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. […]
Foster’s Form of Network Synthesis
Foster’s Form of Synthesis Foster has given two type of network synthesis for one-port reactive network Series combination of parallel LC networks 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 […]
Network Synthesis-Part-1
Network Synthesis Network analysis: You are given a network then you analyse the behaviour (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 behaviour. Let us consider the network equations in terms of impedance […]
Positive Real Function (prf)
Positive Real Function (prf) We know that the driving point impedance (Z(s) and driving point admittance (Y(s))are of the following type: N(s) = P(s) / Q(s) The function is prf if: N(s) is real for s real Q(s) is Hurwitz polynomial If N(s) has poles on (jw) axis, poles are simple and residues thereof are […]
Routh Hurwitz Polynomial
Properties of the Hurwitz Polynomial: A polynomial to be Hurwitz when- P(s) is real when s ir real The roots of P(s) have real parts which are zero or negative. Properties of Hurwitz polynomial P(s) = ansn + an-1sn-1 +…………….a1s + a0 are: Coefficient of s must be positive Both odd and even parts of […]
Magnitude and Phase angle of the coefficients in the network function
Let the network function be written as : N(s) = P(s) / Q(s) Above equation consist of factors of general form where pr and pn are complex frequencies. Their difference is also a complex frequency which can be written as: Where Mnr is the magnitude of the phasor and Φnr is the phase angle of […]
Stability of a system based on Pole-zero
Stability of a system from Pole-zero concept Given a polynomial N(s) = P(s) / Q(s) By factorising the numerator and denominator polynomials, we can easily show that the polynomial becomes zero when the ‘s’ terms in the numerator polynomial have the values s=0, -z1,-z2…….-zn, thus the roots of numerator define the zeros. Also the roots […]
Concepts of Network functions (driving point and transfer function)
General Terminologies of a Two-Port networks: Network: A network is an interconnection of passive elements and dependent sources. There are no active or independent sources inside the box. The network is treated to be part of the square box shown in figure. Terminal: A terminal is the end point of the conductor which is connected […]
Open Circuit and Short Circuit impedance and Image Impedance
Open circuit and Short circuit impedance of a two-port network in terms of ABCD parameters From the generalized ABCD parameter equation V1=AV2 – BI2 I1=CV2 – DI2 Applying Open circuit at port-2; I2=0 we get V1= AV2; I1= CV2 Z1O = V1/I1= A/C ——————————(i) Applying the short circuit at port-2; V2=0, we get V1= […]
