Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6 002 Electronic Circuits Lab 3 Second Order Networks Handout F05 49 Fall 2005 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 November 14 and November 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 in your lab notebook on or before November 23 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 web mit edu 6 002 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 Signal Generator R IN 50 vIN t C L Figure 1 Second order network R vOUT t that vOUT t takes the form vOUT t VTO e T t sin T t T 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 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 a separate graph repeat this exercise for R 1000 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 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 3 4 Assume that the network is in sinusoidal steady state Determine the response of vOUT 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 3 5 Let L 47 mH C 0 0047 F and R 220 On separate graphs graph log HS 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 a separate graph repeat this exercise for 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 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 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 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 F capacitor a 220 resistor and a 1000 resistor from your lab kit to the instrument desk and use the GenRad impedance meter to measure these 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 L RP where 2 1 kHz To measure the capacitor set the meter for 1 kHz the parallel model and the appropriate element type and value range The meter will now directly read the capacitor value It will also read D from which you can determine GP from D GP C where 2 1 kHz 3 2 Construct the second order network shown in Figure 1 using the measured inductor capacitor and 220 resistor 3 3 Set the signal generator to produce a 10 V peak to peak square wave at 50 Hz with a 5 V offset so that its open circuit output voltage steps between 0 V and 10 V Also obtain a BNC to BNC cable from the stockroom and connect one end to the SYNC output of the function generator A BNC connector is shown in Figure 3 Connect the other end to one of the …
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