Shifting Amperage and the Oscillograph - Research Paper Example

Running head: Alternating current (AC) and Cathode Ray Oscilloscope (CRO) Student’s name Institution Course Professor Date of Experiment Date of Submission Abstract This report describes the experimental procedure that helped the students familiarize with; the use of a function generator to produce sinusoidal waveforms of various frequencies and amplitudes, the use of an oscilloscope to measure the period or frequency and amplitude of sinusoidal waveforms and also the use of digital multimeter for measuring A.C voltage. The equipments used in the experiment included; oscilloscope (CRO), function generator and the digital Multimeter (DMM). In the experiment, the Function Generator was set up to produce a sine wave of frequency approximately 1 KHz whereas the amplitude control was set to its mid position. With the measured results, graphs of the frequency response of the DMM and the CRO were plotted which enabled comparison between calculated and measured period of oscillation were made and also the DMM reading and the amplitude of the oscillation. Table of Contents Abstract 2 1.0Introduction 4 1.1Theory 4 2.0Materials and methods 6 2.1Procedures 7 3.0Calculation and results 8 3.1Table A 8 3.2Table B 8 4.0Discussion and analysis 11 5.0Conclusion 11 6.0References 13 1.0Introduction This laboratory report described the experimental procedure that helped the students to compare the calculated and measured period of oscillation and also compare the DMM reading and the amplitude of the oscillation. The objectives of the experiment were to the students to familiarize with the following: 1) The use of a Function Generator to produce sinusoidal waveforms of various frequencies and amplitudes 2) The use of an oscilloscope to measure the period or frequency and amplitude of sinusoidal waveforms 3) The use of Digital Multimeter to measure alternative current (A.C) voltage 1.1Theory Cathode ray oscilloscope (CRO) is versatile measuring equipment that displays real-time plots of voltage against time or voltage versus voltage. Cathode ray tube (CRT) is the main component and has a cathode, grid, anode and fluorescent screen at the end of glass envelope. Inside the CRT, along the part of electron beam between the anode and the screen lie two pairs of deflecting plates. One pair deflects the beam horizontally and the other vertically. It uses cathode rays to display waveforms on the fluorescent screen. There are three distinct sets of controls in an oscilloscope. One set controls the electron gun and adjust the trace focus and intensity. The other controls the internally or externally applied voltage to the horizontal plates and adjusts the electron beams horizontal sweep speed. The third set controls the externally applied voltage to the vertical deflection plates and adjust the vertical trace amplitude When a voltage is applied across the horizontal plates, the electron beam will experience a horizontal force and is either deflected to the left or right depending on the polarity of the deflection voltage. When AV voltage is applied, the beam will be deflected horizontally back and forth. Moreover, if the frequency of the AC voltage signal is high, then the spot will trace a continuous horizontal line across the screen. Indeed, the magnitude of the deflection of the spot from the center of the screen depends on the magnitude of the voltage applied to the deflection plates. The X-plates and Y-plates produce horizontal and vertical deflection respectively. The X-plates are connected to the time-base circuit. The simultaneous application of input voltage at Y-plates and time base voltage can cause the movement of the spot on the screen in two dimensions. This produces two dimensional image of the input voltage on the screen. The use of AC voltage on the Y-plates with the time base on leads to production of a waveform. The signal is fed into the Y-plates on the CRO with the time base on. The time base control is adjusted to give one or more cycles of the input signal on the screen Peak to peak voltage, Vp-p= Number of vertical divisions * Volts/div Peak voltage, Vp= Vp-p/2 Amplitude of the wave, A= No of divisions * Volts/div For a sinusoidal waveform, the root-mean-square (rms) value of the voltage is given as The period of a wave is determined by counting the number of horizontal divisions for one complete cycle of the waveform. Period, T= Number of divisions * time base setting The reciprocal of the period gives the frequency. Frequency, f=1/T 2.0Materials and methods The following were the equipments required during the experiment Cathode ray oscilloscope (CRO) Digital Multimeter (DMM) Function Generator Fig 1 Cathode ray oscilloscope 2.1Procedures In the first exercise, the Function Generator was set up to produce a sine wave of frequency approximately 1 kHz. Also the amplitude control was set to its mid position. The output was connected to the channel 1 of the CRO while the horizontal control of CRO was set to 0.2ms per division. Moreover, the vertical control of the CRO was adjusted so that the displayed waveform could occupy most of the CRO screen. Thereafter, the period and the amplitude of the waveform were measured from the CRO screen and also the DMM was used to measure the voltage output from the Function Generator. The values were compared. In the second exercise, the output frequency of the Function Generator was adjusted to be 400 kHz. The controls of the oscilloscope were changed such that 1 or 2 cycles were shown on the screen. The timebase was set to be 0.5μs/cm. Then the voltage on the DMM, the period and amplitude on the CRO were checked and noted down. 3.0Calculation and results The results were tabulated as follows 3.1Table A Wavelength Frequency (Hz) Voltage readings (V) Time Div (s) DMM CRO 5 10 2.64 3.8 20ms 2.5 20 2.64 3.8 20ms 4 50 2.66 3.8 5ms 2 100 2.66 3.8 5ms 2.5 200 2.65 3.8 2ms 2 500 2.63 3.8 1µs 2.5 1000 2.58 3.8 0.5µs 2 2000 2.49 3.8 0.2µs 2 5000 2.31 3.8 0.1µs 5 10000 2.25 3.8 20µs 2.5 20000 2.67 3.8 20µs 2 50000 3.73 3.8 10µs 2 100000 1.77 3.8 5µs 2.5 200000 0.10 3.8 2µs 2 500000 0.00 3.8 1µs 3.2Table B Wavelength Frequency (Hz) Period (ms) V(DMM) V(CRO) Time Div 5 10 100 2.59 3.2 20ms 2.5 20 50 2.6 3.2 20ms 4 50 20 2.6 3.2 5ms 2 100 10 2.61 3.2 5ms 2.5 200 5 2.6 3.2 2ms 2 500 2 2.57 3.2 1µs 2.5 1000 1 2.52 3.2 0.5µs 2 2000 0.5 2.43 3.2 0.2µs 2 5000 0.2 2.24 3.2 0.1µs 5 10000 0.1 2.16 3.2 20µs 2.5 20000 0.05 2.52 3.2 20µs 2 50000 0.02 3.31 3.2 10µs 2 100000 0.01 1.34 3.2 5µs 2.5 200000 0.005 0.06 3.2 2µs 2 500000 0.002 0 3.2 1µs Table C Frequency (Hz) Angular frequency (ω=2πf) Amplitude (Volts) Delta t (ms) Sine wave 10 62.8 1.6 20 -0.95174 20 125.6 1.6 20 -1.5301 50 314 1.6 5 -1.14367 100 628 1.6 5 -1.59962 200 1256 1.6 2 -1.5301 500 3140 1.6 0.001 0.002548 1000 6280 1.6 0.0005 0.002548 2000 12560 1.6 0.0002 0.942105 5000 31400 1.6 0.0001 0.002548 10000 62800 1.6 0.02 -0.95174 20000 125600 1.6 0.02 -1.5301 50000 314000 1.6 0.01 -1.59962 100000 628000 1.6 0.005 -1.59962 200000 1256000 1.6 0.002 -1.5301 500000 3140000 1.6 0.001 -1.59962 Table D CRO DMM Frequency (Hz) Period in milliseconds (ms) Time div (ms) Divs Vpkpk Vpk Vrms=Vp*0.7 Vms 10 100 100 5 3.2 1.6 1.1312 2.59 20 50 50 2.5 3.2 1.6 1.1312 2.6 50 20 20 4 3.2 1.6 1.1312 2.6 100 10 10 2 3.2 1.6 1.1312 2.61 200 5 5 2.5 3.2 1.6 1.1312 2.6 500 2 2 2 3.2 1.6 1.1312 2.57 1000 1 1 2.5 3.2 1.6 1.1312 2.52 2000 0.5 0.5 2 3.2 1.6 1.1312 2.43 5000 0.2 0.2 2 3.2 1.6 1.1312 2.24 10000 0.1 0.1 5 3.2 1.6 1.1312 2.16 20000 0.05 0.05 2.5 3.2 1.6 1.1312 2.52 50000 0.02 0.02 2 3.2 1.6 1.1312 3.31 100000 0.01 0.01 2 3.2 1.6 1.1312 1.34 200000 0.005 0.005 2.5 3.2 1.6 1.1312 0.06 500000 0.002 0.002 2 3.2 1.6 1.1312 0 Calculations In exercise one, The values of time period = 4.9 squares * 0.2ms 0.98ms The amplitude = 3.8 squares * 2 =7.6V 2.69V Alternatively, in exercise two the output frequency of the function generator was 400 kHz. Time base was set to be 0.5μs/cm The time period = 5 squares 5 *(0.5*106) 2.5* 106 The amplitude = 3.8 * 2 = 7.6 2.69V 4.0Discussion and analysis The input frequencies from the function generator were similar to the frequency of the signal on the oscilloscope. The percentage error when calculated was 0%. For instance Function generator frequency = 10Hz Calculated signal frequency =10Hz Thus error = 100%* (calculated frequency-function generator frequency)/function generator frequency = 0% From the table of results, it was determined that the voltage i.e the root-mean square value of voltage is independent of the frequency it is emitted at. The sine wave (wave functions) do not affect the period of an oscilloscope and the frequency emission value. 5.0Conclusion At the end of the laboratory experiment, the students were able to familiarize with the operation of Cathode ray oscilloscope (CRO) and the function generator. One was able to understand and use the basic functions of an oscilloscope. For instance, the Y-gain and time base controls. From the experiment the amplitude and frequency of a periodic waveform were determined. Indeed, the equipment was able to display and measure electrical signals such as AC voltage, frequency, peak-to-peak voltages and root mean squares values of the signals. There are two sources of errors especially in the measurement i.e the calibration and reading errors. The equipment was observed to be important due to its capability to provide large quantity of information about the signal being measured 6.0References A.K. Sawhney,”A course in Electrical & Electronics Measurement and Instrumentation”, Dhanpat Rai & Co. Pvt. Ltd, 2000 Anthony Nicolaides,”Electrical and Electronic Principles First Edition,” Pass Publications, 2008 Deshpande,”Electron Dev & Cir-Prin & App,” Tata McGraw-Hill Education, 2008 Read More