re: [SI-LIST] : Formulas for Calculating PTH Capacitance

fabrizio zanella (fabrizio=zanella%eng%[email protected])
Tue, 23 Sep 97 14:50:12 -0400

Chris, look in page 257 of Howard Johnson's book: High Speed Digital Design,
A Handbook of Black Magic", for a formula to calculate via capacitance.
(book ISBN: 0-13-3957244, Prentice Hall).
The formula is C (in pF) = (1.41*Er*T*D1)/( D2-D1)

T=board thickness
D1 = Diameter of pad
D2 = Dia of clearance
Another book highly recommended is "Computer Circuits Electrical Design",
by Ron Poon, Prentice Hall ISBN 0-13-213471-3)
Both are practical books on high speed issues.

Fabrizio Zanella
Sr. Design Engineer
Hardware Engineering
_/ _/ email:
[email protected]
_/_/_/_/ _/ _/ _/_/_/ _/ voice: (508) 435-1000 Ext.
_/ _/_/ _/_/ _/ _/ Fax: (508) 435-8949
_/_/_/_/ _/ _/ _/ _/ _/_/_/
_/ _/ _/ _/ EMC Corporation
_/_/_/_/ _/ _/ _/_/_/ 171 South Street
Hopkinton, MA 01748-9103
Original Text
From: Chris_Heard/US/3Com%[email protected], on 9/23/97 9:40 AM:
To: [email protected]@EMCHOP1["si-list" <[email protected]>]

FROM too long. Original FROM is
"Chris Heard/US/3Com" <Chris_Heard/US/3Com%[email protected]>

---------------------- Original Message Follows ----------------------
Does anyone know of a way to calculate the capacitance of a plated thru
considering the following parameters:

a) PCB thickness
b) Number of layers where a clearance to a plane is used
c) Diameter of each clearance
d) Diameter of hole

Chris Heard
3Com Corporation
Southboro, M.A

----- Previous Message ----------------------------------------------------

To: si-list @ silab.Eng.Sun.COM @ SMTP1
AHardie @ @ SMTP1
cc: bcwadell @ @ SMTP1
From: bcwadell @ ("Brian C. Wadell") @ SMTP1
Date: Sunday September 21, 1997 06:08 PM
Subject: RE: [SI-LIST] : Transmission Line Conductors
On Thursday, September 18, 1997 6:19 PM, Alastair
Hardie[SMTP:[email protected]] wrote:
> All the transmission line impedance formulae that I can find do not take
> into account the
> conductor's properties such as conductivity and frequency dependant
> permeability (mu).
> Alastair Hardie.


Formulas for Z0 have an implicit or explicit term of eta0 (aka Z0 of free
space, 377 ohms). This is the Sqrt[(mu0 * murel)/(epsilon0 * epsilonrel)].

The mus are permeability and the epsilons are permittivities, the subscript
means "of free space".

Similarly, the propagation constant is more generally calculable as Sqrt[j
omega mu (sigma + j omega epsilon)] (2.2.27 in TLDH) which includes all the
terms you requested. Usually this is just reduced to the imaginary part
because the losses are small. Remember seeing all those 1/sqrt(eeff)'s?

These formulas can be modified for other mus and epsilons by plugging in
appropriate epsilon-rel-effective (er,eff) or mu-rel-effective (ur,eff).
is the reason I tried to make the eta0 (h0) explicit where ever I could in
book (for those of you who were wondering!).

Getting the values of mur,eff and er, eff for non-homogeneous dielectrics
microstrip line) is the big trick. Also, if you stray too far you open
regarding the mode's propagation.

> Does anyone know how a change in transmission line material part of the
> along it's length
> affects the transmission line's performance?

"Changing the material along its length" creates a different transmission
line. Model it as a new line in series along with the associated

BTW, in a related vein the value of tan delta you use is an "effective"
for the total dielectric structure. So tan delta,effective for stripline
the same as tan delta of the dielectric. However, tan delta,effective for
microstrip line (partly air dielectric) is lower than the actual tan delta
the dielectric.



Brian C. Wadell
Guided Wave Solutions
"Products That Make Waves"
73 Mount Vernon Street
Reading, MA 01867
Voice/Fax: (617)-942-WAVE