Circuits and Networks

Inverse Transformation

Inverse Transformation: We already discussed Laplace transforms of a functions f(t). If the function in frequency domain F(s) is given, the Inverse Transformation can be determined by taking the partial fraction expansion which will be recognizable as the transform of known functions. Laplace Transform of Periodic Functions: Periodic functions appear in many practical problems. Let […]

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Laplace Theorem

Laplace Theorem: The Laplace theorem is given by Differentiation Theorem Integration Theorem Differentiation of Transforms Integration of transforms First Shifting Theorem Second Shifting Theorem Initial Value Theorem Final Value Theorem (a) Differentiation Theorem: If a function f(t) is piecewise continuous, then the Laplace transform of its derivative d/dt [f(t)] is given by (b)Integration Theorem: If

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Laplace Properties

Laplace Properties: Laplace transforms have the following Laplace Properties. (a) Superposition Property: The first Laplace Properties is Superposition Property. The Laplace transform of the sum of the two or more functions is equal to the sum of transforms of the individual function, i.e. if Consider two functions f1(t) and f2(t). The Laplace transform of the

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Definition of Laplace Transform

Definition of Laplace Transform: The Definition of Laplace Transform is used to solve differential equations and corresponding initial and final value problems. Laplace transforms are widely used in engineering, particularly when the driving function has discontinuities and appears for a short period only. In circuit analysis, the input and output functions do not exist forever

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Transient Response of RLC Circuit

Transient Response of RLC Circuit: Consider a Transient Response of RLC Circuit consisting of resistance, inductance and capacitance as shown in Fig. 12.11. The capacitor and inductor are initially uncharged, and are in series with a resistor. When switch S is closed at t = 0, we can determine the complete solution for the current.

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Transient Response of RC Circuit

Transient Response of RC Circuit: Consider a Transient Response of RC Circuit consisting of resistance and capacitance as shown in Fig. 12.6. The capacitor in the circuit is initially uncharged, and is in series with a resistor. When the switch S is closed at t = 0, we can determine. the complete solution for the

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Transient Response of RL Circuit

Transient Response of RL Circuit: Considers a Transient Response of RL Circuit consisting of a resistance and inductance as shown in Fig. 12.1. The inductor in the circuit is initially uncharged and is in series with the resistor. When the switch S is closed, we an find the complete solution for the current. Application of

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