# Electronics

# Solution: NAS MT-1 March 2020

# Solutions of Problems on RC Circuits

Solutions of Problems on RC Circuits Solution of problems on RC circuits

# Cauer Form of Circuit Realization

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

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