Solutions of Problems on RC Circuits Network Analysis by Ravinder Nath Rajotiya - October 10, 20200 Solutions of Problems on RC Circuits Solution of problems on RC circuits
Cauer Form of Circuit Realization Network Analysis by Ravinder Nath Rajotiya - April 22, 2020June 4, 20200 Cauer Form of Circuit Realization Cauer introduced two forms of circuit realization from the network function. These are known as Cauer 1st Form of network/circuit realization : The network function used for realization is such that of n>m,where n is the degree of numerator (P(s)) polynomial and m is the degree of the denominator polynomial. This leads to a pole at ω=0 producing inductor as the first element. This form of circuit realization produces ladder type of circuit realization with 1st element as an inductor and the parallel element is a capacitor and this way a ladder is formed. Also to note that id the degree of denominator is more than the degree of numerator by one i.e. m>n then a zero
Foster’s Form 1 and 2 of Network Synthesis with examples Network Analysis by Ravinder Nath Rajotiya - April 22, 2020June 4, 20200 Foster's Form of Synthesis Foster has given two types of network synthesis for one-port reactive network Series combination of parallel LC networks The parallel combination of series LC networks Foster 1st Form When numerator polynomial is of higher degree than the denominator polynomial The first element capacitor is represented by A0/s The last element Inductor is represented by Hs corresponds t a pole at infinity 2Ai/(s2 + ω 2) represents the conjugate poles results in LC resonance. When no terms in the denominator of Z(s), there will not be any A0/s term indicating the absence of capacitor. Example: Obtain the first form of the Foster Network for the driving point impedance of LC network given as: Z(s) = 10(s2+4)(s2+16) / s(s2+9) Solution: It is observed from the
Network Synthesis Part-1 Lecture Notes Network Analysis by Ravinder Nath Rajotiya - April 22, 2020June 4, 20200 Network Synthesis Lecture Notes Network analysis: You are given a network then you analyze the behavior (output) by applying certain excitation. Network Synthesis: You know the output response for certain excitation, then you are required to find appropriate Z(s) or Y(s) that will give that desired behavior. Let us consider the network equations in terms of impedance and admittance: Process of network synthesis: let us first consider figure-1(a) Z(s) = Z1(s) + Z2(s) Rearranging, Z2(s) = Z(s) - Z1(s) That is we find Z2(s) by removing Z1(s) from Z(s). This removal of Z1(s) from Z(s) can be performed in following different ways: Removal of a pole at infinity: It means that the degree of P(s) is of one degree higher than the degree of Q(s). It infers that