Distributed shunt admittance

[ktx2222]

Dear everyone,
I found an equation about the relation between distributed shunt admittance and permittivity:



I have not seen this equation before. Can anyone show me where I can look for concept about this or relation equations? Thank.

 

[FvM]

For a mathematically correct equation, a length quantity is missing.

It would be definitely helpful if you briefly explain the meaning of "distributed shunt admittance" or tell where you found the quote.

 

[ktx2222]

Dear FvM,

As we know a transmission line can be modeled with series L (H/m) and shunt C (F/m) lump elements. And distributed shunt admittance is Y (S/m)= j*w*C (where w is angular frequency and C (F/m) is model lump element). And in a paper, the authors mention the above relation.

I only know the distributed capacitor model and epsilon have same unit (F/m).

 

[FvM]

I think it's always problematic to use a well-known formula sign like C or Y for a different quantity like characteristic or "distributed" capacitance. It would prefer a sign like δC or C'. But I see that some textbooks are using this ambiguous symbols.

Technically, the formula has the right unit. Presumed that ε really means permittivity and not a second equivocal quantity, there is a geometry factor linking ε and C'. In case of a coaxial line, you get

C' = 2 pi ε/ln(ro/ri)

so the geometry factor is 2 pi/ln(ro/ri).

 

[ktx2222]

I also think that the ε cannot be equal to distributed capacitance δC. So the equation may be incorrect. I'm not sure about this.

Anyway, thank FvM.