Given is the parallel connected RLC network as depicted in the figure below. L C R ↑ )I(t) The controllable current source (t) is the system input. The current ia(t) flowing through a resistive load is the system output. The constant system parameters are the resistance R, the capacitance C, and the inductance L. a) Using the Kirchhoff's current and voltage laws, derive and write down the linear differential equation which describes the input-output behavior of the RLC network. Based on that, derive the input-output transfer function. Calculate the poles and zeros of the system. Determine the parametric condition (i.e. relationship between R, L, and C values) for which the system has only the real poles and is, thus, not oscillatory.
Given is the parallel connected RLC network as depicted in the figure below. L C R ↑ )I(t) The controllable current source (t) is the system input. The current ia(t) flowing through a resistive load is the system output. The constant system parameters are the resistance R, the capacitance C, and the inductance L. a) Using the Kirchhoff's current and voltage laws, derive and write down the linear differential equation which describes the input-output behavior of the RLC network. Based on that, derive the input-output transfer function. Calculate the poles and zeros of the system. Determine the parametric condition (i.e. relationship between R, L, and C values) for which the system has only the real poles and is, thus, not oscillatory.
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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Circuit Theory
Electric circuits are a network that comprises of a closed-loop, which helps in providing a return path for the current through a switch. When the switch is activated, the load operates, and the current accepts a path to finish the circuit at a low potential level from the opposing high potential level. Electric circuits theory is a linear analysis that helps in establishing a linear relation of voltage and current for R (resistance), L (inductance), and C (capacitance).
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