Re: [SI-LIST] : EFFECT OF LUMPED LOAD ON TRANSMISSION LINES

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From: David Instone (david_instone@uk.xyratex.com)
Date: Thu May 24 2001 - 07:28:43 PDT


Hi Chandan,
  Comments distributed <g> in you message below.
Dave

Chandan wrote:
>
> Hi,
>
> Here are my comments:
> For a transmission line with several CMOS receivers, I
> am convinced that the input capacitance of the CMOS
> receivers can be considered as a distributed load on
> the transmission line. In which case, equation 4.77 on
> page 173 of " A Handbook of Black magic" is
> applicable. My concern was for a net topology in which
> a trace is connected to a SINGLE receiver at the end
> of the line. My understanding is that the single
> receiver should be considered as a lumped load for the
> following reasons:
> 1. The SINGLE receiver is placed at one point of the
> line.
> 2. There is an element of non-uniformity that I cant
> put in words; The SINGLE receiver
> represents a good deviation in capacitance. (Typically
> CMOS receivers have an input capacitance of 10pF,
> whereas typical line capacitances are in the range of
> 2 to 3pF - assuming a line with an unloaded
> characteristic impedance of 60 ohm & a velocity of 6
> inch/ns).
> In fact I imagined TWO LUMPED loads; the driver's
> output capacitance & the receiver's input
> capacitance.

I <think> that the driver capacitance acts as a load on the driver,
slowing the risetime, but not affecting the TL impedance only in as much
that the spacing between the distibuted capacity has to be greater in
order not to affect the line impedance as seen by the signal.
 
> Kindly comment, since I am not fully convinced that a
> single receiver on a transmission line can be
> considered as a distributed load.

You're right, it can't; except when the line is shorter than 1
risetime. In this case the wave front can't "separate" the Rx capacity
from the line capacity. so you use the loaded Z0 and work out the
unloaded capacity of line in capacity /risetime length.
>
> I also acknowledge that capacitive loading on a
> transmission line will reduce its characteristic
> impedance. However, I was curious to understand the
> relationships involved for lumped loads. The equation
> that I presented in my initial e-mail (from page 10 of
> Motorola's AN1051) as well as eqn. 4.77 of Howard
> Johnson's book are one & the same and speak of the
> effect of distributed capacitance on a transmission
> line. Howard Johnson also speaks about
> "distributing the capacitance uniformly". In the case
> of a single receiver, the designer
> cannot distribute capacitance uniformly as there is
> only one (or 2) capacitance to distribute.

This is true and and in cases when the capacity can be distributed then
if the distance between the caps is greater than 1 risetime it really
can't be classed as distributed capacity and you use the unloaded Z0.
Now the handbooks forget to mention this and have you working out the
capacity of the unloaded line in units of pF/inch or cm, when really
what matters is the pF/(length_equivalent_to_1_risetime). The corrolary
is when working out how much capacitve loading you can put on a line
before the impedance is pulled below a certain value, again use
c/risetimelength, not c/inch.

Of course there is the added subtlety that the risetime get's longer as
it travels down the line!

>
> Too some extent, I agree with Dave's
> (david_instone@uk.xyratex.com) analysis. I believe
> that
> if the load at the end of the TL is not visible to
> the driver during its transition (H to L
> or L to H), then the driver "sees" an unloaded
> characteristic impedance. PLease comment.
>
> ANOTHER QUESTION:
> If the net topology in which a trace is connected to a
> SINGLE receiver at the end is indeed a
> distributed-load transmission line, do you think that
> I would get a good approximation of the
> value of loaded characteristic impedance by
> substituting N = 2 in equation 4.77 (page 173 of
> Black magic)?
>
> Thanks,
> Chandan
>
> --- David Instone <david_instone@uk.xyratex.com>
> wrote:
> > Well if Chandan isn't confused I am!
> > A simple experiment with a TDR shows that if the
> > line is long enough for
> > a pulse edge to have left the driver and not yet
> > reached the capacitor
> > the line looks like a TL of Z0 (ignoring the cap)
> > and the capacitor acts
> > as a capacitive load. In this case the series
> > resistor+Rdriver should
> > match Z0. If the line is short enough or the rise
> > time long enough that
> > the pulse has not completely left the driver before
> > it hits the
> > capacitor then it should probably be considered as a
> > distributed
> > capacitance when calculating the series resistor.
> > The problem comes
> > when the range of risetimes possible spans both
> > conditions!
> > Or am I being over simplistic?
> > Now on the same theme, I believe that if lumped caps
> > are distributed
> > along a TL and the distance between them is greater
> > than a rise time
> > then the TL should be treated as a TL of unloaded Z0
> > with capacitive
> > discontinuities and the terminators should match
> > unloaded Z0 (unless
> > they are closer than a risetime to a cap), only if
> > the caps are closer
> > together than a risetime should Z0 be considered to
> > have been lowered
> > and the terminators matched to loaded Z0 (unless
> > they are further from
> > the last/first cap than a risetime).
> > Again am I right or over simplistic/just plain
> > wrong.
> >
> > Dave
> >
> > Degerstrom, Michael J. wrote:
> > >
> > > Ken,
> > >
> > > No problem - I was trying to do the same thing for
> > Chandan
> > > as my feeling was that he was trying to apply this
> > > Zoprime formula when it wasn't apparent that he
> > understood
> > > its utility. I'm sure many of us have difficulty
> > interpreting
> > > the original posts to this bulletin board.
> > Hopefully one
> > > or both of our posts were beneficial.
> > >
> > > Mike
> > >
> _______________________________________________________________
> > > Mike Degerstrom Email:
> > degerstrom.michael@mayo.edu
> > > Mayo Clinic; 200 1st Street SW ; Rochester, MN
> > 55905
> > > Phone: (507) 538-5462 FAX: (507) 284-9171
> > > WWW:
> > http://www.mayo.edu/sppdg/sppdg_home_page.html
> > >
> ______________________________________________________________
> > >
> > > > -----Original Message-----
> > > > From: Ken Cantrell
> > [mailto:Ken.Cantrell@srccomp.com]
> > > > Sent: Wednesday, May 23, 2001 12:02 PM
> > > > To: Degerstrom, Michael J.
> > > > Subject: RE: [SI-LIST] : EFFECT OF LUMPED LOAD
> > ON TRANSMISSION LINES
> > > >
> > > >
> >
> > > > Mike,
> > > > What I was getting at, if you re-examine at
> > Chandan's
> > > > message, is that he
> > > > doesn't understand the basic material yet. Note
> > his formula
> > > > for Zoprime. I
> > > > thought your answer was more advanced than the
> > question that
> > > > he asked, and I
> > > > didn't want him to miss the fundamentals.
> > > > Ken
> > > >
> > > > -----Original Message-----
> > > > From: owner-si-list@silab.eng.sun.com
> > > > [mailto:owner-si-list@silab.eng.sun.com]On
> > Behalf Of
> > > > Degerstrom, Michael
> > > > J.
> > > > Sent: Wednesday, May 23, 2001 9:37 AM
> > > > To: Ken.Cantrell@srccomp.com;
> > si-list@silab.eng.sun.com
> > > > Subject: RE: [SI-LIST] : EFFECT OF LUMPED LOAD
> > ON TRANSMISSION LINES
> > > >
> > > >
> > > > Ken,
> > > >
> > > > I'm not sure why you would recommend to use an
> > approach that
> > > > takes more effort to implement and then provides
> > less accurate
> > > > SI results. You can use this technique where
> > lumped load
> > > > capacitance is included into the transmission
> > line capacitance
> > > > only for certain net topologies. But using this
> > approach will
> > > > not allow you to see the capacitive reflections
> > and any stubbing
> > > > effects from package leads. Also, you may not
> > be predicting
> > > > the delay from your source to your load
> > accurately.
> > > >
> > > > Mike
> > > >
> > > >
> >
> _______________________________________________________________
> > > > Mike Degerstrom Email:
> > degerstrom.michael@mayo.edu
> > > > Mayo Clinic; 200 1st Street SW ; Rochester, MN
> > 55905
> > > > Phone: (507) 538-5462 FAX: (507) 284-9171
> > > > WWW:
> > http://www.mayo.edu/sppdg/sppdg_home_page.html
> > > >
> >
> _______________________________________________________________
> > > >
> > > >
> > > > > -----Original Message-----
> > > > > From: Ken Cantrell
> > [mailto:Ken.Cantrell@srccomp.com]
> > > > > Sent: Wednesday, May 23, 2001 9:55 AM
> > > > > To: Degerstrom, Michael J.;
> > chandan_career@yahoo.com;
> > > > > si-list@silab.eng.sun.com
> > > > > Subject: RE: [SI-LIST] : EFFECT OF LUMPED LOAD
> > ON TRANSMISSION LINES
> > > > >
> > > > >
> > > > > Chandan,
> > > > > The receiver capacitance is modeled as part of
> > the toal distributed
> > > > > capacitance where the new capacitance (Cprime)
> > is equal to the [line
> > > > > capacitance plus (the load capacitance * the
> > number of loads
> > > > > divided by the
> > > > > length of the transmission line)]. Zo prime
> > is then equal to sqrt
> > > > > (L/Cprime). It's effect will be to lower Zo.
> > I refer you to Howard
> > > > > Johnson's book, page 173, section 4.4.3.1.
> > The only time I
> > > > treat the
> > > > > receiver capacitance as lumped is in a
> > bi-directional mode where the
> > > > > receiver capacitance introduces a group delay
> > equal to 2*Zo*Cl.
> > > > > Ken
> > > > >
> > > > > -----Original Message-----
> > > > > From: owner-si-list@silab.eng.sun.com
> > > > > [mailto:owner-si-list@silab.eng.sun.com]On
> > Behalf Of
> > > > > Degerstrom, Michael
> > > > > J.
> > > > > Sent: Wednesday, May 23, 2001 7:39 AM
> > > > > To: chandan_career@yahoo.com;
> > si-list@silab.eng.sun.com
> > > > > Subject: RE: [SI-LIST] : EFFECT OF LUMPED LOAD
> > ON TRANSMISSION LINES
> > > > >
> > > > >
> > > > > Model the transmission line as a transmission
> > line and the
> > > > > load should be modeled as a lumped
> > capacitance. You
> > > > > may also want to model the package inductance
> > and capacitance
> > > > > depending on your application. Some of the
> > load capacitance
> > > > > may have series resistance due to ESD filter
> > circuitry but
> > > > > I rarely see vendors supplying this
> > information unless it
> > > > > it is factored into the IBIS model package
> > resistance.
> > > > >
> > > > > Mike
> > > > >
> _____________________________________________________________
> > > > > Mike Degerstrom Email:
> > degerstrom.michael@mayo.edu
> > > > > Mayo Clinic; 200 1st Street SW ; Rochester,
> > MN 55905
> > > > > Phone: (507) 538-5462 FAX: (507) 284-9171
> > > > > WWW:
> > http://www.mayo.edu/sppdg/sppdg_home_page.html
> > > > >
> >
> _______________________________________________________________
> > > > >
> > > > >
> > > > > > -----Original Message-----
> > > > > > From: Chandan
> > [mailto:chandan_career@yahoo.com]
> > > > > > Sent: Wednesday, May 23, 2001 4:00 AM
> > > > > > To: SI FORUM
> > > > > > Subject: [SI-LIST] : EFFECT OF LUMPED LOAD
> > ON TRANSMISSION LINES
> > > > > >
> > > > > >
> > > > > > Hi,
> > > > > >
> > > > > > Consider a long trace - long enough for it
> > to be
> > > > > > considered as a transmission line. Let this
> > trace be
> > > > > > connected between a CMOS driver & a CMOS
> > receiver. The
> > > > > > receiver can therefore be modeled as a
> > capacitive
> > > > > > load at the end of the line.
> > > > > >
> > > > > > 1. Should this capacitor be considered as a
> > lumped
> > > > > > element or distributed?
> > > > > > This question assumes importance when
> > point-to-point
> > > > > > clock traces are routed between a
> > synthesizer & a
> > > > > > receiver. Ideally, the value of series (or
> > source)
> > > > > > termination resistance that must be used is
> > the
> > > > > > difference between the characteristic
> > impedance and
> > > > > > the driver's internal resistance. I was
> > wondering if I
> > > > > > should use the loaded characteristic
> > impedance or
> > > > > > unloaded characteristic impedance. I then
> > began to
> > > > > > wonder if I should consider the load as
> > distributed or
> > > > > > lumped. Kindly comment.
> > > > > >
> > > > > > 2. Does the lumped capacitance affect the
> > properties

> > > > > > of a transmission line? If so, how?
> > > > > >
> > > > > > 3. The following approximation describes the
> > > > > > relationship between the loaded
> > characteristic
> > > > > > impedance, unloaded characteristic impedance
> > and
> > > > > > the value of DISTRIBUTED capacitance:
> > > > > >
> > > > > > Z0' = Z0/ROOT OF (1 + CL/CO)
> > > > > >
> > > > > > where Z0' = Loaded characteristic impedance
> > > > > > Z0 = Unloaded (Intrinsic) characteristic
> > impedance
> > > > > > CL = Load capacitance/unit length
> > > > > > C0 = Intrinsic capacitance/unit length
> > > > > >
> > > > > > Is there any relationship between loaded
> > > > > > characteristic impedance, unloaded
> > characteristic
> > > > > > impedance and the value of LUMPED
> > capacitance?
> > > > > >
> > > > > > Thanks,
> > > > > > Chandan
>
> __________________________________________________
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-- 
Regards

Dave Instone. Compliance Engineer Storage Systems Development, MP24/22 Xyratex, Langstone Rd., Havant, Hampshire, P09 1SA, UK. Tel: +44 (0)23-92-496862 (direct line) Fax: +44 (0)23-92-496014 http://www.xyratex.com Tel: +44 (0)23-92-496000

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