Conditions For Driving Point Function: The restrictions on pole and zero locations in the Conditions For Driving Point Function with common factors in P(s) and Q(s) cancelled are listed below. 1. The coefficients in the polynomials P(s) and Q(s) of network function N(s) = P(s)/Q(s) must be real and positive. 2. Complex poles or imaginary […]
Poles and Zeros of Transfer Function
Poles and Zeros of Transfer Function: Poles and Zeros of Transfer Function defines that, in general, the network function N(s) may be written as where a0,a1,…a2 and b0,b1,…bm are the coefficients of the polynomials P(s) and Q(s); they are real and positive for a passive network. If the numerator and denominator of polynomial N(s) are factorized, the […]
Transfer Function of Two Port Network
Transfer Function of Two Port Network: For a one-port network, the driving point impedance or impedance of the network is defined as The reciprocal of the impedance function is the driving point admittance function, and is denoted by Y(s). For the Transfer Function of Two Port Network without internal sources, the driving point impedance function […]
Gate Function in Network Function
Gate Function in Network Function: Gate Function in Network Function – By the use of step functions, any pulse of unit height can be realized. The pulse of width a can be generated by combining unit step function u(t) and delayed inverted unit step function by a time interval a as shown in Fig. 14.6. […]
Unit Ramp Function
Unit Step Function | Unit Ramp Function | Unit Impulse Function | Unit Doublet Function: a) Unit step function: This function has already been discussed in the preceding It is defined as one that has magnitude of one for time greater than zero, and has zero magnitude for time less than zero. A unit step […]
Application of Laplace Transform
Application of Laplace Transform: Application of Laplace Transform methods are used to find out transient currents in circuits containing energy storage elements. To find these currents, first the differential equations are formed by applying Kirchhoff’s laws to the circuit, then these differential equations can be easily solved by using Laplace transformation methods. Consider a series […]
Laplace Transform Partial Fraction
Laplace Transform Partial Fraction: Most transform methods depend on the partial fraction of a given transform function. Given any solution of the form N(s) = P(s)/Q(s), the inverse Laplace transform can be determined by expanding it into partial fractions. The Laplace Transform Partial Fraction depend on the type of factor. It is to be assumed […]
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 […]
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 […]
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 […]