Massachusetts Institute Technology Massachusetts Institute ofofTechnology Department of Electrical Engineering andComputer Computer Science Department of Electrical Engineering and Science Electronic Circuits 6 0026 002 Electronic Circuits Fall 2004 Fall 2005 Homework Homework 9 9 Handout F04 046 Issued 11 8 2005 Due 11 18 2005 Issued 11 04 2004 Due 11 12 2004 Helpful readings for this homework Chapter 12 Helpful Readings for this Homework Chapter 12 Exercise 9 1 Using one 3 nF capacitor and two resistors construct a network that has the Exercise 9 1 Using one 3 nF capacitor twostep resistors construct a network that hasofthe following zero state following zero state response ZSR to aand 1 V input Provide a diagram the network and response a 1 V of step input a diagram of the network and specify the values of the two resistors specify the to values the twoProvide resistors v1 t v2 t 1V v1 t Network t Exercise 9 2 v2 t 1V 2 V 3 2 1 t 20 s V V e 3 3 t Exercise 12 4 Chapter 12 p 985 Exercise9 2 9 3 Exercise Consider12 4 a linear time invariant system Exercise Chapter 12 page 695 Suppose its ZSR to a unit step applied at t 0 is A 1 e t What would be its ZSR to the input S Mt applied at t 0 where S and M are constants Exercise 9 3 Consider a linear time invariant system Suppose its ZSR to a unit step applied Problem 9 1 Problem 12 6 Chapter 12 p 991 at t 0 is A 1 e t What would be its ZSR to the input S M t applied at t 0 where S andProblem M are constants 9 2 In the network shown below the inductor and capacitor have zero states prior to t 0 At t 0 a step in voltage from 0 to V 0 is applied by the voltage source as shown Problem 9 1 Problem 12 2 Chapter 12 page 697 a di Find v C v L i and at t 0 dt Problem 9 2 Problem 12 6 Chapter 12 page 698 b Argue that i 0 at t so that i t has no constant component Problem 9 3 In the network shown below the inductor and capacitor have zero states prior to a second order equation which describes behavior of i t asfor t 0 t 0 At t c 0 Find a step in voltagedifferential from 0 to Vo is applied by thethe voltage source shown a Find vc vl i and di dt at t 0 b Argue that at t i 0 so that i t has no constant component response of the network shown below to the impulse Hint Before solving this problem directly consider the relation between step and impulse responses Save a copy of your answers to this problem They will be useful during the pre lab exercises for Lab 3 i t vL v t L V0 v t R vR C t vC Problem 9 3 Problem 12 7 Chapter 12 p 991 Use the values R1 4 75k Rn 25 L1 10 m W1 1 m c Find a second order differential equation which describes the behavior of i t for t 0 Cp 1nF Lp 4mH for the underdamped case and use R1 750 Lp 6 25mH with the rest the same for the overd Following part b the current i t takes the form i t Ie t sin t Find I damped case and Explicitly set up the characteristic equation for the circuit and then use intuitive analysis i e without finding the full e Suppose that equations the inputtoisfind a voltage impulse with See areasection o in 12 7 Volt seconds o for Vthe solutions to differential the form of the responses You don t where have to solve o the voltage Vo is the amplitude the voltage below initil andand is a given constant maximum amplitude in either case butofimportant valuesstep such shown as frequencies final values time time constants decay the envelopes etc of should be indicated when applicable Hint use circuit analysis to set up a differenFind response the network tonumerically the impulse tial equation but don t solve it Use the constants from the differential equation along with your initial conditions to Save athecopy of yournecessary answersfortoyour thisplots problem Theyabout will initial be useful the pre labyour exercises determine parameters Don t forget slopesduring when you determine initial conditions for Lab 3 Comparing your results with Problem 10 8 from Chapter 10 is optional but highly recommended Problem 9 4 Problem 12 7 Chapter 12 page 699 with the following parts a Explicitly set up the characteristic equation for the circuit For parts b and c use the values Rn 25 L1 10 m W1 1 m and Cp 1nF Use intuitive analysis to find the form of the responses Solve for the frequency initial and final values time constants and decay envelopes You don t have to solve for the maximum amplitude b Sketch vP for the underdamped case Use R1 4 75k and Lp 4mH c Sketch vP for the overdamped case Use R1 750 and LP 6 25mH d Compare the results from parts b and c with that for the inductor acting alone as shown in Figure 10 107 on page 582
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