+-vIN(t) CLRvOUT(t)+-RIN50Ω=Signal GeneratorMassachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6.002 – Electronic Circuits Lab 3: Second-Order Networks Handout S07-49 Spring 2007 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 between April 23 and April 27. 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 in your lab notebook on or before May 2. Before asking to get checked off, make sure you meet all the requirements in the checkoff list at the end of the In-Lab Exercises Bring in your favorite CD for In-Lab Exercise 3-5; it is meant to be a fun experiment and its results will not be needed for the post lab exercises. Pre-Lab Exercises You are strongly encouraged to use Matlab to generate the graphs for Exercises 3-2 and 3-5. Matlab will not only save you time, but will also help you generate graphs that are extremely accurate and precise. See the appendix for help with Matlab. There are also two Matlab scripts which you can download from the class website. By filling in a few relations and changing resistor values these scripts will produce the graphs in the pre-lab excercises. (3-1) Assume that the network in Figure 1 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 Figure 1: Second-order network. Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].that vOUT(t) takes the form vOUT(t) = VTOe−αTt sin(ωTt + φT). Hint: You are free to use the results from Homework Problem 9-3 for this exercise. (3-2) Let L = 47 mH, C = 0.0047 µF, R = 220 Ω 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 a separate graph, repeat this exercise for R = 1000 Ω. Hint: See the Matlab appendix and download the transient.m matlab script from web.mit.edu/6.002. (3-3) For both values of R, compute the voltage VTP (the first peak voltage of the transient response), the frequency ωT at which the transient response oscillates, and the rate αT at which the transient response decays. Note that peaks of the transient response occur at times such that tan(ωTt + φT) = ωT/αT; you should verify this. (3-4) Assume that the network is in sinusoidal steady state. Determine the response of vOUT(t) to the input vIN(t) = VSI cos(ωSt). Note that vOUT(t) will take the form vOUT(t) = VSO(ωS) cos(ωSt + φS(ωS)). (3-5) Let L = 47 mH, C = 0.0047 µF and R = 220 Ω. On separate graphs, graph log HS(ωS)| |and φS(ωS) versus log(ωS/(2π × 10 kHz)) for 2π × 1 kHz ≤ ωS ≤ 2π × 100 kHz where HS(ωS) ≡ VSO(ωS)/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 a separate graph, repeat this exercise for R = 1000 Ω. 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 φS. Hint: See the Matlab appendix and download the forcedosc.m matlab script from web.mit.edu/6.002 . (3-6) For both values of R compute the peak value HSP of HS, the frequency ωSP at which the peak occurs, and Q. Note that Q is defined as Q ≡ ωSP/2αT, and that HS(ωS) will have fallen from its peak value of HSP by a factor of √2 at ωS ≈ ωSP ± αT. In-lab Exercises The in-lab exercises involve measuring both the step response and sinusoidal response of the network shown in Figure 1 for two values of R. Afterwards, you will use the same network to filter a signal from a CD player. Real network elements do not always behave the way we model them in 6.002. For example, a real inductor might be better modelled as an ideal inductor in series with a resistor, RP , 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 modelled as an ideal capacitor in parallel with a parasitic conductance, GP , 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 µF capacitor, a 220 Ω resistor, and a 1000 Ω resistor from your lab kit to the instrument desk and use the GenRad impedance meter to measure Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].LRPCGPInductor ModelCapacitor Modelthese elements and determine the parasitic resistance and conductance of the inductor and capacitor, respectively. To measure the inductor, set the meter for 1 kHz, the series model, and the appropriate element type and value range. The meter will directly read the inductor value. It will also read Q from which you can determine RP from Q = ωL/RP, where ω = 2π × 1 kHz. To measure the capacitor, set the meter for 1 kHz, the parallel model, and the appropriate element type and value
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