Lab report using Scope. Need the report with all the calculations and the Waveforms including Pre Lab

ECE2160 Electronics II University of Manitoba 1 Lab 2: Oscilloscope Review and RC Circuits Prelab Assignment : 1) Read Section 1.6.4 of Sedra and Smith 6th Edition and section E.4 of Appendix E (available on the CD that comes with the book or download from course website). Also read the theoretical material appearing below in this document. Note: For the cases below, all component values for resistors, capacitors etc. must be selected from the list of values given in the Appendix at the end of this Lab Document. 2) In Figure 4, choose the resistor and capacitor values such that the output voltage reaches 98% of its final value in 4ms. 3) Design the circuit in Figure 5 such that its output voltage drops to 37% of its initial value 1.8ms after applying a step voltage to the input. 4) Design an RC high -pass filter with a corner frequency of 1000Hz. Calculate 2 pairs of answers, so that for one pair the capacitor value is higher than 1μF and for another pair the capacitor value is less than 1μF. Intr odu ctio n In the first part of this lab, we shall review the basics of oscilloscope (or simply scope) operation and application. In the second part of the lab, we will examine the step response of RC c ircu it s. The last part deals with the frequency response of the RC circuits and their application as frequency selective filters. Based on the theory provided in these manual and reading assignments, you should design circuits to meet certain time and/or frequency requirements. Read the manual and design the circuits of different parts as required. Simulate the RC circuits of this lab with Mult i sim . Use transient analysis for circuits in Part 2, and AC analysis for Part 3. ECE2160 Electronics II University of Manitoba 2 To find the step response, perform transient analysis on the circuit with a pulse source as the input. The voltage source should generate a 1V pulse waveform (1= 0V, 2= 1V) with very short rise and fall times (1ns or less), and its voltage should remain high (i.e., 1V) for 10ms after the input step edge. Perform AC analysis, using a signal source with an AC amplitude of 1V, to plot the frequency response of the circuit for the frequency range of 10Hz to 1MHz (with logarithmic Y- axis). Save and describe the frequency responses of the circuits in Figure 4 and Figure 5. Part 1: Oscilloscope Review Figure 1 The Tektronix TDS1002 Front Panel Figure 2 Screen capture of oscilloscope in SCOPY ECE2160 Electronics II University of Manitoba 3 We typically use digital oscilloscopes with two input channels made by Tektronix (Figure 1). However, the introduction given below is fairly general and may be applied to working with other scopes with little modification. In this lab, we will use the oscilloscope module in SCOPY from ANALOG DEVICES (ADALM2000) as shown in Figure 2 . There are three coupling modes for each channel: DC, AC, and GND (ground). The coupling mode for each channel may be selected by turn on/off the software AC coupling in the channel setting . When the input is DC coupled (AC coupling is off ), you will see both the AC and DC parts of the input signal on the screen. This is the mode that we use most often in this lab. If the input is AC coupled, however, only the AC portion of the input signal is displayed and any DC value is blocked by a large capacitor at the input of the scope. This mode is useful when you want to measure a small AC signal that is superimposed on a large DC voltage, and you are not interested in monitoring the DC value. The GND coupling mode simply shorts the input channels to ground and only be used for calibration or trace finding purposes which is not available in SCOPY . Normally, when you look at the screen, the horizontal axis represents time † and the vertical axis is the magnitude of the input signal in volts, possibly with a different scale for each of the channels. Scale for each of the channels (in volts/division) can be individually adjusted in the right channel setting section in Figure 2. The time scale (in seconds/division) and position can be also adjusted if necessary. These settings should be adjusted such that you see a few cycles (2 -5) of the input signal on screen with easily measurable amplitudes. The waveforms can be shifted up and down by setting the Position value in the vertical setting section. To see a stable (non -moving) waveform on screen, the refresh rate of the screen must be synchronized with the input signal frequency. This is done by adjusting the triggering controls in the right bottom are a of Figure 2. In most cases, Normal or Auto triggering modes can result in a stable waveform. And you can select the signal source for triggering as well the triggering level and condition. To assist user during measurements, the scope s in SCOPY can provide you with information on the peak -to-peak (pk -pk) amplitude, mean value (DC), frequency, or period of the signal applied to each of the channels. Simply click the Measure at right botto m of Figure 2, specify the source (channel 1 or 2), and the quantity of interest. There are also a couple of vertical and horizontal cursors which can be used by enabling ECE2160 Electronics II University of Manitoba 4 cur sors at right bottom , and then moving them to the point you are interested . Cursors may be used whenever the difference in two levels or times are to be measured. †This is called YT mode. The other possible operation mode is XY mode, in which vertical axis represents the changes of the signal on channel 1 and the horizontal axis represents the changes of the signal applied to channel 2. XY mode is useful for observing how the changes of one signal affects the other one (e.g., when you want to plot the characteristic curve of a device or circuit). 1. Basics of Wa vefo rm Monitoring Based on the Pinout of ADALM2000 in Figure 3, connect the output of Signal generator in SCOPY (namely Analog Output 1 ) to Channel 1 (Analog Input 1 Positive ,1+ ) and t he Analog Input 1 Negtive ,1- connect to the Ground . Then apply a 1V peak -to-peak sine wave with a frequency of 1kHz in the Signal generator and click run . The output waveform should be seen in the screen of Oscilloscope in SCOPY. Adjust the controls on scope such that you can easily see a stable waveform on screen (2 -5 cycles) and measure the peak -to-peak amplitude, mean, and frequency of the signal on channel 1. Compare your measurements with values set on the Signal generator . Then change the waveform to a 1kHz, 1V peak -to-peak triangular waveform and add 2V of offset to the signal . Save all the waveforms and your measurements. Figure 3 Pinout of ADALM2000 ECE2160 Electronics II University of Manitoba 5 Figure 4. Low -pass RC circuit. 2. Step Response of RC Circuits Theory: Consider the RC circuit in Figure 4. This circuit has a single time constant (STC) which is = . The step response of any STC system or circuit is of the form shown below: ()= [(0)− (∞ )]−/+ (∞ ) (1) where (0) is the initial condition, (∞ ) is final value of the output, and is the system time constant. It can be checked that at t ≈ 4, the output variable reaches 98% of its final value. Also, when = , y reaches 1-1/e = 63.2% of its final value if it’s charging (or reaches within 36.8% of its final value if it’s discharging). For example, if = 0 at = 0 and is switched on with volts DC, then it’s obvious that = at = ∞ . However, the transient response (time and curve it takes to reach ), is given by (1) as ()= (0− )−+ and simplifies to ()= (1− −) which equals 0.632V after one time constant, . You can easily verify that if = at = 0 and is switched off, then ()= − equals 0.368 VO after one time constant, . Procedure and Observations: Use the component values you calculated for the second prelab question and wire up the circuit on your breadboard. Co nne ct t he o ut put o f sig nal g en e ra to r to the board as input source IN. Apply a 10Hz square wave with 2V peak -to-peak amplitude and 1V DC offset to the input (so the input voltage changes between 0 and 2 volts). Monitor the input voltage on Channel 1 and output voltage on Channel 2. Remember to connect the Ground of Scope, Negative terminals of channel 1 and 2 with the Ground of your breadboard. S a v e t h e w a v e fo r m s a n d estimate the time constant of the circuit compar ing with your design target value. Find the expression for the step response of the high pass filter circuit in Figure 5. How many time constants, , does it take for the output voltage to drop to 37% of its initial value? Use the values you calculated for the fourth prelab question and wire up the circuit on your breadboard. Apply a square wave to the input as you did for the low -pass circuit. Estimate and compare it to the expected value. What is the reason for possible existing difference? C R + + ECE2160 Electronics II University of Manitoba 6 Figure 5. High -pass RC circuit. 3. Frequency Response of RC C ircuits 3.A. If the input of the circuit in Figure 5 is a pure sine wave (i.e., ()= cos ), we can use phasors to find the output voltage: = + 1 = 1+ (3) from which we can derive: ()= √1+( )2× sin ( − ∅) , ∅ = tan −1( ) (4) It is seen that the output voltage amplitude now depends on the frequency of the input sine wave; changing from almost zero at very low frequencies ( → 0) to almost VP for very high frequencies ( → ∞ ). This is the reason for the name “high -pass filter” for this circuit, as the high frequency signals pass with little distortion, while the low frequency signals are blocked. The frequency 0= ( )−1 is called the corner frequency of the filter, or more commonly, for reasons beyond the scope of this lab, the natural frequency of the circuit. At = 0, the magnitude of the output voltage drops to 1 √2= 0.707 of the input voltage magnitude (-3dB). Wire up one of the RC high -pass filters that you designed in answer to the fourth question of the prelab. Apply a sine wave with 2V peak -to-peak amplitude (0 DC) to the input of the circuit and monitor it on channel 1. Monitor the output on channel 2. Increase the frequency of the input signal from ~10Hz to ~100kHz. Record | | || for these frequencies: 10, 50, 100, 500, 1k, 5k, 10k, 50k, 100kHz. Plot | | || as a function of frequency. Use the other pair of component values that you obtained for Question 4 of the prelab and compare its result with the first pair of values. Is there any difference? Why? C R + + ECE2160 Electronics II University of Manitoba 7 3.B. Find out the phasor and time domain expressions for the output voltage of the circuit shown in Figure 4, when the input is a sine wave (i.e., ()= cos ). Explain why this circuit is called a “low -pass filter”. Wire up the circuit on your breadboard with the R and C, which better meet the specification, asked in question 2 of the prelab. What is the corner frequency of this circuit? Record your measurements for the same frequencies as in Part 3 . A . Plot | | || as a function of frequency. Appendix: Available components in the lab: Capacitors: 100pF, 1000pF, 10nF, 22nF, 100nF, 1μF, 10 μF, 10 μF, 100 μF Resistors: 10 Ω, 12 Ω, 15 Ω, 18 Ω, 22 Ω, 27 Ω, 33 Ω, 39 Ω, 47 Ω, 56 Ω, 68 Ω, 82 Ω, and their multiplication by 10 until 10M Ω, for instance: 180 Ω, 1.8k Ω, 18k Ω, 180k Ω, 1.8M Ω.