[SI-LIST] Re: AC Coupled Signals
- From: "Dmitriev-Zdorov, Vladimir" <vladimir_dmitriev-zdorov@xxxxxxxxxx>
- To: <si-list@xxxxxxxxxxxxx>
- Date: Tue, 25 Sep 2007 12:13:22 -0700
Hi Steve,
> Would either of you agree that AC coupling capacitor location may
> matter with a lossy interface to the capacitor?
Here is an example where the position of series capacitor affects the
transfer function (and hence the eye-diagram!) for a completely LINEAR,
LOSSLESS channel with matching end load impedance.
The difference is substantial if the value of the capacitor is not too
small compared to the cumulative capacitor of the transmission line. The
difference is most noticeable at LOW frequency that might be important
for signal patterns with many repeating 'ones' or 'zeros' in a row.
Please see / run this simple Matlab script below. It is supplied with
comments so should be self-explanatory. Try k1 =3D 0.8 and k1 =3D 0.2, =
see
the difference.
% ----------------------START--------------------
% Input: ideal voltage source
% Channel: first T-line segment, Cseries, second T-line segment;
% both line segments have same p.u.l. parameters
% load: matching characteristic impedance of the line
% series capacitor, may be not as big
Cser =3D 100e-9;
% total trace length=20
Lngth =3D 20;
% factor showing how much of the total is the length of seqment 1
k1 =3D 0.8;
% length of seqment 1
l1 =3D Lngth * k1;
% length of seqment 2
l2 =3D Lngth * (1-k1);
% P.U.L. inductance and capacitance
L =3D 1e-6;
C =3D 1e-8;
% 2*pi*frequency, from 1e4 to 1e8, 1000 points total
w =3D logspace(4,8,1000);
% laplace operator
s =3D sqrt(-1)*w;
% propagation opetaror of seqment 1 (defined for all frequencies)
W1 =3D exp(-l1 * s * sqrt(C*L));
% propagation opetaror of seqment 2
W2 =3D exp(-l2 * s * sqrt(C*L));
% characteristica admittance (same for both, constant)
Y0 =3D sqrt(C/L);
% impedance of series capacitor
Zc_ser =3D 1./(s*Cser);
% matched load
Zload =3D sqrt(L/C);
% # of frequency points
N =3D max(size(w));
% transfer function, will be: Voutput / Vinput for all frequencies
Transfer =3D zeros(N,1);
% cycle for frequency
for n=3D1:N,
% take value of propagation function of segment 1
% for a given frequency point
wx =3D W1(n);
=20
% ABCD parameter matrix of segment 1
ABCD1 =3D [ (1+wx*wx)/(2*wx) (1-wx*wx)/(2*wx*Y0);
Y0*(1-wx*wx)/(2*wx) (1+wx*wx)/(2*wx) ];
% take value of propagation function of segment 2
wx =3D W2(n);
% ABCD parameter matrix of segment 1
ABCD2 =3D [ (1+wx*wx)/(2*wx) (1-wx*wx)/(2*wx*Y0);
Y0*(1-wx*wx)/(2*wx) (1+wx*wx)/(2*wx) ];
% ABCD parameter matrix of C series
ABCD_Cser =3D [ 1 Zc_ser(n); 0 1];
=20
% ABCD parameters of entire channel (without load):
ABCD_all =3D ABCD1 * ABCD_Cser * ABCD2;
=20
% Transfer function for a given frequency:
Transfer(n) =3D Zload/(ABCD_all(1,2)+Zload*ABCD_all(1,1));
end
semilogx(w, Transfer,'b');
hold on;
% ------------------------END-------------------
>Msg: #2 in digest
>Date: Tue, 25 Sep 2007 08:45:31 -0700
>From: steve weir <weirsi@xxxxxxxxxx>
>Subject: [SI-LIST] Re: AC Coupled Signals
Stephen you seem to be treating lossy as nonlinear. In my world, losses
=3D
in passive components and structures are linear. I would be very=3D20
curious to see a HSPICE deck that shows a difference between in S21 of a
=3D
channel depending on the sequential order of elements that compose=3D20
same. In linear theory that doesn't happen. Can you share?
Regards,
Steve.
Stephen Zinck wrote:
> Hi Scott and Steve,
> To answer both of your questions, it is the resulting Hspice (with
S-pa=3D
rameters) differential eye patterns, as viewed at the receiver die, that
=3D
were used to make a comparison of source versus destination AC coupling
c=3D
apacitor locations. The system was excited with a string of ones,
followe=3D
d by a single zero, followed by a string of ones.=3D20
>
> I have not specifically designed a test board that varies the AC
coupli=3D
ng capacitor location along a trace.
>
> I understand the "shades of gray" here and agree that one can't make a
=3D
"rule of thumb" generalization in our line of work these days.=3D20
>
> I agree in theory with all you state. Assuming a lossless interface to
=3D
the capacitor, it shouldn't matter where you place it, given a purely
lin=3D
ear system. But the real world is lossy, even when one makes great 3D
sol=3D
ved structures. Manufacturing and other tolerances tend to take the trek
=3D
towards perfection to task.=3D20
>
> Do either of you have real world measured results, that you could
share=3D
, that show no marked difference in received signal characteristics when
=3D
the AC coupling capacitor position is varied through a 30 inch backplane
=3D
system (or similar)?
>
> I believe my experience with capacitor location may prove true if the
c=3D
apacitor interface is lossy (which is the case). A lot of my customers
ar=3D
e just looking for quick ways to maximize performance using standard
comp=3D
onent packages and standard layout practices (in the end, I don't like
to=3D
give anything away that is low lying fruit). Most of the time I am
doing=3D
my analysis after the board is in layout, where I have limited ability
t=3D
o change the design (unless it is really broken). In a perfect world,
whe=3D
re I am involved early, the package optimization and layout structures
ca=3D
n be optimized as you state, but only if the margins warrant it (system
p=3D
erformance issues are expected after initial "what-if" simulations have
o=3D
ccurred). The right tool for the right job rules the day...
>
> Would either of you agree that AC coupling capacitor location may
matte=3D
r with a lossy interface to the capacitor?
>
> All the best,
> Steve
>
> Stephen P. Zinck
> Interconnect Engineering Inc.
> P.O. Box 577
> South Berwick, ME 03908
> Phone - (207) 384-8280
> Email - szinck@xxxxxxxxxxxxxxxxxxxxxxxxxxx
> Web - www.interconnectengineering.com
>
>
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