Exp. #2-6 : Measurement of the Characteristics of,, and Circuits by Using an Oscilloscope

Transcription

1 PAGE 1/14 Exp. #2-6 : Measurement of the Characteristics of,, and Circuits by Using an Oscilloscope Student ID Major Name Team No. Experiment Lecturer Student's Mentioned Items Experiment Class Date Submission Time Submission Place Introductory Physics Office Report Box # Students should write down Student s Mentioned Items at the cover page of Experiment Reports, and then complete Experiment Reports by adding contents to the attached papers (if needed) in terms of the following sections. Contents of the reports should be written by hand, not by a word processor. Instead, it is allowed that figures and tables are copied and attached to papers. Completed Experiment Reports should be submitted to the place due to the time specified by Experiment Lecturers. The Experiment Report score per each Experiment Class is evaluated by max. 50 points (basically 15 points). Solutions of Problems in Experiment Reports are not announced to the public according to the General Physics Laboratory - Administration Rule. If a student permits other students to pirate one s Experiment Reports or a student pirates Experiment Reports of other students regardless of permission of original creators, the corresponding Experiment Report score and Active Participation score will be zero in case of exposure of such situation. Unless Experiment Reports are submitted to the place due to the time specified by Experiment Lecturers, the corresponding Experiment Report score will be zero. If the submission rate of Experiment Reports is less than or equal to two thirds, the grade of General Physics Laboratory will be F level. In order to decide grades of General Physics Laboratory at the end of current semester, the detailed scores of General Physics Laboratory will be announced at Introductory Physics Office homepage. Based on the announcement, students can raise opposition of score error. Since the public evidence is needed for the confirmation of opposition, students should keep one s Experiment Reports completed evaluation by Experiment Lecturers until the Experiment Report score decision If a student is absent from the Experiment Class because of proper causes, the corresponding student should submit documents related to absence causes to Introductory Physics Office regardless of cause occurrence time until the grade decision of General Physics Laboratory. If a student moves the Experiment Class arbitrarily without permission of Introductory Physics Office, it is noted that the total Experiment Scores will be zero. Lecturer's Mentioned Items Submission Time/Place Check Experiment Report Points Evaluation Completion Sign 50

2 PAGE 2/14 1. Objective Student ID Name The peak-to-peak voltage and the frequency of alternative signals generated by the function generator are measured by using an oscilloscope and the usage of the oscilloscope is understood through this procedure. The characteristics of various circuits composed of a resistor (), a capacitor (), and an inductor () are measured by using an oscilloscope. 2. Theory (1) Oscilloscope and function generator 1) Oscilloscope the clockwise direction completely, CAL (calibration) mode is set and the time is the same value as that indicated by TIME/DIV. When VAR is rotated in the counterclockwise direction, the time is at max. 2.5 times longer than that indicated by TIME/DIV. 5 TRIGGER : If a specific voltage condition set by the trigger is satisfied, a stationary signal can be shown on the screen. TRIGGER LEVEL / TRIGGER SLOPE : It is used to control the level of TRIGGER voltage. It is possible to Invert the polarity of the TRIGGER LEVEL by pushing in or pulling out the TRIGGER LEVEL knob. The function of TRIGGER SLOPE is provided in some models. TRIGGER MODE : It is used to select the trigger mode such as AUTO or NORM. TRIGGER SOURCE : It is used to select the trigger source such as INT or EXT. The oscilloscope is a basic experimental instrument used in the laboratory for various fields. Signals can be shown on the fluorescent screen of the oscilloscope similar to the cathode ray tube in a television by sweeping the electron beam. The values of X-axis and Y-axis in the oscilloscope are voltages actually, but the values of X-axis corresponds to the time in most cases. The sweep oscillator loaded inside the oscilloscope sweeps the electron beam along the X-axis at a constant rate. Buttons and knobs in an oscilloscope can have different names, but most of them have the same function among various oscilloscope models. In some models with 2 channels, each signal selected can be shown or two signals can be shown simultaneously. 6 VOLT/DIV : It is used to set the voltage scale in one vertical division. The function of VAR for VOLT/DIV is similar to that of TIME/DIV. 7 AC, GND, DC : It is used to select the coupling mode for the vertical signal amplifier. AC : The vertical signal amplifier is coupled through a condenser so that alterative signals can pass while direct signals are blocked. GND : The vertical signal amplifier is coupled with the ground. DC : The vertical signal amplifier is directly coupled so that all the signals including the alternative and direct signals can pass. 1 INTENSITY : It is used to control the intensity of the screen. 2) Function generator 2 FOCUS : It is used to control the focus of the electron beam. 3 TRACE ROTATION : It is used to rotate the trace in the screen which can be biased by geomagnetism, etc. 4 TIME/DIV : It is used to set the time scale in one horizontal division. In addition, there is the fine adjust knob of TIME/DIV, called VAR. When VAR is rotated in Various signals with the following waveform, frequency, and amplitude can be generated by using the function generator. Waveform : Sine wave, square wave, triangular (sawtooth) wave Frequency : a few Hz ~ about MHz Amplitude : 0 ~ a few V Signals can be added by DC offset.

3 PAGE 3/14 (2) Characteristics of the circuit A battery with the electromotive force, a resistor (), and a capacitor () are connected in series as shown in Fig. 1. Fig. 1. circuit. 1) If the switch is connected to position A at, the electric current starts to flow through and the electric charges are stored in. As the more electric charges are stored in, the increase of potential difference across prevents the flow of the electric current so that the electric current no longer flows after a sufficiently long time. For the quantitative understanding, the sum of potential difference over the circuit gives the following equation. (Eq. 1) Here, is the electric charges stored in and is the electric current flowing through. By solving the above equation with the initial condition at, the following result can be obtained. (3) Characteristics of the circuit A battery with the electromotive force, a resistor (), and an inductor () are connected in series as shown in Fig. 2. (Eq. 2) Here, is called the capacitive time constant of the circuit. It represents the changing rate of the electric charge and current depending on the time. Using and, the potential difference across and can be found respectively. 2) If the switch is connected to position B when is sufficiently charged, the electric charges stored in start to discharge through. As the discharging progresses, the electric charges stored in vanish and the electric current no longer flows. For the quantitative understanding, the sum of the potential difference over the circuit gives the following equation. (Eq. 3) By solving the above equation with the initial condition at, the following result can be obtained. Fig. 2. circuit. 1) If the switch is connected to position A at, the electric current starts to flow through. prevents the flow of the electric current according to Faraday's law of induction, but the electric current approaches to the value without the effect of. For the quantitative understanding, the sum of potential difference over the circuit gives the following equation. (Eq. 5) (Eq. 4) By solving the above equation with the initial condition at, the Using be found respectively. and, the potential difference across and can following result can be obtained. (Eq. 6)

4 PAGE 4/14 Here, is called the inductive time constant of the circuit. It (4) Characteristics of the circuit represents the changing rate of the electric current depending on the time. Using and, the potential difference across and can be found respectively. An alternative voltage source with the angular frequency and the amplitude, a capacitor (), an inductor (), and a resistor () are connected in series as shown in Fig. 3. 2) If the switch is connected to position B when the electric current has a constant value, the battery can no longer provide the electromotive force. prevents the rapid change of the electric current, but eventually the electric current vanishes. For the quantitative understanding, the sum of the potential difference over the circuit gives the following equation. (Eq. 7) By solving the above equation with the initial condition at, the following result can be obtained. (Eq. 8) Using and, the potential difference across and can be found respectively. Answer the following questions. 1. Derive (Eq. 8) by solving the differential equation (Eq. 7), and then find. Fig. 3. circuit. The values of the reactance of and depend on the angular frequency of the alternative voltage source, and the electric currents flowing through and have a phase difference of and with respect to the voltage, respectively. Therefore, the impedance in the circuit connecting,, and in series is given by (Eq. 9) In the above equation, has the minimum value and the current amplitude has the maximum value when. is called the resonance frequency, and the phenomena that the current amplitude has the maximum value at this frequency is called the resonance. In the resonance phenomena, it is worth investigating the change of the current amplitude depending on the frequency. The current amplitude at the resonance frequency is and the difference of two frequencies where the current amplitude has half maximum is, which is called the resonance width. As becomes smaller, the maximum value of the current amplitude becomes larger while the resonance width becomes narrower. Answer the following questions. 2. In case of sin, find and respectively, and then consider the meaning of the condition for.

5 PAGE 5/14 3. Experimental Instruments Items Quantity Usage Clean up method Oscilloscope 1 ea. It is used to measure alternative signals. Function generator 1 ea. It is used to generate alternative signals. It should be placed at the center of the experiment table. It should be placed at the center of the experiment table. characteristics measurement instrument Oscilloscope -to-wall power connection cable Function generator -to-wall power connection cable BNC cable 1 ea. It is used to constitute,, and circuits. 1 ea. It is used to connect the oscilloscope to the wall power. 1 ea. It is used to connect the function generator to the wall power. They are used to complete the connection among 5 ea. characteristics measurement instrument, the oscilloscope and the function generator. It should be placed inside the basket of the experiment table. It should be placed inside the basket of the experiment table. It should be placed inside the basket of the experiment table. They should be placed inside the basket of the experiment table. T connectors 2 ea. They are used to connect BNC cables. They should be placed inside the basket of the experiment table. Terminator for ground 1 ea. It is used to provide the ground to characteristics measurement instrument. It should be placed inside the basket of the experiment table.

6 PAGE 6/14 4. Experimental Procedures (1) Understanding of the usage of the oscilloscope 1) Measurement of the peak-to-peak voltage and the frequency of the sine wave 1 Generate a sine wave with the proper amplitude and the frequency of khz by using the function generator. 2 Connect the signal generated by the function generator to the channel 1 of the oscilloscope. 3 Control the TIME/DIV and VOLT/DIV of the oscilloscope to observe the signal on the screen of the oscilloscope. 4 Draw the signal shown on the screen of the oscilloscope and measure the peak-to-peak voltage and the frequency of the sine wave. 3) Constitute the circuit as the following diagram. Connect the voltage across the capacitor to the channel 1 of the oscilloscope. Draw the signal shown on the screen of the oscilloscope and write down the formula describing the observed signal. 2) Measurement of the peak-to-peak voltage and the frequency of the square wave 1 Generate a square wave with the proper amplitude and the frequency of k H z by using the function generator. 2 Connect the signal generated by the function generator to the channel 1 of the oscilloscope. 3 Control the TIME/DIV and VOLT/DIV of the oscilloscope to observe the signal on the screen of the oscilloscope. 4 Draw the signal shown on the screen of the oscilloscope and measure the peak-to-peak voltage and the frequency of the square wave. (2) Measurement of the characteristics of the circuit 4) Measure the capacitive time constant of circuit from the voltage across the capacitor during charging and discharging processes respectively and compare it to the theoretical value. 1) Set the resistor and the capacitor to k Ω and nf, respectively. Generate a square wave with the proper amplitude and the frequency of khz by using the function generator. Connect the signal generated by the function generator to the channel 2 of the oscilloscope. 2) Constitute the circuit as the following diagram. Connect the voltage across the resistor to the channel 1 of the oscilloscope. Draw the signal shown on the screen of the oscilloscope and write down the formula describing the observed signal.

7 PAGE 7/14 4) Measure the inductive time constant of circuit from the voltage across (3) Measurement of the characteristics of the circuit the resistor during increasing and decreasing processes of the voltage respectively and compare it to the theoretical value. 1) Set the resistor and the inductor to k Ω and mh, respectively. Generate a square wave with the proper amplitude and the frequency of khz by using the function generator. Connect the signal generated by the function generator to the channel 2 of the oscilloscope. 2) Constitute the circuit as the following diagram. Connect the voltage across the resistor to the channel 1 of the oscilloscope. Draw the signal shown on the screen of the oscilloscope and write down the formula describing the observed signal. (4) Measurement of the characteristics of the circuit 1) Set the inductor and the capacitor to mh and nf, respectively. Generate a sine wave with the proper amplitude and the frequency by using 3) Constitute the circuit as the following diagram. Connect the voltage across the inductor to the channel 1 of the oscilloscope. Draw the signal shown on the screen of the oscilloscope and write down the formula describing the observed signal. a function generator. Connect the signal generated by the function generator to the channel 2 of the oscilloscope. 2) Constitute the circuit as the following diagram. Connect the voltage across the resistor to the channel 1 of the oscilloscope.

8 PAGE 8/14 3) Control the frequency of the signal generated by the function generator and measure the current amplitude at various frequencies. Determine the resonance frequency and the resonance width. 4) After changing the resistance of the resistor, repeat the experimental procedures and investigate the relation between the resistance and the resonance width. 5) If all the measurements are finished, turn off the function generator and the oscilloscope. Finally, clean up the experiment instrument according to the suggested method.

9 PAGE 9/14 5. Experimental Values (1) Understanding of the usage of the oscilloscope Sketch the signals shown on the screen of the oscilloscope and calculate the peak-to-peak voltage and frequency measured by the oscilloscope. Waveform and frequency of the signal generated by the function generator Voltage (V) Sine wave, khz Voltage (V) Square wave, khz Signal shown on the screen of the oscilloscope Peak-to-peak voltage measured by the oscilloscope DIV V/DIV = V DIV V/DIV = V Frequency measured by the oscilloscope ( DIV s/div ) -1 = Hz ( DIV s/div ) -1 = Hz

10 PAGE 10/14 (2) Measurement of the characteristics of the circuit Resistance of the resistor Capacitance of the capacitor Waveform and frequency of the signal generated by the function generator kω nf Square wave, khz Sketch the signals shown on the screen of the oscilloscope and write down the formulas describing the observed signals. Measurement Time vs. Time vs. Voltage (V) Voltage (V) Signal shown on the screen of the oscilloscope decreasing : charging : Formula increasing : discharging : Capacitive time constant Theoretical value (s) Experimental value (s) charging discharging Average Error (%)

11 PAGE 11/14 (3) Measurement of the characteristics of the circuit Resistance of the resistor Inductance of the inductor Waveform and frequency of the signal generated by the function generator kω mh Square wave, khz Sketch the signals shown on the screen of the oscilloscope and write down the formulas describing the observed signals. Measurement Time vs. Time vs. Voltage (V) Voltage (V) Signal shown on the screen of the oscilloscope increasing : decreasing : Formula decreasing : increasing : Inductive time constant Theoretical value (s) Experimental value (s) increasing decreasing Average Error (%)

12 PAGE 12/14 (4) Measurement of the characteristics of the circuit Inductance of the inductor Capacitance of the capacitor mh nf Theoretical value of the resonance frequency Th (khz) Waveform of the signal generated by the function generator Sine wave Frequency of Resistance of the resistor (Ω) Peak-to-peak voltage across the resistor the signal generated by the function generator (khz) log Exp Resonance width (khz) Quality factor Exp 2 DIV 4 DIV 8 DIV Exp 4 DIV 2 DIV 2 DIV 4 DIV 8 DIV Exp 4 DIV 2 DIV Exp : Experimental value of the resonance frequency.

13 PAGE 13/14 6. Results and Discussions (This page should be used as the first page of the corresponding section. If the contents exceed this page, additional contents should be written by attaching papers. Contents should be written by hand, and not by a word processor. Attaching copied figures and tables to the report is allowed.) Write down contents in terms of the following key points. 1. Regarding the error of the time constant in circuit as the error of resistance or capacitance, calculate the actual resistance or capacitance. 2. Regarding the error of the time constant in circuit as the error of resistance, calculate the actual resistance. (Use the difference between the maximum of and.) 3. (1) By using the error of the resonance frequency in circuit, calculate the actual inductance or capacitance. (2) By using the error of the resonance width obtained from the comparison between Ω and kω experiments, calculate the actual resistance. In addition, compare it to the error analysis result of and circuits 4. Explain the meaning of the time constant in and circuits. (Relate it with the reason why the khz square wave is used in and circuits.) 5. Comparing the signal shown on the screen of the oscilloscope to,, and obtained from the differential equation, explain the tendency of the value changes from the time to when the sufficiently long time passes.

14 PAGE 14/14 7. Solution of Problems (This page should be used as the first page of the corresponding section. If the contents exceed this page, additional contents should be written by attaching papers. Contents should be written by hand, and not by a word processor. Attaching copied figures and tables to the report is allowed.) 8. Reference