1 / 16

Lecture #17 EGR 260 – Circuit Analysis

Lecture #17 EGR 260 – Circuit Analysis. Reading Assignment: Chapter 7 in Electric Circuits, 9 th Ed. by Nilsson . Example: Capacitor charging circuit. Find v(t) for t > 0. Example: Capacitor discharging circuit. Find v(t) for t > 0.

tybalt
Download Presentation

Lecture #17 EGR 260 – Circuit Analysis

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Lecture #17 EGR 260 – Circuit Analysis Reading Assignment:Chapter 7 in Electric Circuits, 9th Ed. by Nilsson Example: Capacitor charging circuit. Find v(t) for t > 0. Example: Capacitor discharging circuit. Find v(t) for t > 0.

  2. Lecture #17 EGR 260 – Circuit Analysis 1st-order Circuits with Dependent Sources Dependent sources affect the resistance seen by the inductor or capacitor and therefore affect the value of  for the circuit. Two approaches can be used to find : 1) When REQ seen by an inductor or a capacitor, remove the L or C, kill any independent sources, and place any value independent source at the terminals. Then 2) Write a DE for the circuit (any variable) and  can be easily determined from the DE since it has the form:

  3. Lecture #17 EGR 260 – Circuit Analysis Example: Find v(t) for t > 0 if v(0) = 2 V. A) Use method 1: Find t = REQC using

  4. Lecture #17 EGR 260 – Circuit Analysis Example: (continued) Find v(t) for t > 0 if v(0) = 2 V. B) Use method 2: Write a DE for v(t).

  5. Lecture #17 EGR 260 – Circuit Analysis • Unit Step Functions • Unit step functions have several important uses in electrical engineering, including: • representing piecewise-continuous signals • representing switches • defining functions for use with one-sided Laplace transforms (in EGR 261) Definition: u(t) = unit step function where and u(t) is represented by the graph shown below.

  6. Lecture #17 EGR 260 – Circuit Analysis • A good way to think of a unit step function is as follows: • u(argument) = 1 for argument > 0 • u(argument) = 0 for argument < 0 • the transition in u(argument) occurs where argument = 0 Example: Graph 4u(t - 2) u(argument) = 0 for argument < 0. Note that for t < 2, u(t - 2) has a negative argument. For example, when t = 1, u(t - 2) = u(1 - 2) = u(-1) = 0. u(argument) = 1 for argument > 0. Note that for t > 2, u(t - 2) has a positive argument. For example, when t = 3, u(t - 2) = u(3 - 2) = u(+1) = 1. The transition occurs when the argument = 0. Note that when t = 2, u(t - 2) = u(2 - 2) = u(0).

  7. Lecture #17 EGR 260 – Circuit Analysis • Example: Graph the following functions: • 1) -2u(t - 10) • 2) 3u(t + 2) • 4u(-t) • 4) 4u(2-t)

  8. Lecture #17 EGR 260 – Circuit Analysis Example: Graph the following functions (continued): 5) 6u(-4-t) 6) u(-t) 7) Show that 1 - u(t) = u(-t) 8) sin(t) and sin(t)u(t)

  9. Lecture #17 EGR 260 – Circuit Analysis Example: Graph the following functions (continued): 9) u(t) - u(t - 2) 10) f(t) = 2t 11) 2t[u(t) - u(t - 2)] - discuss the concept of a “window”

  10. Lecture #17 EGR 260 – Circuit Analysis Example: Graph the following functions (continued): 12) f(t)[u(t - 2) - u(t - 4)] for any f(t) 13) (2t + 6)[u(t + 2) - u(t - 2)]

  11. Lecture #17 EGR 260 – Circuit Analysis • There are two common types of problems in representing functions using unit step functions: • 1) Determining the function that represents a given graph • Approach: Represent each unique portion of the function using unit step “windows” • 2) Graphing a function specified by unit steps • Approach: As each unit step function “turns on”, graph the cumulative function. • Examples of determining the function that represents a given graph: • Approach: Represent each unique portion of the function using unit step “windows”

  12. Lecture #17 EGR 260 – Circuit Analysis • Examples of graphing a function specified using unit steps functions: • Approach: As each unit step function “turns on”, graph the cumulative function. • 1) Graph f(t) = 2u(t) + 4u(t – 2) – 8u(t – 4)

  13. Lecture #17 EGR 260 – Circuit Analysis 2) Graph f(t) = (t + 2)u(t + 1) + (3 – t)u(t – 2) - (2t-5)u(t – 4) 3) Graph f(t) = 4sin(4t)[u(t) – u(t – 1)]

  14. Lecture #17 EGR 260 – Circuit Analysis Using unit step functions to replace switches in circuits Unit step functions are commonly used to represent switches in circuits. Consider the following examples. • Example: A unit step function is used below to replace a switch connecting a voltage source. • Discuss the value of VX. • Discuss the forms of the solution.

  15. Lecture #17 EGR 260 – Circuit Analysis • Example: A unit step function can be used to replace a switch disconnecting a current source. • Discuss the concept of a “make before break” switch • Discuss the value of IX. • Draw two possible circuits using unit step functions that are equivalent to the • circuit shown below.

  16. Lecture #17 EGR 260 – Circuit Analysis Example: Determine an expression for v(t) in the circuit below. Use the “shortcut method.”

More Related