What is LC immitance function Explain with an exampleSolutio

What is LC immitance function? Explain with an example

Solution

LC Immitance Function

Property 1: Z_LC (s) or Y_LC (s) is the ratio of odd to even or even to odd polynomials

Consider the impedance Z(s) of passive one-port network.

                                                      Z(s)= M1(s)+M2(s)/N1(s)+N2(s)        

                                                               (M is even N is odd)

As we know, when the input current is I, the average power dissipated by one-port network is zero:

Average Power= 1/2 Re[Z(jw)]I² =0

Property 2:The poles and zeros are simple and lie on the jw axis

Z(s)=M1(s)/N2(s) or Z(s)=N1(s)/M2(s)

Since both M and N are Hurwitz, they have only imaginary roots, and it follows that the poles and zeros of Z(s) or Y(s) are on the imaginary axis.

For Ex:

Z(s)=a₄S⁴+a₂S²+a₀ /b₅S⁵+b₃s³+b₁s

In order for the impedance to be positive real à the coefficients must be real and positive.

Impedance function cannot have multiple poles or zeros on the jw axis.

The highest powers of the numerator and the denominator polynomials can differ by, at most, unity.

Property3:The poles and zeros interlace on the      jw    axis.

Property4:The highest powers of the numerator and denominator must differ by unity; the lowest powers also differ by unity.

Property5:There must be either a zero or a pole at the origin and infinity.

Ex: