Module 2

Two port networks

1

Contents

Circuit Theorems

2

• Short- circuit Admittance parameters
• Open- circuit Impedance parameters
• Transmission parameters
• Hybrid parameters

Introduction to two port networks

3

Short- circuit Admittance parameters

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5

6

7

Open- circuit Impedance parameters

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9

Transmission Parameters

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11

12

Hybrid Parameters

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14

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Module 2

Laplace transform and its Applications

1

Definition of Laplace Transform

The Laplace Transform is an integral transformation of a function f(t) from the time domain into the complex frequency domain, giving F(s)

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• s: complex frequency
• Called “The One-sided or unilateral Laplace Transform”.
• In the two-sided or bilateral LT, the lower limit is -∞. We do not use this.

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Properties of Laplace Transform

Step Function

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The symbol for the step function is K u(t).

Mathematical definition of the step function:

f(t) = K u(t)

Properties of Laplace Transform

Step Function

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A discontinuity of the step function may occur at some time other than t=0.

A step that occurs at t=a is expressed as:

f(t) = K u(t-a)

Properties of Laplace Transform

Impulse Function

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The symbol for the impulse function is δ(t).

Mathematical definition of the impulse function:

Properties of Laplace Transform

Impulse Function

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• The area under the impulse function is constant and represents the strength of the impulse.
• The impulse is zero everywhere except at t=0.
• An impulse that occurs at t = a is denoted K δ(t-a)

f(t) = K δ(t)

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Initial Value Theorem

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Final Value Theorem