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 = 10kΩ . Problem 4.1: A voltage source can be represented as the series connection of an ideal DC voltage source and a r esistance RIN = 1kΩ, as illustrated in Figure 1a. The model of the voltage sour ce also includes a small signal voltage source vi to represent the noise generated by the source. Assume VI = 10 V and vi = 50 mV . VI vi RIN VI vi RIN RL vo + VO (a) Unloaded voltage source. (b) Loaded voltage source. Figure 1: Simple model of a non-ideal voltage sour ce. In practice, connecting the non-ideal voltage source to a load resistance RL, as in Figure 1b, may resu lt in undesirable effects. This p roblem studies such effects 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 kΩ and RL = 4 kΩ. 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 VI RLvD vo + VO vi (a) Voltage source connected to a Zener diode. vD (V ) 0.6 V −5 V 1 A/V 1 A/V (b) i−v characteristic for a Zener diode. Figure 2: The use of a Zener diode can correct some of the u ndesirable effects 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 Ω N + -vI + -vA iA Figure 3: Circuit used in Problem 4.2. (a). Write an equation which relates th e voltage vA to the inpu t voltage vI . (b). Solve for the voltage vA when vI = 10 V . Note that this r equ ires 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 ΔvA/ΔvI . (d). Find the value for the incremental resistance of the n onlinear 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 sh own in Figure 3. (f). Find the ratio ΔvA/ΔvI 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
View Full Document
Unlocking...