Hello  Chunho Lee,

I made once the effort to demonstrate Johnson via capacitance my-myself, here is my demonstration and conclusion

- picture the via being a cylinder diameter=D1
- picture a second cylinder wrapped around the first one D2>D1
        - this second one represents power/gnd planes
- both cylinders are iso-potential
- un-fold both cylinders and you end up with two parallel plates.
        - the separation between the plates is the via clearance 1270-711(D2)
        - the height of both cylinders is the board thickness (T)
        - the width of the cylinder is the via circumference times pi=3.1416... (pi*D1).

Now let do the math using Johnson example as a reference:

- er=4.7
- T=63mil  ---> 1600um
- D1=28mil ---> 711um
- D2=50mil ---> 1270um

....Cvia = 1.41*4.7*0.063*0.028/(0.050-0.028) = 0.53pF

Now using two parallel plates capacitance formula:

Cvia= er*eo*A/d = er*eo*T*D1*pi/(D2-D1), eo=8.85aF/um

= 8.85aF/um*4.7*1600um*711um*pi/(1270um-711um)
= 265795aF = 0.265pF

Now here is something curious, if we then multiply again by 2

Cvia = 0.531pF !!! bang on

Assuming my demonstration process is fine, 
have they assumed the circumference is 2*pi*diameter?

Pierre-Luc Cantin
Sr. ASIC Designer /
SI Team Leader

[email protected]

phone (514) 931-5335 x217
fax.  (514) 931-9923


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-----Original Message-----
From: [email protected]
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[email protected]
Sent: Saturday, September 16, 2000 1:08 AM
To: [email protected]
Subject: [SI-LIST] : parasitic value for via

Hello everyone.

I am looking for parasitic value for via.
and Dr Johnson's derivation is ...

 where D2= diameter of clearance hole in GND plane,
       D1= diameter of pad surrounding via,
       T = thickness of PCB,
       Er= permeability.

parasitic inductance of via :
  L= 5.08h[ln(4h/d)+1]
 where h= length of via,
       d= diameter of via.

Let me explain
How this equation is derived?



 Chunho Lee,                                
 Senior Engineer,        
 E-CIM, Management Innovation Team,
 416, Maetan-3dong, Paldal-gu,
 Suwon city, Korea                                  
 Tel : 82-31-200-3097
 email: [email protected]

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