Document Sample

First Order Circuits: RC and RL • A zero order circuit has zero energy storage elements. (Called a “purely resistive” circuit.) • A first order circuit has one (irreducible) energy storage element. • The equations that solve it are first order differential equations. • A second order circuit has two (irreducible) energy storage elements. • The equations that solve it are second order differential equations. Natural response • It is found by setting the input (forcing function) to zero. • It is characteristic of the circuit, not of the sources (i.e. forcing functions) • It will have the same number of arbitrary constants as the order of the differential equation. (These constants are determined from boundary conditions.) • It provides a transition from the initial values of x (voltage or current) to the final value. • It is also called the transient response. • It is also called the complementary solution. • It is also called the free response Source Free RL Circuit • There is no voltage through a inductor if the current is not changing with time. A inductor is therefore an open circuit to dc. • A finite amount of energy can be stored in a inductor even if the voltage through the inductor is zero, when the current across it is constant. • The inductor never dissipates energy, but only stores it. Source Free RL Circuit • Initial current through inductor i(0) ≠ 0 • Initial current will decay to zero overtime i(∞) = 0 General Solution • Apply KVL around the loop • Put the equation into “standard” form • Separate the variables-i and t Integrate Both sides Solve for i(t) Source Free RL Circuit • The time constant of a circuit is the time required for the response to decay by a factor of 1/e or 36.8% of its initial value. • i(t) decays faster for small and slower for large . Source Free RC Circuit • There is no current through a capacitor if the voltage is not changing with time. A capacitor is therefore an open circuit to dc. • A finite amount of energy can be stored in a capacitor even if the current through the capacitor is zero, when the voltage across it is constant. • The capacitor never dissipates energy, but only stores it. Source Free RC Circuit • Initial charge through capacitor v(0) ≠ 0 • Initial voltage will decay to zero overtime v(∞) = 0 General Solution • Apply KCL around the loop • Put the equation into “standard” form • Separate the variables v and t Integrate Both sides Solve for v(t) Time Constant זּ • The time constant of a circuit is the time required for the response to decay by a factor of 1/e or 36.8% of its initial value. • v decays faster for small and slower for large . Decays more slowly Time constant RC Decays faster Keys for Source-Free Circuit • RC Circuits • RL Circuits • = זּRC • = זּR/L • Find v(0) • Find i(0) • v(t)=v(0)e– t/ • i(t)=i(0)e– t/

DOCUMENT INFO

Shared By:

Categories:

Tags:
RC Circuit, RL Circuit, step response, time constant, Electric Circuits, Mesh analysis, capacitor voltage, Nodal analysis, RL circuits, Final Exam, Circuit Analysis, natural response, step function, free circuit, Transient analysis, New Delhi, RC circuits, Circuit Elements, Chapter 7, initial condition, RLC circuit, differential equation, Amp Circuits, Electric Circuit Analysis, ohms law, free circuits, how to, time t, complete response, DC Circuit, New Delhi, RC circuits, Circuit Elements

Stats:

views: | 2428 |

posted: | 4/1/2010 |

language: | English |

pages: | 17 |

OTHER DOCS BY bilalhasan

Docstoc is the premier online destination to start and grow small businesses. It hosts the best quality and widest selection of professional documents (over 20 million) and resources including expert videos, articles and productivity tools to make every small business better.

Search or Browse for any specific document or resource you need for your business. Or explore our curated resources for Starting a Business, Growing a Business or for Professional Development.

Feel free to Contact Us with any questions you might have.