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

From: Chandan ([email protected])
Date: Sat May 26 2001 - 23:16:32 PDT

Thanks for your repsonses.

The foregoing analysis indicates that fast rise times
can be a blessing in those cases where one wants to
avoid overloading of a driver AS WELL AS maintain
close spacing between the driver & receiver. In this
case, all one needs to do is to place the receiver
little more than ONE risetime-length away from the
driver. The transmission line from the driver to the
receiver will now be unaffected by the receivers input
capacitance. Am I right?
This could also be good layout guideline for a
multipoint bus (one with several loads). All I
need to tell the PCB designer is to place the devices
a little more than a risetime-length apart.

This way all I need to worry about is the flight time

By the way, how does one decide the rise time length?
Sometime in April, Abe Riazi (ServerWorks)
provided us with the BELOW formula for critical
length. (Refer to "Source termination of transmission
line, April 23)

Lc = k(Tr)/(Tpd)
Where, Tr is rise time and Tpd is signal propagation
delay.
A good value for coefficient k is 1/6; and assuming
FR-4 substrate

Could someone derive this for me? or this this an
empirical result?

I thought of using the following relationship:
velocity = distance/time
Therefore, Critical length = velocity of signals on
the PCB * rise time
Assuming a PCB propagation velocity that is half the
speed of light,
Critical length = 15cm/ns * rise time

Thanks
Chandan

--- Ken Cantrell <[email protected]> wrote:
> Chandan,
> N = 1.
> Ken
>
> -----Original Message-----
> From: [email protected]
> [mailto:[email protected]]On Behalf Of
> David Instone
> Sent: Thursday, May 24, 2001 8:29 AM
> To: Chandan
> Cc: David Instone; [email protected]
> Subject: Re: [SI-LIST] : EFFECT OF LUMPED LOAD ON
> TRANSMISSION LINES
>
>
> Hi Chandan,
> Comments distributed <g> in you message below.
> Dave
>
> Chandan wrote:
> >
> > Hi,
> >
> > Here are my comments:
> > For a transmission line with several CMOS
> > 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
> > ([email protected]) 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 <[email protected]>
> > 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
> > > 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:
> > > [email protected]
> > > > 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:[email protected]]
> > > > > Sent: Wednesday, May 23, 2001 12:02 PM
> > > > > To: Degerstrom, Michael J.
> > > > > Subject: RE: [SI-LIST] : EFFECT OF LUMPED
> > > 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: [email protected]
> > > > > [mailto:[email protected]]On
> > > Behalf Of
> > > > > Degerstrom, Michael
> > > > > J.
> > > > > Sent: Wednesday, May 23, 2001 9:37 AM
> > > > > To: [email protected];
> > > [email protected]com
> > > > > Subject: RE: [SI-LIST] : EFFECT OF LUMPED
> > > 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:
> > > [email protected]
> > > > > 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:[email protected]]
> > > > > > Sent: Wednesday, May 23, 2001 9:55 AM
> > > > > > To: Degerstrom, Michael J.;
> > > [email protected];
> > > > > > [email protected]
> > > > > > Subject: RE: [SI-LIST] : EFFECT OF LUMPED
> > > 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: [email protected]
> > > > > > [mailto:[email protected]]On
> > > Behalf Of
> > > > > > Degerstrom, Michael
> > > > > > J.
> > > > > > Sent: Wednesday, May 23, 2001 7:39 AM
> > > > > > To: [email protected];
> > > [email protected]
> > > > > > Subject: RE: [SI-LIST] : EFFECT OF LUMPED
> > > 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:
> > > [email protected]
> > > > > > 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:[email protected]]
> > > > > > > Sent: Wednesday, May 23, 2001 4:00 AM
> > > > > > > To: SI FORUM
> > > > > > > Subject: [SI-LIST] : EFFECT OF LUMPED
> > > 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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