lumped model equivalent capacitance

[VERI]

Hello, I want to ask which is the right way to compute the equivalent capacitance of the lumped model? Can we transform C11,C22 to an equivalent capacitance between Port1,Port 2 nodes? thanks!

 

[BigBoss]

It depends on which type of capacitor you used. Lumped or Integrated..
As I can see you're using an Integrated Bonding Wire Equivalent Circuit and it doesn't need an extra Lumped Models for Stray Capacitors, Instead, you should find stray Cxx Capacitors to characterize this circuit properly.
Cxx Capacitors are already Ideal Stray Capacitors and they have not be modeled again.
In order to find those elements, there are few Bonding Wire Extractors or EM Simulators. They will give an equivalent circuit that will resemble to your circuit ( or SPICE Model Equivalent )

 

[VERI]

Is there a simplified equation for capacitance between nodes 1 and node 3 ?
Is it right to say that it is equal to ((C12*C22)/(C12+C22))+C11 for node 1 and for node 3 ((C34*C44)/(C34+C44))+C33?

 

[FvM]

Capacitance to gnd (C11 and C22) and capacitance C12 between port 1 and 2 are not related in any way. In so far the calaculation makes no sense.

 

[KlausST]

Hi,

Capacitance to gnd (C11 and C22) and capacitance C12 between port 1 and 2 are not related in any way. In so far the calaculation makes no sense.

I´m not experienced with HF .. but for low frequency the formula makes sense.

It could also be expressed as:
C_diff = C12 + 1/(1/C11 + 1/C22).

Explanation:
C11 and C22 act as if they were in series, thus: 1/(1/C11 + 1/ C22)
and then the equivalent capacitance is in parallel to C12, thus they are added.

****
For sure in a HF view only a part of the trace length is active.
Thus the capacitors combined with the inductances form the characteristic_impedance of the traces.
(independent of trace length)

Klaus

 

[volker@muehlhaus]

the right way to compute the equivalent capacitance

What is "the" equivalent capacitance? If you try to further reduce this model, you first need to define what mode you model, differential mode or common mode.

 

[KlausST]

Hi,

equivalent capacitance between Port1,Port 2 nodes

My guessing was that "between ports" means differential. I could be wrong.

Klaus

 

[PlanarMetamaterials]

What is "the" equivalent capacitance? If you try to further reduce this model, you first need to define what mode you model, differential mode or common mode.

I think in post 3 the poster indicates they are looking for a terminal-domain value, not a modal one.

That being said, the OP (#1) seems to suggest they want the differential-mode response (although differential and common modes would only exist if the components are symmetric about the center horizontal axis).

 

[volker@muehlhaus]

I think in post 3 the poster indicates they are looking for a terminal-domain value, not a modal one.

But for the general 4-port, we already have the minimum possible model in the original post !?

If the task is indeed to find the simplified model for differential mode, as you already mentioned we would expect symmetry about the centerline (e.g. C11=C22) which helps to simplify the model.

It would help to have some background information what the task is here. The pi model could represent a line segment (1,2 to 3,4) or a transformer (1,3 and 2,4), so the method for extracting equivelent values would be rather different.