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Realization of RL Functions:: Points To Keep in Mind

This document discusses the realization of RL functions in network synthesis. It outlines 5 properties that an RL immitance function must possess, including having simple poles and zeros located alternately on the negative real axis of the s-plane. It also notes that the admittance of an inductor is similar to the impedance of a capacitor, so RL admittance can be considered the dual of RC impedance and vice versa. Finally, it provides brief explanations of Foster Form I and II and Cauer Form I and II, and gives expressions for the RL immitance function ZRL(s) and admittance function YRL(s).

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Prashant Sharma
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218 views2 pages

Realization of RL Functions:: Points To Keep in Mind

This document discusses the realization of RL functions in network synthesis. It outlines 5 properties that an RL immitance function must possess, including having simple poles and zeros located alternately on the negative real axis of the s-plane. It also notes that the admittance of an inductor is similar to the impedance of a capacitor, so RL admittance can be considered the dual of RC impedance and vice versa. Finally, it provides brief explanations of Foster Form I and II and Cauer Form I and II, and gives expressions for the RL immitance function ZRL(s) and admittance function YRL(s).

Uploaded by

Prashant Sharma
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Network Synthesis

Realization of RL functions

Theory

Realization of RL Functions:
For a given function to be RL immitance function, it should posses
following properties:
1) Poles and Zeros are simple and should be located on the
negative real axis of s-plane.
2) Poles and Zeros should be alternate to each other.
3) Lowest critical frequency must be zero which may be near to
origin.
4) Highest critical frequency must be a pole near to infinity.
5) Residues evaluated at the poles of ZRL(s) are real and
negative while that of

()

are real and positive.

Note: The admittance of an inductor is similar to the


impedance of a capacitor. Thus properties of RL admittance
function are identical to those of an RC impedance function
and vice-versa.
It can be represented as follows,
ZRC(s) = YRL(s)
ZRL(s) = YRC(s)
Hence, RL admittance can be considered as the dual of RC
impedance and Vice-versa.

Points to keep in mind:


1. Foster I form is obtained by P.F.E of impedance function

()

2. Foster II form is obtained by P.F.E of the admittance function


Y(s).
1

Network Synthesis

Realization of RL functions

Theory

3. Cauer I form is obtained by C.F.E of given function about the


Pole at Infinity ().
4. Cauer II form is obtained by C.F.E of given function about
the Pole at Origin.
5. While realizing Cauer II forms arrange the Numerator and
Denominator polynomials in ascending order of s.
NOTE: For an RL immitance function:
ZRL(s) =

and

YRL(s) =

Both these expressions are used in realizing Foster Forms.

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