Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6 002 Circuits Electronics Spring 2007 Homework 4 Handout S07 023 Issued 03 01 2007 Due 03 09 2007 Helpful readings for this homework Chapter 4 Chapter 6 1 6 6 6 10 Exercise 4 1 Exercise 4 3 from Chapter 4 of A L page 231 Exercise 4 2 Exercise 6 5 from Chapter 6 of A L page 323 Use Figure 6 59 c instead and assume that R6 R7 10k Problem 4 1 A voltage source can be represented as the series connection of an ideal DC voltage source and a resistance RIN 1k as illustrated in Figure 1a The model of the voltage source also includes a small signal voltage source vi to represent the noise generated by the source Assume VI 10 V and vi 50 mV RIN RIN VI VI vi RL vo VO vi a Unloaded voltage source b Loaded voltage source Figure 1 Simple model of a non ideal voltage source In practice connecting the non ideal voltage source to a load resistance RL as in Figure 1b may result in undesirable e ects This problem studies such e ects and how to correct them by introducing a Zener diode into the circuit Figure 2a a In Figure 1b calculate vo i e output noise and VO i e DC output voltage for RL 2 k and RL 4 k What can you say about vo and VO as a function of RL b Repeat part a for the voltage source in Figure 2a In this setting how do vo and VO change with RL c In Figure 2a what is the minimum value of RL that would guarantee that the circuit operates as in part b 1 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 iD mA RIN 1 A V vD V 5 V VI vD RL 0 6 V vo VO vi 1 A V b i v characteristic for a Zener diode a Voltage source connected to a Zener diode Figure 2 The use of a Zener diode can correct some of the undesirable e ects in non ideal voltage sources Problem 4 2 Consider the circuit containing the nonlinear element N as shown below in Figure 3 The i v relation for the element N is given by iA 10 A 1 e vA 5V 1 2 iA vI N vA Figure 3 Circuit used in Problem 4 2 a Write an equation which relates the voltage vA to the input voltage vI b Solve for the voltage vA when vI 10 V Note that this requires that you solve the equation in part a iteratively for vA Hint Use the exponential term to solve for vA as a function of the assumed value of vA and then iterate Taking logs on both sides may facilitate convergence c Find the incremental change in vA for a 2 increase in vI and calculate the ratio vA vI d Find the value for the incremental resistance of the nonlinear element N by linearizing the expression for iA about the operating point when vI 10 V e Draw the incremental circuit model for the circuit shown in Figure 3 f Find the ratio vA vI from the incremental circuit model and compare it with your exact model from part c Problem 4 3 OPTIONAL Problem 4 3 from Chapter 4 of A L page 233 234 Hint You may want to read section 4 4 of A L on Piecewise Linear Analysis of non linear devices 2 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
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