From: Tom Woodward ([email protected])
Date: Thu Oct 21 1999 - 12:33:17 PDT
>> From: "Ingraham, Andrew" <[email protected]>
>>
>> An interesting question is what happens if you have a power/ground sandwich
>> around a high-Er material and another around a low-Er material, with the two
>> sets of planes stitched together regularly, which is what I think Tom
>> Woodward was asking. Can that let your noise source get access to more
>> "points" on the high-Er sandwich?
>>
>> Andy
This is indeed the question I was asking about. I've got a related question ---
see below.
>
>Andy - You bring up an interesting question that I considered some time
>ago. Suppose we have the stackup below with two parallel power planes
>referenced to a center ground plane. The relative permitivity of one
>dielectric is 4 and the other is 16:
>
>
> ======================== Vdd plane ======================
>
> eR=4 Vel = 0.5 * light
>
> ======================== Gnd plane ======================
>
> eR=16 Vel = 0.25 * light
>
> ======================== Vdd plane ======================
>
>If we started a plane wave on the edge of the PCB by stimulating each
>Vdd plane wrt the Gnd plane, a disturbance would propagate on the top
>layer wrt Gnd at half the speed of light (velocity is proportional to
>1/sqrt(eR) ) and at 1/4 the speed of light on the bottom plane. At the
>frequencies that we are concerned about in signal integrity, skin
>effect will keep the current on the top surface of the ground plane
>away from the bottom surface of the ground plane, and the top and
>bottom disturbances just move down the PCB without interfering with
>each other, one twice as fast as the other. The velocity is 1/sqrt(LC)
>where L is the inductance per inch and C is the capacitance per inch
>(easily calculated). If the dielectric thicknesses are the same, the
>capacitance of the bottom plane is 4x the capacitance of the top
>plane.
>
>Now suppose we stitch vias from the top Vdd plane to the bottom Vdd
>plane at regular intervals along the way. Neglecting the inductance of
>the vias, the top and bottom plane must be at the same potential wrt
>the Gnd plane. The wavefront on the top and bottom plane must now move
>at the same velocity, or at least re-adjust themselves at every via
>along the way.
>
>A good way to look at the stitched-together power planes is capacitors
>in parallel and inductors in parallel. It turns out that the
>inductance per inch of the connected power planes is half of the two
>independent power planes. The capacitance per inch is C + 4C = 5C,
>where C is the capacitance per inch of the top power plane and L is the
>inductance per inch of either power plane. So the velocity of the
>combined planes is 1/sqrt(0.5L*5C) = 1/sqrt(LC) * 1/sqrt(2.5). It ends
>up being 0.316 times the speed of light, which is somewhere between the
>velocity of each individual dielectric.
>
>In a real PCB, an ASIC or uP that draws power from the power plane is
>likely to located in the center of the board. In this case, a radial
>disturbance will emanate out from the noise source at a velocity that
>is consistent with the combined dielectrics.
>
>Hans Mellberg brought up the possibility of these same power planes
>providing return current for signal traces. This is certainly possible
>and commonly done. If there are signal traces adjacent to the Vdd
>planes (top and bottom in the above stackup), signals on those traces
>propagate at the velocity of light reduced by 1/sqrt(eR) where eR is
>the relative permitivity of whatever dielectric is between the trace
>and the Vdd plane. Once again, with copper power planes of normal
>thickness (1 or 1/2 oz copper), skin effect prevents any coupling
>between power plane currents and signal return currents at the
>frequencies that we are concerned about in signal integrity (greater
>than 10 MHz).
>
>regards,
>Larry Smith
>Sun Microsystems
Now suppose that the ground and power planes are perforated by
the anti-pads of many vias. Each anti-pad in a plane provides a skin
connection between the top and bottom surfaces of that plane. How
would the disturbances propagating on the top and bottom surfaces
interact with each other at these connection points?
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