Bài giảng Electrical and electronic principles: Chương 7 - ThS. Ngô Quốc Cường

Những nội dung chính được trình bày trong bài giảng Electrical and electronic principles - Chương 7 gồm có: Laplace transform, circuit element models, circuit analysis, transient analysis. Mời các bạn cùng tham khảo.

• Trigonometric Fourier series

• Plot function - MATLAB

• Circuit Application (Applying Fourier series)

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• The Laplace transform is an integral transformation of a

function f (t) from the time domain into the complex frequency domain, giving F (s)

• Where s is a complex variable: 𝑠 = 𝜎 + 𝑗𝜔

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• Determine the Laplace transform of

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• Laplace transform

pairs (f(t) = 0, for t < 0)

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• Laplace transform

pairs (f(t) = 0, for t < 0)

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• Inverse Laplace transform

1 Decompose F(s) into simple terms using partial fraction

expansion

2 Find the inverse of each term by matching entries in the

previous table

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• Find the inverse Laplace transform of

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• Answer:

𝑓 𝑡 = 3𝑢 𝑡 − 5𝑒−𝑡𝑢 𝑡 + 3 sin 2𝑡 𝑢(𝑡)

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• Find f(t) given that

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• Answer:

𝑓 𝑡 = (2 − 8𝑒−2𝑡 + 7𝑒−3𝑡)𝑢(𝑡)

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• For a resistor

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• Representation of an inductor:

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• Representation of a capacitor:

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• Impedance of elements in the s-domain (zero initial condition)

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• Steps in applying the Laplace transform

1 Transform the circuit from the time domain to the s-domain

2 Solve the circuit using nodal analysis, mesh analysis,

sourcetransformation, superposition, or any circuit analysis

techniquewith which we are familiar

3 Take the inverse transform of the solution and thus obtain

thesolution in the time domain

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• Find v o (t) in the circuit, assuming zero intial condition

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• Answer:

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• The switch closes the circuit at t = 0 Find i(t) for t > 0

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i(t)

• Multisim computes the circuit’s response as a function of

time

• Each input cycle is divided into intervals, and a DC analysis

is performed for each time point in the cycle

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