[SI-LIST] Re: plane RLGC Debye model
- From: "Yuriy Shlepnev" <shlepnev@xxxxxxxxxxxxx>
- To: "'Istvan Nagy'" <buenos@xxxxxxxxxxx>, <si-list@xxxxxxxxxxxxx>
- Date: Mon, 17 Nov 2008 13:04:25 -0800
Istvan,
Chapter 2.4.3 of the book provides exact analytical solution for 1-pole
Debye model only (one value of the complex dielectric constant gives exactly
two equations). Such model may be OK considering the dielectric constant
approximation, but the loss tangent in such model drops quickly to zero and
the approximation error may grow up to 50% even over one frequency decade
(see more on the dielectric approximation with multi-pole Debye models in
app note #2008.06 at
http://www.simberian.com/AppNotes.php).
Debye model with more than 1 pole requires solution of an over-determined
system of linear equations and there is no analytical solution for that.
Multi-pole model used in Swaminathan & Engin's book is a simple
approximation by superposition of independent 1-pole models assuming that
the poles are far enough. It may actually work - just check the model
against a target benchmark dielectric model (wideband Debye or
Djordjevic-Sarkar model is good for benchmarking) or against your
measurements.
Best regards,
Yuriy Shlepnev
www.simberian.com
-----Original Message-----
From: si-list-bounce@xxxxxxxxxxxxx [mailto:si-list-bounce@xxxxxxxxxxxxx] On
Behalf Of Istvan Nagy
Sent: Monday, November 17, 2008 12:14 PM
To: si-list@xxxxxxxxxxxxx
Subject: [SI-LIST] Re: plane RLGC Debye model
hi
thanks for everyone, i got very useful answers.
but: for parallel conductance: it changes its value by 10x every decade
(G=2pi*F*tgDELTA*C), so if i want to use lossy plane model, then at least i
need to know a single value (at what frequency?) to use, or use the debye
model.
on the other hand, i found an analitical solution for a debye ladder model
in Swaminathan's book (Power Integrity Modelling and Design for
Semiconductors and Systems, chapter 2.4.3), so no curve fitting is needed
for this at each simulation because of the simple formulas. why not to use
it?
regards,
Istvan Nagy
Concurrent Technologies Plc
----- Original Message -----
From: Scott McMorrow
To: Istvan Novak
Cc: Istvan Nagy ; shlepnev@xxxxxxxxxxxxx ; 'steve weir' ;
si-list@xxxxxxxxxxxxx
Sent: Monday, November 17, 2008 2:30 PM
Subject: Re: [!! SPAM] [SI-LIST] Re: plane RLGC Debye model
I'm going to add to Istvan Novak's comments on causality of plane
structures. Even with time domain analysis, with all of the possible
signal, power, power-coupling coupling, via-plane coupling, and
signal-signal coupling paths, causality of the power plane pair simulations
is generally a non-issue. Signal traces do not follow the minimum distance
straight line route from Tx to Rx. Neither does signal-signal coupling.
But, via-power, power-power, coupling does follow the minimum radial
distance path between a Tx and an Rx. It is therefore possible for coupled
energy to arrive at the destination prior to signal arrival, showing what
appears to be non-causal Rx waveforms, where noise occurs prior to the
expected rising edge. This can occur EVEN when there is only one signal
measured or analyzed, and one power plane pair, if the signal vias
transition through the planes.
IMO non-causal variations in group delay, due to modeling of the planes,
is insignificant relative to all the other potential causal phase delay
variations of multiple sources in a real system.
Scott McMorrow
Teraspeed Consulting Group LLC
121 North River Drive
Narragansett, RI 02882
(401) 284-1827 Business
(401) 284-1840 Fax
http://www.teraspeed.com
Teraspeed- is the registered service mark of
Teraspeed Consulting Group LLC
Istvan Novak wrote:
Hi Istvan,
In my experience it has not yet been necessary to use full causal plane
models for power distribution designs. If you want to characterize
materials accurately, yes, it is needed.
For successful PDN designs at most you need is the skin resistance and
DC resistance. Capacitance, inductance and conductance also change with
frequency, but if you ignore those frequency dependencies, a good PDN
still will be fine. Reason: these frequency dependencies primarily
impact resonance frequencies and time-of-flight parameters. In a good
PDN you want to suppress resonances anyway, so their very exact
frequency matters less. Time of flight would matter only if we wanted
to simulate time-domain waveforms accurately; this, however, would
require the accurate knowledge of time-domain excitation current data,
which is seldom if at all is available.
If for reasons of curiosity you are still interested in simulating
frequency dependent plane models in free Berkeley SPICE, you can simply
run SPICE in batch mode, create the frequency dependent parameters for a
given frequency, run SPICE at that single frequency, read in the result,
change frequency and repeat. That same solution also works if you want
skin resistance only.
Regards,
Istvan Novak
SUN Microsystems
Istvan Nagy wrote:
hi
thanks, this answers my question, but opens a new one.
"fit it with 3-4 real poles evenly distributed over you frequency band to
get rational approximation form"
-probably this would be the most difficoult part for me, i think. at least i
have no idea how to do it (theory, c program).
but probably its not a signal/power integrity problem already, but
mathematics.
on chapter 7, you mean chapter 4.2.1.6, figure 4.6d ? ok, it doesnt matter.
regards,
Istvan
----- Original Message -----
From: "Yuriy Shlepnev" <shlepnev@xxxxxxxxxxxxx>
To: "'Istvan Nagy'" <buenos@xxxxxxxxxxx>; "'steve weir'" <weirsi@xxxxxxxxxx>
Cc: <si-list@xxxxxxxxxxxxx>
Sent: Saturday, November 15, 2008 7:48 PM
Subject: RE: [SI-LIST] Re: plane RLGC Debye model
Istvan,
If you have dielectric constant value at 1 MHz, dielectric constant at 20
GHz may be about 10% smaller for a composite PCB material (as observed in
multiple experiments). It may be not important for practical PDN design as
Steve mentioned and simple 1-frequency approximation for G and C may work
just fine. The same is valid for R and L. Though, in case of very closely
spaces planes (with less than 5 mils distance), the effect of internal
inductance of the metal planes in combination with the dielectric
dispersion
can cause significant shifts of resonances even at lower frequencies
important for PDN design.
If you want to build the lattice-type equivalent circuit model valid over
3-4 decades in frequency and accounting for frequency variations of
dielectric constant and internal plane inductance, it can be done with the
broadband transmission plane model (see my paper "Transmission plane
models
for parallel-plane power distribution system and signal integrity
analysis"
in proceedings of 22-nd ACES symposium, 2006, p. 382-389, also available
at
http://www.shlepnev.com/Publications/ACES2006c.pdf). The model is
validated
with experiments in I. Novak, J. Miller Frequency-domain characterization
of
power distribution networks - Artech House, 2007, chapter 7 and in J.
Miller, G. Blando, B. Williams, I. Novak "Impact of PCB Laminate
Parameters
on Suppressing Modal Resonances" - DesignCon2008.
Here are possible steps to build broad-band SPICE model for PDN:
1) Use equation (3) from the cited ACES paper for frequency-dependent
admittance per square Ys and fit it with 3-4 real poles evenly distributed
over you frequency band to get rational approximation form (9)
2) Use equation (11) for sheet impedance of the plane pair Zs and fit it
with 3-4 real poles to get the rational approximation form (12)
3) Define cell size dx and dy for your equivalent lattice model
4) Compute admittance of one sell as Ys*dx*dy - the rational approximation
from step 1 immediately gives you the second Foster form of GC or RC
network
for the cell node
5) Compute impedance of one sell as Zs*dx/dy for x-axis and as Zs*dy/dx
for
y-axis - the rational approximation from step 2 immediately gives you the
second Foster form of RL network for the x and y branches of your cell
6) Combine cells into a 2D equivalent circuit of the plane pair
Note that the final 2D model is similar to a lumped broad-band model for a
transmission line.
Best regards,
Yuriy Shlepnev
www.simberian.com
-----Original Message-----
From: si-list-bounce@xxxxxxxxxxxxx [mailto:si-list-bounce@xxxxxxxxxxxxx]
On
Behalf Of Istvan Nagy
Sent: Saturday, November 15, 2008 4:45 AM
To: steve weir
Cc: si-list@xxxxxxxxxxxxx
Subject: [SI-LIST] Re: plane RLGC Debye model
hi
the only thing what i have is the dielectric thickness, and Er@1MHz, as
usual. i normally dont haave measurement data.
the simple RLGC models dont take the frequency-dependeny of the Er into
account, skin effect,...
these can be described by simple equations, but how to kame a lumped model
based on equations containing E^x... and similar things.
at least these 2 effects should be included.
Er(f)=Er(f0)*(jf/f0)^(-0.006366) this gives a frequency dependency for C
and G
R is dependent on f because of the skin effect.
somehow L is also dependent on frequency?
because it is for a unit-cell model, it shouldnt need more then very few
parameters, like dielectric thickness, Er(f0), f, cell size.
Istvan
----- Original Message -----
From: "steve weir" <weirsi@xxxxxxxxxx>
To: "Istvan Nagy" <buenos@xxxxxxxxxxx>
Cc: <si-list@xxxxxxxxxxxxx>
Sent: Saturday, November 15, 2008 12:29 PM
Subject: [SI-LIST] Re: plane RLGC Debye model
Istvan what data do you have? Do you have measurements from material
samples?
For most power work, it is sufficient to use a single value for tangent
loss. If you get the other parameters correct, then the models will
tend to show slightly higher peak impedances at the modal resonances
than measurements out above 1GHz, but the difference is typically not
great.
Steve.
Istvan Nagy wrote:
hi
how can i calculate the Ri, Li, Gi, Ci parameters for a frequency
dependent unit-cell Debye RLGC model for a power/gnd plane pair? 1st
order or up to 3rd order Debye model would be good.
are there any equations?
(Debye models introduce additional RL and GC elements into the 4 element
original RLGC model to reflect the frequency-dependency, and with
staying
with basic circuit elements, suitable for spice)
i would like to make frequency dependednt spice 3f5 models (not
w-element
model, since its not compatible with most of the spices) from arbitrary
power planes, with lumped-element grid.
I found application notes where in the examples they just shown the
calculated values, without describing the calculation.
regards,
Istvan Nagy
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