## General Mechanical

Topics relate to Mechanical Enterprise, Motion, Additive Print and more

#### Capacitance analysis of parallel plate capacitors in MAPDL

• ty_jpn
Subscriber

Dear everyone

Hi,The following script was created to determine the fringe capacitance of parallel plate electrodes in MAPDL.

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do,i,0,100,10 !変数，初値，終値，増幅度(ループの始まり)

fini
/cle

/vie,1,1,1,1
/sys,del file*.png

/PREP7

C*** Plate dimensions (um scale)
eps0=8.854e-12 ! FREE SPACE PERMITTIVITY

width = (100*1e-6) + (i*1e-6)
height = 20*1e-6
thickness = 3*1e-6
separation = 10*1e-6

d_dmn = 10*1e-6 ! DEPTH SURROUNDING DOMAIN EXTENDS BEYOND ELECTRODES
d_inf = 5*1e-6 ! DEPTH OF INFINITE BOUNDARY ELEMENT MESH

esz = 3*1e-6  ! MESH SIZE

V = 0.01 ! APPLIED VOLTAGE

C*** Configured for electrostatic analysis of 3D 8-node elements
ET,1,SOLID123

C*** Define infinite element
ET,2,111,2,1

C*** Material properties (relative dielectric constant in vacuum)
!MP,PERX,1,8.854e-12 ! THIS IS ABSOLUTE PERMITTIVITY IN MKS, WHICH WORKS OK, BUT...
MP,PERX,1,1 ! WE GENERALLY USE RELATIVE PERMITTIVITY INSTEAD

BLOCK,0,width,0,height,0,-thickness
cm,electrode1_a,area

C*** Create second plate
asel,none
BLOCK,0,width,0,height,separation,separation+thickness
cm,electrode2_a,area

C*** SURROUNDING DOMAIN
alls
cm,scrap1_v,volu
*get,xmin,kp,,mnloc,x
*get,xmax,kp,,mxloc,x
*get,ymin,kp,,mnloc,y
*get,ymax,kp,,mxloc,y
*get,zmin,kp,,mnloc,z
*get,zmax,kp,,mxloc,z
vsel,none
bloc,xmin-d_dmn,xmax+d_dmn,ymin-d_dmn,ymax+d_dmn,zmin-d_dmn,zmax+d_dmn
cm,scrap2_v,volu
alls
vsbv,scrap2_v,scrap1_v

C*** MESH
esiz,esz
vmes,all

C*** ELECTRODE VOLTAGE
da,electrode1_a,volt
da,electrode2_a,volt,V

fini

C*** SOLVE
/solu
alls
save
solv
fini

C*** POST PROCESS
/post1

etab,w,sene ! BASED ON ENERGY
ssum
*get,Wnet,ssum,,item,w
C1 = 2*Wnet/(V**2)

nsel,s,d,volt ! BASED ON CHARGE & VOLTAGE
fsum
*get,q,fsum,,item,chrg
c2 = q/v

C_nominal=eps0*(height*width)/separation ! NOMINAL FRINGE FREE VALUE

/tla,-0.35,0.90,Capacitance (ANSYS, energy) = %C1% Fd ! ANNOTATION
/tla,-0.35,0.85,Capacitance (ANSYS, Q/V) = %C2% Fd
/tla,-0.35,0.80,Capacitance (nominal fringe-free) = %C_nominal% Fd

alls ! CAPPED SECTION PLOTS
wpro,,,90
wpof,,,width/2
/type,1,7
/cpl,1

*enddo  !指定の値で終わり

plns,volt
/sho,png \$plns,volt \$/sho,close \$/wait,2
plve,ef,,,,vect,,on
/sho,png \$plve,ef,,,,vect,,on \$/sho,close \$/wait,2

/eof
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The capacitance of only the overlapping electrodes can be determined by a theoretical formula, but how should the capacitance be approached taking into account the electric field of the fringes?
In this script, the do syntax is turned and parsed using the length of the electrode as a parameter.

Best regards, and thank you.

Takabayashi

• Bill Bulat
Ansys Employee

Hi Yuuhi,

I'm sorry I don't quite understand your question. The input file creates annotated images such as the one below. The first two lines of annotation report the MAPDL-calulated capacitance including fringing deduced from results in two different ways. The third line reports the analytical fringe-free value, which is, as we expect, smaller.

Maybe I'm missing something, but I don't see how you are using loop variable "i" to vary the size or separation of the plates. Are you asking how to vary the geometry in a do loop to investigate the effect of geometry on fringing and capacitance?

Or are you asking for an analytical expression that accounts for field fringing so that you can validate the calculated value from the finite element model? You might have to search the internet for that. I don't think that this article is exactly what you want, but it might help give you an idea what kind of articles you might find if you look further:

(PDF) Effect of Fringing Fields on the Capacitance of Circular Microstrip Disk (researchgate.net)

Kind regards,

Bill

• ty_jpn
Subscriber

Hi Bill．

Thank you very much for reply.

The effect of the fringe electric field is simulated for each of the given capacitor dimension parameters, with the aim of deriving an approximate analytical expression. (e.g. the respective effects when looping the capacitor width in the do syntax from 0-200).

I understand about the annotations on theoretical values and fringe electric field estimation.

I want to output a list of the results when I loop through the results with the do syntax for this purpose.

Best regards, and thank you.

Takabayashi