[SI-LIST] Re: Need technical ammunition for switching to single ground plane !

--- In si-list@xxxxxxxxxxxxxxx, "Gilles Aminot" <gilles.aminot@...> 
wrote:
>
> Hi Everyone,
>  
> I'm working on a new design and would like to eliminate split ground
> planes. In the past we've always split the analog ground plane (for
> analog audio circuits and codecs) and joined it at one location
> (sometimes shorting or through an inductor). I've read lot's of 
postings
> on this group explaining good reasons not to split ground planes, 
but
> the only real supporting documentation I have seen is the following
> article: 
> 
http://www.analog.com/analog_root/static/pdf/raq/RAQ_groundingADCs.pdf
> 
<http://www.analog.com/analog_root/static/pdf/raq/RAQ_groundingADCs.pd
f>
> and it does not provide much depth..
>  
> I have been meeting some resistance to eliminating the split ground
> planes and I am looking for technical articles showing the 
advantages of
> using a single ground plane in designs with mixed high speed 
digital and
> sensitve analog circuits. I keep bumping my head against datasheets 
or
> articles that say analog & digital grounds should be separated 
(such as:
> http://www.ultracad.com/articles/planesplits.pdf), which makes it
> difficult to convince my peers that changing our approach is the 
way to
> go. Can anyone share or point me to articles which may help me 
plead my
> case. I would also appreciate if anyone could share some real life
> experiences of going from split to single ground plane.
>  
> Kindest Regards,
> Gilles Aminot, P.Eng
> Hardware Design Engineer
>  
> Librestream Technologies Inc
> Unit 200 - 55 Rothwell Rd
> Winnipeg MB. Canada
> R3P-2M5
> PH: 204-487-0612 Ext 218
> FX: 204-487-0914
Dear Gilles,

I've also worried about the question of whether or not to use split 
analogue and digital ground planes. At first I was convinced to split 
the planes by the argument in the note "MT-031: Grounding Data 
Converters and Solving the Mystery of AGND and DGND" by Walt Kester, 
James Bryant and Mike Byrne which is on the analog devices website.  
My understanding of their argument is that noisy digital switching 
currents flowing in the distributed inductance of the ground plane 
can be modelled as a noisy emf generator in series with the ground 
return; so, one splits the ground plane into an analogue section and 
a digital section in order to prevent the noisy digital emf adding to 
an analogue signal. The noisy emf in the digital ground return  still 
adds to digital signals, but this does not matter because the 
discrete digital levels have typically 300mV of noise immunity. 

However, nowadays I'm not convinced that the physical situation is 
correctly modelled by an emf generator in series with the ground 
return. I've not been able to bounce my argument off anyone else, so 
I'll try it out on the readers of SI-list.
 
Let the power and ground planes be the x-y planes in the coordinate 
system. The z-axis is perpendicular to the power and ground planes.  
It seems reasonable to assume that the electric field between the 
planes is purely in the z-axis (TM mode) and is constant along the z-
axis in the gap between the planes of the pcb. In other words the 
electric field is E(x,y,z)=3DEz(x,y)ez where the unit vectors are 
ex,ey,ez. Now, instead of solving the equations for the electric and 
magnetic fields, one writes them in terms of a scalar potential V and 
a vector potential A. The electric field is,
E=3D-grad(V)-iwA                      (1)
where the time-dependence of the fields is exp(iwt). It seems to me 
that one can take the scalar potential as,
V(x,y,z)=3D-Ez(x,y)z                  (2)
and then by taking the gradient,
grad V=3D-z(@Ez/@x)ex-z(@Ez/@y)ey -Ez(x,y)ez  
where @ denotes the partial derivative, one gets the electric field 
as,
E=3DEz(x,y)ez=3D-(grad V)-z(@Ez/@x)ex-z(@Ez/@y)ey  (3).
Upon comparing equations (1) and (3) one finds that the vector 
potential is,
A=3D-z(@Ez/@x)ex-z(@Ez/@y)ey                     (4).
I don't think that there is anything wrong with taking the scalar 
potential as in equation (2) because the scalar and vector potentials 
are not unique; they overdetermine the E and B fields and so one is 
always free to impose a gauge condition (e.g. div(A)=3D0) which is just 
some additional equation satisfied by the scalar and vector 
potentials.  Now suppose one works out how things appear in terms of 
a circuit model. Suppose one takes a circuit path  PQRS as shown in 
figure 1. The gap between the power and ground planes is a height h.

    power plane  z=3Dh   R------------------S
                       |
    ground plane z=3D0   Q----------P
              Figure 1: Circuit path
Integrate the total E field on the LHS of (3) along the path PQ in 
the ground plane.
S E.dl=3D-S grad(V).dl  -S{z(@Ez/@x)ex.dl +z(@Ez/@y)ey.dl}     (5)
Here S is the integral sign and dl is the line element and the dot is 
the dot product. The total electric field on the LHS is in the z-axis 
so the line integral in the ground plane is zero on the LHS of (5).
The integral of the vector potential is also zero because the ground 
plane path PQ is always at z=3D0. The only non-zero term is the 
integral over the gradient of the potential. Therefore, (5) becomes,
0=3D-V(Q)+V(P)                   (6)
which shows that the potential is a constant on the ground plane; 
there is no emf generator in series with a ground path. Also putting 
z=3D0 in (2) shows the ground plane is at zero volts. Now integrate (3) 
over the path PQR in figure 1. Now one gets,
hEz(x,y)=3D-V(R)+V(P)
and so,
V(R)-V(P)=3D-hEz(x,y)                  (7)
so that the potential difference between R and Q can be modelled by 
an emf generator -hEz(x,y) between the power and ground planes. (The 
vector potential also contributes an emf generator in the path RS in 
the power plane.) So, it seems to me that the gauge freedom allows 
one to consider the ground plane as an equipotential and all the 
switching noise appears as a noise emf generator connected from 
the ground to the power rail. Using this argument, I convinced myself 
that one should use a contiguous ground plane and split the analogue 
and digital power planes; the argument in MT-031 is wrong because the 
noisy emf generator is not in series with the ground return, but is 
connected between the ground and power rails.

Yours sincerely
Stephen Blake
International Metrology Systems Ltd
2 Dryden Place
Bilston Glen Industrial Estate
Loanhead, Scotland EH20 9HP
Tel: 44 131 440 7506






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