# Re: [SI-LIST] : Impedance of micro-strip over wide ground trace

[email protected]
Thu, 26 Mar 1998 15:36:08 -0800

Hi Roland,

Your original question concerned the impedance of a 40 conductor flex
circuit; it is not clear how this new question relates to your original

The general rule of thumb is that the finite width ground plane will be
indistinguishable from an infinite width ground plane (within a few percent)
when the edges of the ground are at least 3 times the height from edge of
the signal line, that is:

W > 6H + w

However, I should also say that with modern tools it is not necessary to
make such approximations. It is quite simple to calculate the impedance of
such lines with any width and spacing and including conductor thickness and
realistic dielectric shapes. In general the impedance is complex (real and
imaginary parts) and frequency dependent and this complex impedance can be
calculated in the low frequency limit, the high frequency limit, or in the
transition region. Even if there is no analytic expression for your
geometry of interest, one can often create a one or two dimensional curve
fit to a series of calculated data points when parameter variation is required.

Eric
---------------------------------------------------------------
Eric Wheatley Ph.D. (760) 942-9426 (phone)
Alterra Technology Co. (760) 942-2366 (fax)
435 Dunsmore Ct. [email protected]
Encinitas, CA 92024 US
---------------------------------------------------------------

At 02:13 PM 3/26/98 -0800, you wrote:
>[The following is related to a question I sent to the si-list about a 2
>layer flex circuit.]
>[My thanks to all of you who replied.]
>
>All the equations I have read assume an infinitely wide ground plane
>when
>calculating the impedance of a micro-strip. But in practice, how wide
>does the ground
>reference really need to be?
>
>As the width of the ground trace increases beneath the fixed width of
>the signal trace,
>at what width does the ground trace begin to take on the characteristics
>of a ground plane?
>
>In other words, if a signal, 'w' mils wide, was centered over a 'W' mil
>wide ground trace, at what width W would the resulting impedance be
>within a reasonable tolerance to the same signal trace over an infinitly
>wide ground plane?
>
>
> ----- w signal
> H
> --------------- W ground
>
>
>Could it be related to the equation for current distrubution under a
>trace?
>
>i(D) = (Io/piH) * 1/(1+ (d/h)sqrd)
>
>where
>
>Io = total signal current (Amps)
>H = height of trace above ground plane
>D = perpendicular distance from the signal trace (inches)
>i(D) = signal current density (Amps/inch)
>pi = 3.1415...
>
>[taken from "High Speed Digital Design" by Howard Johnson & Martin
>Graham; eq 5.1, pg 190]
>
>
>Roland
>
>--
>Roland F. Portman
>BiT Microsystems, Inc.
>48499 Milmont Drive
>Fremont, CA 94538
>
>(510) 623-2341 Ext 129
>(510) 623-2342 Fax
>
>[email protected]
>http://www.bitmicro.com
>
>
>
>