Designing a Foster 1 Network for Impedance Testing

[DODGEVIPER13]

Homework Statement

Design and show a foster 1 network

z=(x^2+4)/(x(x^2+2))

Homework Equations

The Attempt at a Solution

So first I did the partial fraction expansion and I got (2/x)-(x/(x^2+2)). Next I got everything in the denominator so (1/x/2)-(1/(x+(2/x)) when I do this though I get all capacitors I get one series capacitor at (1/2) and one capacitor at 1 which is in parallel with (1/2) iis this wrong?

 

[DODGEVIPER13]

I guess what I should ask is a foster netwrok possible with only capacitors

 

[DODGEVIPER13]

Well actually it will be an LC network not RC and Z(0)=infinity and Z(infinity)=1 so there will be a series inductor. This also means one of the capcitors will actually be an inductor with a value of 1/8. But how do you test Zsmall and Zlarge?