[SI-LIST] Re: TDR and line losses
- From: Steve Corey <steven.corey@xxxxxxxxxxxxxx>
- To: si-list@xxxxxxxxxxxxx
- Date: Wed, 26 Nov 2003 12:15:46 -0800
List members -- this is a repost since my original post of this message
has been in email zombie land for several days. My apologies if you
receive duplicate messages.
****
Steve -- Skin effect tends to decrease inductance as frequency
increases. At low frequencies, fields are able to penetrate the
imperfect conductors, so there is magnetic flux present internal to
those conductors. At higher frequencies, the fields are unable to
penetrate the conductors. You can think of it as reduced flux linkage
between conductors, smaller effective loop area, or less energy storage,
but the net effect is decreased inductance. As a result, characteristic
impedance decaying to a high-frequency asymptote is not uncommon. One
text that addresses the interplay between skin effect and inductance is
"Analysis of Multiconductor Transmission Lines" by Clayton R. Paul.
-- Steve
-------------------------------------------
Steven D. Corey, Ph.D.
Time Domain Analysis Systems, Inc.
"The Interconnect Analysis Company."
http://www.tdasystems.com
email: steven.corey@xxxxxxxxxxxxxx
phone: (503) 246-2272
fax: (503) 246-2282
-------------------------------------------
steve weir wrote:
> Dan, if we take those assumptions, then yes the jwC in the denominator
> reduces the net impedance, however the effect is pretty slight,
taking off
> perhaps one ohm in the range of 100MHz to 1GHz, and perhaps 0.1 ohms
from
> 1GHz to 5GHz. However, I think it is disingenuous, because skin
effect is
> going to tend to push us right back up to level and then some.
>
> Regards,
>
> Steve.
>
> At 11:54 AM 11/24/2003 -0800, Kyung Suk (Dan) Oh wrote:
>
>>Hi Steve,
>>
>>Let me clarify my statement using the following expression for
>>the characteristic impedance:
>>
>>Zc = sqrt[(R+jwL)/(G+jwC)]
>>
>>In general, all RLGC parameter can be frequency varying but
>>we can safely assume they are constant for our discussion.
>>Strictly speaking the following my argument is true when the
>>dc conductance is very low so let me assume that G is zero for
>>this discussion. Then,
>>
>>Zc = sqrt[R/jwC+L/C]
>>
>>Now it is clear that Zc is larger than Zc_inf (=sqrt(L/C)) when
>>frequency decreases due to R term.
>>I think the confusion here is that you were mentioning the "impedance
>>of line" not the characteristic impedance line.
>>
>>If I somehow missed your point, we can discuss this one off-line.
>>Thanks,
>>
>>___________________________
>>Kyung Suk (Dan) Oh, Ph.D.
>>Pricipal Signal Integrity Engineer
>>Rambus Inc.
>>doh@xxxxxxxxxx
>>650-947-5363
>>
>>steve weir wrote:
>>
>>>Dan,
>>>Language may be an issue here, but respectfully, your description seems
>>>inverted. The low frequency limit of inductive reactance is zero. The
>>>low frequency limit of conductor resistance is the bulk resistance /
>>>square. Both of those value increase monotonically with frequency.
I am
>>>at a total loss for your statement:
>>>"At these lower frequencies the characteristic impedance is larger than
>>>Zc_inf due to the resistance term AND the internal inductance term."
>>>How, is it possible for a series impedance composed of two parts that
>>>each increases monotonically with frequency to have a higher value at
>>>lower frequency than at high frequency?
>>>Are you perhaps trying to express the shunt effects of dielectric
losses
>>>at high frequency?
>>>Regards,
>>>
>>>Steve.
>>>At 09:34 AM 11/24/2003 -0800, Kyung Suk (Dan) Oh wrote:
>>>
>>>
>>>>Hi, I would like to add one comment to this issue.
>>>>The conductor loss definitely contributes to this upward creep but
>>>>there is also an additional physics which contributes to this upward
>>>>creep and this one is often forgotten and I would like to clarify them.
>>>>
>>>>The initial impedance level should be corresponding to the lossless
>>>>characteristic impedance. After initial impedance level there are
>>>>two mechanisms which make the impedance profile to creep upward.
>>>>The first one is resistive loss as others pointed out and
>>>>the second one is the internal inductance which increases
>>>>the characteristic impedance at low frequencies.
>>>>
>>>>It is important to first understand that the upward creep is NOT due
>>>>to the reflected wave along the transmission line but it is the
>>>>reflected wave of the initial edge at the beginning of the
>>>>transmission line.
>>>>
>>>>Mathematically, it is the convolution between the input edge
>>>>and the characteristic impedance only and not related with
>>>>the propagation constant.
>>>>Physically, this reflected wave does not contain any reflection
>>>>along the line (assuming it is uniform) until the reflection from
>>>>the other end comes back.
>>>>
>>>>At the very beginning, the input edge actually sees the
>>>>characteristic impedance at the very high frequency which is
>>>>the impedance based on L over C, say Zc_inf.
>>>>And the later response sees the characteristic impedance
>>>>at lower frequencies. At these lower frequencies the characteristic
>>>>impedance is larger than Zc_inf due to the resistance term AND
>>>>the internal inductance term.
>>>>
>>>>As you make the line longer, you would see the increasing in the
>>>>impedance profile which can be mistakenly thought as due to the
>>>>increase in the loss. As this creeping is not due to the "loss"
>>>>mechanism along the transmission line, but it is due to the change
>>>>in the characteristic impedance due to loss; hence, it is not
>>>>depending on the line length.
>>>>
>>>>If you increase the line length to fairly large this creep will
>>>>eventually saturate to the characteristic impedance at dc which
>>>>would be finite if there is any dc conductance loss. Otherwise it
>>>>will continue to grow as the characteristic impedance becomes infinite
>>>>at dc without dc conductance.
>>>>In reality, the characteristic impedance measurement shows a finite
>>>>value at low impedance so the upward creep should be saturate beyond
>>>>a certain length.
>>>>
>>>>"The bottom line is that if your characteristic impedance varies
>>>>significantly from dc to high frequency, the upward creep will be
>>>>there (assuming the impedance changes from high to low as the
>>>>frequency increases)"
>>>>
>>>>I have attached the simulated TDR response using Hspice w/
>>>>the following three characteristic impedances to demonstrate
>>>>the impact of the internal
>>>>inductance:
>>>>
>>>>case 1: sqrt(L/C)
>>>>case 2: sqrt((Ro+Rs*sqrt(f)+jwL)/(jwC))
>>>>case 3: sqrt((Ro+Rs*sqrt(f)(1+j)+jwL/(jwC))
>>>>
>>>>Regards,
>>>>
>>>>-Kyung Suk (Dan) Oh
>>>>
>>>>
>>>>Dima Smolyansky wrote:
>>>>
>>>>
>>>>>Suresh,
>>>>>
>>>>>The upward slope of the TDR trace is indicative of losses.
However, the
>>>>>losses will need to be quite substantial for the upward "creep" to be
>>>>>clearly visible. In other words; your transmission trace (TDT)
will show
>>>>>even fairly small losses through rise time amplitude degradation;
however,
>>>>>when you begin to see the "creep" in the reflection (TDR), that will
>>>>
>>>>show up
>>>>
>>>>
>>>>>as large rise time and amplitude degradation in TDT.
>>>>>
>>>>>Also, Howard Johnson did an article once, where he played with
skin effect
>>>>>and dielectric loss, and showed how they affect different portion of
>>>>
>>>>the TDT
>>>>
>>>>
>>>>>waveform. You can do the same in IConnect's lossy line model by
varying the
>>>>>skin effect and dielectric loss parameters independently, and
evaluating
>>>>>their effect on the TDT (or TDR) waveform.
>>>>>
>>>>>Thanks,
>>>>>
>>>>>-Dima
>>>>>
>>>>>----- Original Message -----
>>>>>From: "Suresh Subramaniam" <Suresh.Subramaniam@xxxxxxxxxx>
>>>>>To: <si-list@xxxxxxxxxxxxx>
>>>>>Sent: Friday, November 21, 2003 2:00 PM
>>>>>Subject: [SI-LIST] TDR and line losses
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>>If I TDR (rise time 26ps) a long lossy transmission line, should
I expect
>>>>>>the impedance profile to gradually creep up to a higher value
(assuming I
>>>>>>start out with a 50 Ohm impedance?). In other words, how does the TDR
>>>>>>take into account the effect of losses?
>>>>>>
>>>>>>Thanks
>>>>>>Suresh
>>>>>>
>>>>>>
>>>>>>
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>>>>>
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>>>>
>>>>
>>>>
>>>>-- Binary/unsupported file stripped by Ecartis --
>>>>-- Type: application/pdf
>>>>-- File: tdr_study.pdf
>>>>
>>>>
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