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Suppose that you have a series RLC circuit with driving input signal vin (t) and output Vout(t). The input-output relationship of this system can be written as Vin (t) = LC + RC dvout (t) dt d²vout(t) dt² Now suppose that for a specific circuit, the values of R, L and C are chosen such that we end up with the following differential equation describing the system. d²vout(t) dt² Vin (t) = 9! -6 dvout (t) dt +6 + Vout(t). + Vout(t). (a) Derive H(jw), the transfer function of the system. (b) Derive h(t), the impulse response of the system.

Suppose that you have a series RLC circuit with driving input signal vin (t) and output Vout(t). The input-output relationship of this system can be written as Vin (t) = LC + RC dvout (t) dt d²vout(t) dt² Now suppose that for a specific circuit, the values of R, L and C are chosen such that we end up with the following differential equation describing the system. d²vout(t) dt² Vin (t) = 9! -6 dvout (t) dt +6 + Vout(t). + Vout(t). (a) Derive H(jw), the transfer function of the system. (b) Derive h(t), the impulse response of the system.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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Suppose that you have a series RLC circuit with driving input signal vin (t) and output Vout(t). The input-output relationship of this system can be written as + RC dvout (t) dt d²vout (t) dt² Vin(t) = LC² Now suppose that for a specific circuit, the values of R, L and C are chosen such that we end up with the following differential equation describing the system. d²vout (t) dt² Vin (t) = 9! dvout (t) dt + 6- + Vout(t). + Vout(t). (a) Derive H(jw), the transfer function of the system. (b) Derive h(t), the impulse response of the system.
Transcribed Image Text:Suppose that you have a series RLC circuit with driving input signal vin (t) and output Vout(t). The input-output relationship of this system can be written as + RC dvout (t) dt d²vout (t) dt² Vin(t) = LC² Now suppose that for a specific circuit, the values of R, L and C are chosen such that we end up with the following differential equation describing the system. d²vout (t) dt² Vin (t) = 9! dvout (t) dt + 6- + Vout(t). + Vout(t). (a) Derive H(jw), the transfer function of the system. (b) Derive h(t), the impulse response of the system.
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