5. Finally, let’s imagine taking the two alternating voltage sources from the previous problem, but now graph V1(t) on the x-axis and V2(t) on the y-axis. In oscilloscope terminology, this is called an XY plot. Thus we are graphing V2 vs. V1. Note: this is a voltage vs. voltage graph NOT a voltage vs. time graph. Make a data table using some points of common time provided below and the formulas from the previous sections. Use this table to graph V2 vs. V1. Be sure to label your axes and choose appropriate voltage units per division for your graph.

Section 3: 3.1. Use the oscilloscope to examine the voltage vs. time graphs of many different sine waves, square waves and saw tooth waves created by the function generator (oscillating voltage supply). Be sure to experiment with all sorts of frequencies, voltage amplitudes and DC offsets. Practice making the voltage functions fit nicely on the oscilloscope screen. Take the time to twiddle every knob and switch. Once you feel comfortable with your understanding of each operational control of the oscilloscope and function generator, write a short statement explaining what each control does. Describe the operation of the oscilloscope by writing a short description about the function of each knob, switch and button on the oscilloscope and function generator:

Section 4: 4.1. Use the function generator to create a 5-volt sine wave with 1,000 Hz frequency. Use the oscilloscope (as shown in the picture below) to set the function generator amplitude correctly at 5.0 Volts.

Use this sinusoidal voltage to power a 1,000 Ω resistor. Use the oscilloscope to measure the voltage drop across the resistor (set up as shown in the picture below). What should the voltage drop across the resistor be according to conservation of energy? Be sure your measurement indicates this. Your answer and explanation:

Now switch to a 10 Ω resistor and examine the voltage drop across it. Theoretically, this smaller resistor should still have the same 5 Volt difference (amplitude) as the 1,000 Ω resistor. However, you should notice the voltage amplitude decrease. This is a result of the function generator output changing. The smaller resistor will allow a greater current to flow through the circuit, but the function generator has a maximum current that it is able to produce. Therefore, once the resistance becomes low, the function generator cannot output the full 5 volts. Should you measure the amplitude of the source voltage coming from the function generator before or after you have hooked up the function generator to your circuit? Your answer and explanation:

Vamplitude in with the 10 Ω resistor to find the maximum current amplitude R Iamplitude,max that the function generator is able to produce. Your work and answer:

Use the equation Iamplitude =

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Section 5: 5.1. You may use the oscilloscope to measure two circuit components separately. Set up the function generator to output a 200 Hz square wave with 3 Volt amplitude through a 100 Ω and a 200 Ω resistor in series. Use the oscilloscope to measure the voltage across each resistor simultaneously on both channels by setting up a “bottom ground” (set up as shown in the figure). The voltage between red 1 and ground will tell you the potential difference across both resistors while the voltage between red 2 and ground will tell you the voltage across the 200 Ω resistor. What must you do mathematically to find the voltage across the 100 Ω resistor? Are the two oscillating voltages across the resistors in phase with each other? Determine the amplitudes of the voltage differences across each resistor and explain why this makes sense. Your answers and explanation:

Now use the oscilloscope to measure the voltage across each resistor simultaneously on both channels by setting up a “middle ground” (set up as shown in the figure). Note that the middle ground measurement requires that the function generator NOT be grounded (use a 3-to-2 prong plug adapter). The voltage between red 1 and ground will tell you the potential difference across the 100 Ω resistor while the voltage between red 2 and ground will tell you the inverted voltage across the 200 Ω resistor. Are the two oscillating voltages across the resistors in phase with each other? Determine the amplitudes of the voltage differences across each resistor and explain why this makes sense. Your answers and explanation:

5.2. Using the same set up as in the last problem, measure the changing voltage across both resistors in “X-Y” mode. You should see an “ellipse edge on” i.e. a diagonal line. In section 2.5, you found an elliptical x-y graph because the voltages being plotted were out of phase. However, in today’s lab we don’t have any components that cause phase shifts (i.e. capacitors or inductors). Since both voltages are oscillating temporally in phase they will both reach zero simultaneously. Thus they will trace a diagonal line that some experimentalists simply consider an ellipse viewed “on-edge”. How does the height and width of the “ellipse” in your x-y measurement relate to the voltage amplitudes across each resistor? Be sure to compare “apples to apples” by not confusing the volts-per-div in the y-direction with a different volts-per-div in the x-direction. Your answer:

Section 6: 6.1. A diode is a one-way circuit component. If a potential difference is applied the wrong way across a diode, it will act as an infinite resistance and not conduct electricity. If a voltage is applied correctly across a diode and above a minimum value, the diode will act with zero resistance and allow the current to flow through it. This strange behavior is entirely quantum mechanical and non-Ohmic. Create the powered diode circuit with a light emitting diode (LED) in series with a resistor. On many diode boards, the diode is already soldered in series with a 330 Ω resistor. Do not forget the resistor as it protects the diode! Then set up your oscilloscope in the “bottom ground” set up to measure the voltage across the resistor on the y-axis and the applied voltage on the x-axis (see figure below).

6.2. Experimentally determine if the diode is Ohmic by constructing it’s current versus applied voltage graph (see figure below). Note that you cannot directly measure the current through the LED with the oscilloscope. Therefore, answer the following questions first in order to learn how to construct the ILED vs. Vapplied graph.

In this circuit, how is the current through the LED related to the current through the resistor? Your explanation: Which component of your circuit is known to be Ohmic? Your answer: While the circuit is in operation, if you know the voltage across the resistor and its resistance, what can you find? Your answer: 6.3. Your answers to the previous questions should help you understand that you need to measure the voltage across the resistor in order to find the current through the resistor. Therefore, you need to create the VR vs Vapplied graph and turn it into the ILED vs. Vapplied graph simply by dividing the y-values by the resistors resistance:

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Make measurements to obtain the first graph and use it to calculate and create the second graph. Finally, your measurements allow you to experimentally obtain the quantum mechanical property of the material: the band gap energy Egap. Find the energy of the diode band gap energy using E band gap = q " Vturn on . Select the value of q as that of the charge carrying particles in the circuit. Note that since you must use a middle ground measurement with the oscilloscope, one of the signals will always be inverted on your oscilloscope screen. Fix your sign of one column of your data to “uninvert” this graph. (Make graphs). Your measured Egap:

Report Guidelines: Write a separate section using the labels and instructions provided below. You may add diagrams and equations by hand to your final printout. However, images, text or equations plagiarized from the internet are not allowed! • Title – A catchy title worth zero points so make it fun. • Goals – Write a 3-4 sentence paragraph stating the experimental goals of the lab (the big picture). Do NOT state the learning goals (keep it scientific). [~1-point] • Concepts & Equations – [~5-points] Be sure to write a separate paragraph to explain each of the following concepts. o How does an oscilloscope work? • How/why do you measure time dependent voltage? • How/why do you measure two time dependent voltages? • How/why do you measure two voltages in an XY plot? • How do you use VOLTS/DIV and SECONDS/DIV to get numerical data from the oscilloscope screen? • How do you use all the other various knobs and levers on the oscilloscope? o What does a diode (or a light emitting diode) do in a circuit? Explain what we mean when we say that a diode is a one-way component. • Discuss the concept of time dependent voltages and how to measure them. • Discuss the theory and measurement of diodes. • Procedure & Results – Write a 2-4 sentence paragraph for each section of the lab describing what you did and what you found. Save any interpretation of your results for the conclusion. [~4-points] • Conclusion – Write at least three paragraphs where you analyze and interpret the results you observed or measured based upon your previous discussion of concepts and equations. It is all right to sound repetitive since it is important to get your scientific points across to your reader. Do NOT write personal statements or feeling about the learning process (keep it scientific). [~5-points] • Graphs – All graphs must be neatly hand-drawn during class, fill an entire sheet of graph paper, include a title, labeled axes, units on the axes, and the calculated line of best fit if applicable. [~5-points] o The two graphs from section 6.3. • Worksheet – thoroughly completed in class and signed by your TA. [~5-points.]