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RC Complete Response

Errata: After title slide, the "Steady State Response" ended up under the output in the complete response equation. V-sub-S is the steady state response. This video describes the time domain complete response of an RC low pass filter circuit, with a shunt output capacitor. The video starts with mathematical equations for complete response and verbal equations for complete response in terms of ZIR, ZSR, natural, and step response. Next the video reviews RC natural and step responses, showing the equation alongside the circuits and the graphs of the output voltage. There is a substantial section relating the terms in the RC complete response equation to the simulation plots of complete response circuits with multiple examples of specific circuit values. The steps are shown to rearrange the RC complete response equation, from natural and step response terms to transient and steady state terms. Finally, a comparison is shown between the textbook simulations of complete response, using an initial condition capacitor voltage and an input voltage stepped from zero, to a practical circuit with the same output curves but no initial condition set in the simulation. For more technical background on RC circuits, including both intuition analyses and detailed derivations of natural and step responses, please see this book: “First and Second Order Circuits and Equations – Technical Background and Insights, which is available from John Wiley & Sons ISBN: 978-1-119-91353-5 https://www.wiley.com/en-us/First+and... 00:00 Introduction 00:12 ZIR ZSR Natural Step Responses in Words 00:48 Natural & Step Reponses Graphs 01:12 Complete Response Single Equation 01:23 Complete Response Equation Plots 01:30 Quiz Question Equations & Plots 01:47 Vout at Time Equals Zero 02:30 Complete Response at Time Infinity 03:13 Rearrange Complete Response Equations 03:49 Transient Term Magnitude 04:27 Capacitor IC Equals -0.5V 05:13 Quiz: Circuit Values from Graph 05:31 Simulated Capacitors Have Polarity 05:54 Quiz Answers Vs and Vc(0) from Graph 06:19 Textbook versus Practical 07:17 Same Curves in 2 Different Simulations 07:34 Circuit Theory Book Reference