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

From: Per Viklund (per@dde.dk)
Date: Sun May 27 2001 - 12:27:24 PDT

Hello,

5 cents from me.
What happens is that the electrical signals travels at speed of light in vacuum.
On a PCB, the relative permitivity ('Dielectricity constant' Er) of the insulating board material plays a role and the signal speed is 'degraded' by SQRT(Er) so if
we note ligthspeed with c, we can write v = c/ sqrt(Er) where v is the resulting signal speed on your PCB.

Now, this is not all that trivial because it is not just the Er of the board material but in fact the Er as seen by the conductor.
A deeply embedded strip line will see an Er close to the one of the material. A microstrip that runns on top of the circuit board, have the board materials Er on the under side and the Er of air (pretty much 1.0) on the over side. -The resulting EFFECTIVE Er is not just a mean value but quite complex to calculate.
Howard Johnsons Handbook of Black Magic gives some analytical methids to find the effective Er for various transmission line configurations.
Otherwise, a fieldsolver would come in handy where you also can see the speed as: v = 1/sqrt(L * C)

Now when you know the speed of your signal and you know the risetime, you can find the critical length as the length where a rising or falling edge can travel from the driver to the receiver and reflect back again in te same time as the rise or fall time
The critical length will then be L = v * Trise / 2 (v is the actual signal speed from above.)

> Assuming a PCB propagation velocity that is half the
> speed of light,
> Critical length = 15cm/ns * rise time

Not a bad asumption but depending if your signal is routed as a strip line or as a microstrip, your approximation may be a little rough.
Assuming an Er of 4, you end up with approximately:
Stripline: 15cm/ns
Microstrip: 18.5cm/ns.....as signal speed -not critical length so you need to divide by 2.

Food for thought: 0.40ns risetime: critical length 3cm.......... if the circuit is a large package, how do you fit in the termination components close enough..........

Well, I didn't give you the proofs for the formulae but I hope it can be of some use to you anyway.

Kind regards

Per Viklund

www.dde-eda.com

----- Original Message -----
From: "Chandan" <chandan_career@yahoo.com>
To: "SI FORUM" <si-list@silab.eng.sun.com>
Sent: Sunday, May 27, 2001 8:16 AM
Subject: RE: [SI-LIST] : EFFECT OF LUMPED LOAD ON TRANSMISSION LINES

>
> The foregoing analysis indicates that fast rise times
> can be a blessing in those cases where one wants to
> 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
> 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 <Ken.Cantrell@srccomp.com> wrote:
> > Chandan,
> > N = 1.
> > Ken
> >
> > -----Original Message-----
> > From: owner-si-list@silab.eng.sun.com
> > [mailto:owner-si-list@silab.eng.sun.com]On Behalf Of
> > David Instone
> > Sent: Thursday, May 24, 2001 8:29 AM
> > To: Chandan
> > Cc: David Instone; si-list@silab.eng.sun.com
> > 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
> > 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.
> > >
> > > 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
> > 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
> > 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
> > > > 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
> > > > 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
> > 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
> > > > 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
> > > > 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
> > > > 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
> > > > 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
> > > > 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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