RC Circuits / Differential Equations
RC Circuits / Differential Equations OUTLINE • Review: CMOS logic circuits & voltage signal propagation • Model: RC circuit differential equation for V out(t) • Derivation of solution for V out(t) propagation delay formula EE16B, Fall 2015 Meet the Guest Lecturer Prof Tsu-Jae King Liu • Joined UCB EECS faculty in 1996
Chapter 7 Response of First-order RL and RC Circuits
Circuit model of a discharging RC circuit Consider the following circuit model: For t 0, the capacitor voltage decreases and the energy is dissipated via R
First-Order RC and RL Transient Circuits
First-Order RC and RL Transient Circuits When we studied resistive circuits, we never really explored the concept of transients, or circuit responses to sudden changes in a circuit That is not to say we couldn’t have done so; rather, it was not very interesting, as purely resistive circuits have no concept of time
MODELING FIRST AND SECOND ORDER SYSTEMS IN SIMULINK
Modeling a First Order Equation (RC Circuit) The RC Circuit is schematically shown in Fig 1 below R Vin C Vout Fig 1 The RC Circuit The differential equation for this is as show in (1) below [f(t) x RC 1 x&= −] (1) Where (xdot) is the time rate of change of the output voltage, R and C are constants, f(t) is the
Outline Differential Equations I
1 RC circuit f(t) = eiωt 2 RC circuit with sinωt input Special Case for Exponential Inputs Suppose the solution to the characteristic equation λ = a is also the negative of the exponent of the forcing function as dy(t) dt +ay(t) = ke−at with y(0) = Y 0 (5) The equation has the normal homogeneous solution but the particular solution
Circuits RC, RL, RLC - pagesperso-orangefr
Circuits RC, RL, RLC par Gilbert Gastebois 1 Oscillations libres amorties dans un circuit RLC 1 1 Équation différentielle du circuit Ldi/dt + Ri + q/C = 0
DC Circuits
DC Circuits • Resistance Review • Following the potential around a circuit • Multiloop Circuits • RC Circuits Homework for tomorrow: Chapter 27 Questions 1, 3, 5 Chapter 27 Problems 7, 19, 49
Parallel RLC Second Order Systems
• Then substituting into the differential equation 0 1 1 2 2 + + v = dt L dv R d v C exp() exp()0 1 2 exp + + st = L A sA st R Cs A st • Dividing out the exponential for the characteristic equation 0 2 + 1 + 1 = LC s RC s • Giving the Homogeneous equation • Get the 3 same types of solutions but now in voltage • Just parameters are
Characteristics Equations, Overdamped-, Underdamped-, and
Find characteristic equation from homogeneous equation: a x dt dx a dt d x 2 1 2 2 0 = + + Convert to polynomial by the following substitution: n n n dt d x s = 1 2 to obtain 0 =s2 +a s+a Based on the roots of the characteristic equation, the natural solution will take on one of three particular forms Roots given by: 2 4 2 2 1 1 1,2 a a a s
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