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

Chris Heard/US/3Com (Chris_Heard/US/3Com%[email protected])
23 Sep 97 9:40:33 EDT

Does anyone know of a way to calculate the capacitance of a plated thru hole
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

Thanks,
Chris Heard
3Com Corporation
Southboro, M.A
508-490-5616

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

To: si-list @ silab.Eng.Sun.COM @ SMTP1
AHardie @ compuserve.com @ SMTP1
cc: bcwadell @ guidedwave.com @ SMTP1
Date: Sunday September 21, 1997 06:08 PM
Subject: RE: [SI-LIST] : Transmission Line Conductors
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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.
>

Alastair,

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 0
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 the
appropriate epsilon-rel-effective (er,eff) or mu-rel-effective (ur,eff). That
is the reason I tried to make the eta0 (h0) explicit where ever I could in my
book (for those of you who were wondering!).

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

> Does anyone know how a change in transmission line material part of the way
> 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
discontinuities.

BTW, in a related vein the value of tan delta you use is an "effective" value
for the total dielectric structure. So tan delta,effective for stripline is
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 of
the dielectric.

Regards,

BCW