1401 Lab1

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University of Houston College of Technology Computer Engineering Technology and Electrical Power Technology Freshman Laboratory ELET 1401 Electrical Circuits II Experiment 1(a) Signal Generation Oscillators ©2011 – University of Houston, College of Technology ELET Labs

Table of contents 1 Purpose ............................................................................................................................................. 3 2 Objectives .......................................................................................................................................... 3 3 Equipment ........................................................................................................................................ 3 4 Introduction to Oscillators ............................................................................................................... 4 5 Procedures ......................................................................................................................................... 5 5.1 Procedure 1: Lead-Lag Network ............................................................................... 5 5.2 Procedure 2: Wien-Bridge Oscillator .......................................................................... 9 6 Application: Colpitts Oscillator ..................................................................................................... 12 7 Knowledge Evaluation .................................................................................................................. 13 8 References ....................................................................................................................................... 14 ELET 1401 - Rev. 010511LG © 2011 – University of Houston, College of Technology ELET Labs

1 Purpose This experiment is an introduction to oscillator circuits that produce sinusoidal signals. 2 Objectives At the end of this experiment you will know: 1. How the lead-lag circuits behave. 2. How an untuned oscillator circuit such as the Wien Bridge oscillator behaves. 3. We focus on analyzing the signal as well. 3 Equipment For this experiment, you will need the following:  Multi-meter  Function Generator/Oscilloscope  Soldering Gun/Solder  Proto-board  Resistors: 1.5KΩ, (2) 3.3KΩ  Potentiometer: 10KΩ  Capacitors: 100 nF (4)  LM 741 (Operational Amplifier) 4 Introduction to Oscillators As its name implies an oscillator is a device that produces repetitive waveforms or oscillations. They are widely used in electronic communications for timing and clocking, modulations, and signal generation. Oscillators are constructed using passive components (R-L-C) and active components (OpAmps). Other oscillators take advantage of the “vibrating” characteristics of some minerals, such as quartz crystal. These crystal oscillators replace the LC tank as the frequency-determining component. ©2011 – University of Houston, College of Technology ELET Labs

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Oscillators can be classified into two categories: self-sustaining (free-running) and triggered (one-shot). A self-sustaining oscillator is capable of producing a continuous sinusoidal waveform. A triggered oscillator requires an external input signal to “trigger” the oscillations. In this experiment, we will study free-running oscillators that use both active and passive components for signal generation. Free-running oscillators are also called feedback oscillators because they include a closed-loop feedback used for compensation. A feedback oscillator generates an ac signal part of which part is fed back to the input where it is amplified either by a transistor circuit or an op-amp circuit. The amplified signal appears at the output and the process is then repeated as shown in Figure 1. Figure 1. Model of a closed-loop feedback oscillator In this experiment, you will first study the Lead-Lag network and run a simple simulation to determine its behavior at different frequencies. You will then construct a Wien-Bridge oscillator, an un-tuned oscillator that uses the Lead-Lag network and a closed-loop feedback. The application for this experiment involves the analysis and simulation in Multisim of a Colpitts oscillator, a tuned oscillator that integrates a LC tank for frequency determination and a voltage- divider transistor circuit for amplification and feedback. 5 Procedures 5.1 Procedure 1: Lead-Lag Network A Lead-Lag network is a reactive voltage divider in which the voltage is divided between the impedance Z 1 (series RC) and Z 2 (parallel RC) as shown in figure 2. ELET 1401 - Rev. 010511LG © 2011 – University of Houston, College of Technology ELET Labs

w Figure 2. Lead-Lag Network The frequency of oscillation is found by the equation below f o = 1 2 π RC eq.1 where R= R 1 = R 2 , C =C 1 = C 2 . We are now going to construct a Lead-Lag network that has a frequency of oscillation of 1000 Hz. 1. Calculate C for R = 3.3KΩ and f o = 1 KHz using equation 1. Answer: 4.82 x 10^-8 F 2. Calculate the magnitude and phases of the impedances Z 1 and Z 2 for the frequencies 0, 500, 1000, 1500, 2000, 2500, and 3000 Hz. Draw a table and write the results in polar form with magnitude in one column and phase shift in another column. Xc1 = 1/(2π*f*C1) Z1 = R1 – j* Xc1 Mag(Z1) = √(R1 2 + Xc1 2 ) Phase(Z1) = - tan -1 (Xc1/R1) Xc2 = 1/(2π*f*C2) Z2 = R2*(-j* Xc2)/(R2 – j* Xc2) Mag(Z2) = R2*Xc2/(√(R2 2 + Xc2 2 ) Phase(Z2) = -90 – (- tan -1 (Xc2/R2)) ELET 1401 - Rev. 010511LG © 2011 – University of Houston, College of Technology ELET Labs

Freq Hz Xc1 ohms Xc2 ohms Mag(Z1) (ohms) Ph(Z1) (Deg.) Mag(Z2) (ohms) Ph(Z2) (Deg.) 0 inf inf inf -90 3300 0 500 6,603.94 6,603.94 7,382.55 -63.45 2,951.96 -26.55 100 0 3,301.97 3,301.97 4,668.30 -45.02 2,334.15 -44.98 150 0 2,201.31 2,201.31 3,966.83 -33.71 1,831.27 -56.29 200 0 1,650.98 1,650.98 3,689.95 -26.58 1,476.51 -63.42 250 0 1,320.79 1,320.79 3,554.50 -21.81 1,226.22 -68.19 300 0 1,100.66 1,100.66 3,478.71 -18.45 1,044.12 -71.55 3. Calculate the output voltage (magnitude and phase) at the frequencies. Use the voltage across Z 2 as the output voltage. Assume an input voltage of 4 V p-p . Use Z1 and Z2 obtained in step 2. Convert Z2 to Rectangular form to get its real and imaginary parts (i.e. Re{Z2} and Im{Z2}). Vout = Vin * (Z2/(Z1+Z2)) Mag(Z1+Z2) = √(Re{Z1}+Re{Z2}) 2 + (Im{Z1}+Im{Z2}) 2 ) Phase(Z1+Z2) = tan -1 ((Im{Z1}+Im{Z2})/(Re{Z1}+Re{Z2})) Mag (Vout) = Vin*Mag(Z2)/Mag(Z1+Z2) Phase (Vout) = Phase (Z2) – Phase (Z1+Z2) Freq Hz Re{Z1} ohms Im{Z1} ohms Re(Z2) ohms Im(Z2) ohms Re(Z1+Z2) ohms Im(Z1+Z2) ohms Mag(Z1+Z2) ohms Ph(Z1+Z2) ohms 0 500 3300 6600 2640 -1320 5940 5280 7947.45 41.63 1000 3300 3299 1650 -1650 4950 1649 5217.44 18.42 1500 3300 2199 1015 -1523 4350 676 4367.63 8.90 2000 3300 1649 660 -1320 3960 329 3973.64 4.75 2500 3300 1319 455 -1138 2755 181 3759.36 2.76 3000 3300 1099 330 -990 3630 109 3631.64 1.72 Freq Hz Vout Mag. (Volts) Vout ph.(Deg.) 0 0 90 ELET 1401 - Rev. 010511LG © 2011 – University of Houston, College of Technology ELET Labs

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500 2.98 26.50 1000 2.67 0 1500 2.78 -15.50 2000 2.98 -26.40 2500 3.17 -35.00 3000 3.32 -42.00 Note: At 1 KHz (Frequency of oscillation), The output voltage is maximum and there is no phase shift. 4. Plot a graph of frequency (x-axis) versus output voltage (y-axis). 5. Construct the circuit of Figure 2. I/P voltage set at 4 Vp-p. Frequency Vout (p-p) (V) Phase (Deg.) 500 1.24 V 30 1000 1.38 V 0 1500 1.32 V 13.34 2000 1.19 V 24.62 2500 1.13 V 33.50 3000 1.03 V 36.87 ELET 1401 - Rev. 010511LG © 2011 – University of Houston, College of Technology ELET Labs

7. Compare the measured curve with the calculated one. Write your observations. The calculated curve has a larger shift in numbers compared to the measured values. 8. Compare the phase shifts for all the frequencies. Describe the phase shift at the frequency of oscillation. 9. Turn off the circuit. Do not disconnect this circuit; you will need it in procedure 2. 5.2 Procedure 2: Wien-Bridge Oscillator The Wien Bridge oscillator is shown in figure 3. The Wien Bridge is an oscillator circuit used for the production of sinusoidal waveforms of low frequencies (5 Hz to 1 MHz). The amplifier A 1 is an operational amplifier or op amp. One of the characteristics of the op amp is that it has very high input impedance Z i .; therefore, it does not allow current to flow inside the op amp. It amplifies the voltage difference at its inputs making it easy to adjust its gain with a voltage divider. Its output impedance Z o , however, is very low allowing the op amp to be used in numerous applications. ELET 1401 - Rev. 010511LG © 2011 – University of Houston, College of Technology ELET Labs

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Figure 3. Lead-Lag Network Notice that the circuit shown in Figure 4 (a) is the Lead-Lag network you studied in the previous procedure. You are to attach an amplifier circuit such as the one shown in figure 4 (b) and adjust its gain (amplification of the feedback oscillator). You will use the LM741 op amp, a widely used operational amplifier. To sustain oscillations, the gain of the amplifier circuit should be approximately equal to 3 A = R f Ri + 1 ≈ 3 eq.2 and can be adjusted by placing a potentiometer in place of R b . Figure 4. Wien Bridge ELET 1401 - Rev. 010511LG © 2011 – University of Houston, College of Technology ELET Labs

1. Construct the circuit of Figure 4 (b) with R A = 1.5KΩ and a 10KΩ-pot for R B . (Didn’t have a 10 KΩ pot so used a 5 KΩ pot.) 2. Use +/- 15 Vdc to power the op amp. The data sheet for the 741 Op Amp is provided in Appendix A. 3. With an input voltage of 1 V p-p , connect the source to terminal x and observe the waveform at the output (pin 6) with your oscilloscope. 4. While adjusting R B observe the waveform. Adjust until you get an output voltage that is 3 times the input. (3 V p-p ) 5. Now turn off the circuit. Using the lead lag network that was constructed in procedure 1 and the above circuit, construct the circuit shown in Fig. 5. Figure 5. Wein Bridge 6. If you adjusted the gain exactly in step 4, you should get sustained oscillations at the output (pin 6). If you don’t get the oscillations, keep adjusting the potentiometer till you get sustained oscillations. 7. Measure the frequency of oscillation. Compare with the calculated. 8. Measure the gain of the amplifier. Compare with the calculated. 9. Write all of your observations. ELET 1401 - Rev. 010511LG © 2011 – University of Houston, College of Technology ELET Labs

6 Application: Colpitts Oscillator (Simulation) Figure 6. Colpitts Oscillator The Colpitts oscillator of Figure 6 is a LC oscillator that utilizes a tuned LC tank for the frequency determining components. The frequency of operation is the resonant frequency of the LC tank. The frequency of oscillation can be calculated by equation 3 such as f o = 1 2 π √ LC eq. 3 where C = C 1 C 2 C 1 + C 2 eq.4 The Colpitts oscillator of Figure 6 achieves a positive feedback by using an inverting amplifier plus the 180 0 phase shift across a parallel resonant circuit. 1. Calculate the total capacitance of the LC tank. 2. Calculate the expected frequency of oscillation. 3. Construct the circuit of Figure 6 in PSpice. ELET 1401 - Rev. 010511LG © 2011 – University of Houston, College of Technology ELET Labs

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4. Run the simulation, and provide the screen shot in the report to prove that the simulation was run 5. Insert the output waveform in the report. 7 Knowledge Evaluation Answer the following questions and write them in your Worksheet and your report: 1. What is the effect of varying input frequency on the output voltage of a lead-lag network? 2. What will happen at the output if the ratio R b /R a is  Greater than 2?  Less than 2? 3. To get an output frequency of 10 KHz using a Colpitts oscillator, suggest the value of the inductor if all other components in figure 6 remain the same. 8 References If you want to learn more about the topics related to this lab, see the following references: 1. W. Tomasi, Electronic Communications Systems, Fourth Edition, Prentice-Hall, 2001 2. CLAB resources. [Online] available: http://cot-vyger.cougarnet.uh.edu ELET 1401 - Rev. 010511LG © 2011 – University of Houston, College of Technology ELET Labs

1401 Lab1

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