Laplace Circuit Analysis Preamble In this course we have modeled circuit elements (resistors, inductors, and capacitors) as linear and time invariant. We have used linear differential equations to determine the transients. We have modified this analysis for AC steady state by using jw with inductors and capacitors to form impedance. We coupled this with phasors to solve AC steady state circuits. In the case of Laplace transforms we take the Laplace transform of the voltages and currents that describe the circuit elements (resistors, capacitors, inductors). This converts the circuit models to functions of s as illustrated here. We then use all the methods of analysis that we learned for DC circuits such as nodal, mesh, Thevenin, Norton, to solve the Laplace circuits which we say are in the complex frequency domain. Everything is algebraic and it makes the problem(s) easier to handle than if we carried out everything in the time domain with integral, differential equations. Once we have found the particular variable we seek, such a voltage or current, we then take the inverse Laplace to go to the time domain. Electrical and Computer Engineering Department University of Tennessee Knoxville, Tennessee wlg

Laplace Circuit Analysis Circuit Element Modeling

Laplace Circuit Analysis Circuit Element Modeling Resistance Time Domain Complex Frequency Domain

Laplace Circuit Analysis Circuit Element Modeling Inductor

Laplace Circuit Analysis Capacitor

Laplace Circuit Analysis Linear Transformer

Laplace Circuit Analysis Time domain to complex frequency domain Oh man! What a mess.

Laplace Circuit Analysis Circuit Application: Given the circuit below. Assume zero IC’s. Use Laplace to find vc(t). The time domain circuit: Laplace circuit

Laplace Circuit Analysis Circuit Application:

Laplace Circuit Analysis Circuit Application: Given the circuit below. Assume vc(0) = - 4 V. Use Laplace to find vc(t). The time domain circuit: Laplace circuit:

Laplace Circuit Analysis Circuit Application: Check the boundary conditions vc(0) = - 4 V vc(oo) = 2 V

Laplace Circuit Analysis Circuit Application: Find i0(t) using Laplace

Laplace Circuit Analysis Circuit Application: Find i0(t) using Laplace Mesh 1

Laplace Circuit Analysis Circuit Application: Find i0(t) using Laplace Mesh 2

Laplace Circuit Analysis Circuit Application: Find i0(t) using Laplace Add these 2 equations

Laplace Circuit Analysis Circuit Application: Find i0(t) using Laplace Is final value of i2(t) reasonable?

That’s all Folks !