## Routh Criterion

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 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

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

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 […]

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