Routh Criterion: Routh Criterion – The locations of the poles gives us an idea about stability of the active network. Consider the denominator polynomial To get a stable system, all the roots must have negative real parts. There should not be any positive or zero real parts. This condition is not sufficient. Let us consider …
Stability Criterion in Network Function: Stability Criterion – Passive networks are said to be stable only when all the poles lie in the left half of the s-plane. Active networks (containing controlled sources) are not always stable. Consider transformed active network shown in Fig. 14.13. By applying Millman Theorem, we get From the above transformed …
Poles and Zeros of Time Domain Response: For the given network function, a pole zero plot can be drawn which gives useful information regarding the critical frequencies. The Poles and Zeros of Time Domain Response can also be obtained from pole zero plot of a network function. Consider an array of poles shown in Fig. …
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 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: 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 – 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 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 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: 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 …