Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6 002 Circuits and Electronics Spring 2003 Handout S03 047 Lab 3 Second Order Networks Introduction The purpose of this lab is to give you experience with second order networks and to illustrate that real network elements do not always behave in an ideal manner All exercises in this lab focus on the behavior of the network and network elements shown in Figure 1 You should complete the pre lab exercises in your lab notebook before coming to lab Then carry out the in lab exercises on your assigned lab day between April 14 and April 18 After completing the in lab exercises have a TA or LA check your work and sign your lab notebook Finally complete the post lab exercises in your lab notebook and turn it in to your TA on or before April 28 Pre Lab Exercises 3 1 Assume that the network is initially at rest At t 0 the input voltage vIN t steps from 0 V to VTI Given this input determine the transient response of vOUT t Note that vOUT t takes the form vOUT t VTO sin T t T e T t Hint see Homework Problem 8 3 Spring 2002 at http web mit edu 6 002 www spring02 hw8sol pdf 3 2 Let L 47 mH C 0 0047 F R 220 and VTI 10 V Under these conditions graph the transient response of vOUT t for 0 t 0 3 ms graphing the peaks and zero crossings of the response and a few points in between each peak and zero crossing should be sufficient On separate graphs repeat this exercise for R 560 and R 1000 To save time you may wish to use MatLab on Athena as discussed below 3 3 For all three values of R compute the voltage VTP at the first peak of the transient response the frequency T at which the transient response oscillates and the rate T at which the transient response decays Note that peaks of the transient response occur at times such that tan T t T T T you should verify this Signal Generator R IN 50 vIN t C L Figure 1 second order network R vOUT t 3 4 Assume that the network is in sinusoidal steady state Determine the response of v OUT t to the input vIN t VSI cos S t Note that vOUT t will take the form vOUT t VSO S cos S t S S Hint see Homework Problem 9 1 Spring 2002 at http web mit edu 6 002 www spring02 hw9sol pdf 3 5 Let L 47 mH C 0 0047 F and R 220 On separate graphs graph log H S S and S S versus log S 2 10 kHz for 2 1 kHz S 2 100 kHz where HS S VSO S VSI Ten to fifteen points per graph should be sufficient to clearly outline HS if you space the points more closely near the peak of HS Again on separate graphs repeat this exercise for R 560 and R 1000 You may find it easiest to use log log graph paper for the graph of HS and linear log graph paper for the graph of S Alternatively to save time you may wish to use MatLab on Athena as discussed below 3 6 For all three values of R compute the peak value HSP of HS the frequency SP at which the peak occurs and Q Note that Q is defined as Q SP 2 T and that HS S will have fallen from its peak value of HSP by a factor of 2 at S SP T You are strongly encouraged although not required to use MatLab to plot the graphs outlined above To use MatLab you must first type add matlab at the Athena prompt and then invoke MatLab by typing the command matlab at the Athena prompt The MatLab commands step and bode can then be used to plot the desired graphs You can learn how to use these commands by typing help step and help bode at the MatLab prompt The step command accepts an optional time vector argument to specify the time range over which the step response is to be plotted To define an appropriate time vector T type T linspace 0 3e 4 100 at the MatLab prompt The vector T will then contain 100 evenly spaced points between 0 ms and 0 3 ms The bode command accepts an optional frequency vector argument to specify the frequency range over which the frequency response is to be plotted To define an appropriate frequency vector W type W 2 pi logspace 3 5 100 at the MatLab prompt The vector W will then contain 100 logarithmically spaced points between 103 and 105 Hz Additionally note that the bode command in MatLab uses the frequency variable s where s j Finally figures plotted by MatLab may be printed on an Athena printer using the MatLab print command To learn more type help print at the MatLab prompt In lab Exercises The in lab exercises involve measuring both the step response and sinusoidal response of the network shown in Figure 1 for three values of R You should feel free to measure these responses for only one value of R and then share your measurements with two other partners who have measured the network responses for the other two values of R However should you take this team approach all team members must use the same inductor and capacitor You should also indicate in your lab notebook which responses you measured and which responses you have taken from another team member Finally you are advised to look at all responses on the oscilloscope before you leave the lab so that you see for yourself how they vary as R varies Real network elements do not always behave the way we model them in 6 002 For example a real inductor might be better modeled as an ideal inductor in series with a resistor as shown in Figure 2 The resistor is a parasitic element meaning that it is undesired but unavoidable The resistor accounts for the resistance of the wire used to wind the inductor Yet more complex models could account for core losses and the capacitance between winding turns For this reason the model shown in Figure 2 is not the only possible model In a similar way a real capacitor might be better modeled as an ideal capacitor in parallel with a parasitic conductance which models leakage through the dielectric of the capacitor This is also shown in Figure 2 In the exercises which follow the network in Figure 1 will be exposed to inputs that vary at high enough frequencies that you can ignore the parasitic parallel conductance of the capacitor Therefore we need only be concerned with the parasitic series resistance of the inductor 3 1 Take a 47 mH inductor a 0 0047 F capacitor a 220 resistor a 560 resistor and a 1000 resistor from your lab kit to the instrument desk and use …
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