[SI-LIST] How frequency effects L, C & Z
- From: "Rich Peyton" <p2rich@xxxxxxxxxxxxx>
- To: <steven.corey@xxxxxxxxxxxxxx>, <si-list@xxxxxxxxxxxxx>
- Date: Mon, 1 Dec 2003 09:37:43 -0500
Snipped from TDR & line losses thread
<Steve -- Skin effect tends to decrease inductance as frequency =
increases.>
I started a new thread based on the below reply to another thread. I'm =
a
little confused here--maybe Monday blues again? Can someone steer me to
some info regarding the effects frequency has on overall L, C, & Z. I =
see
that inductance decreases as frequency decreases which would be the =
opposite
for capacitance and then Z=3DsqrtL/C in a lot of my reference material.=20
But then I look at it physically from other reference material and get =
this:
1)Higher freq =3D skin effect =3D decreasing diameter of material (As =
lines are
made wider or thicker or shorter, the magnetic field is reduced and
inductance declines) =3D higher L, which is opposite of above =
statement?
2)Higher freq =3D skin effect =3D decreasing diameter of material =
(decreasing
area of lines) =3D decreases C =20
So I did a quick search on google (Frequency vs Inductance) and got the
following:
I did not fully read these articles--just looked at graphs (not =
promoting
them, just using them for reference):
Pg 4 of 6 shows L increasing as Freq increases & C decreases
http://www.ctsystemes.com/zeland/publi/dg1030.pdf
Pg 8 of 10, graph # 6 shows L decreasing as Freq increases
http://www.asat.com/products/bg1002.pdf
Can someone set me straight on how increasing/decreasing frequency =
effects
the overall reading of L, C, & Z? =20
Reference on the web would be nice.
Thanks,
Rich
-----Original Message-----
From: si-list-bounce@xxxxxxxxxxxxx [mailto:si-list-bounce@xxxxxxxxxxxxx] =
On
Behalf Of Steve Corey
Sent: Wednesday, November 26, 2003 3:16 PM
To: si-list@xxxxxxxxxxxxx
Subject: [SI-LIST] Re: TDR and line losses
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,=20
taking off
> perhaps one ohm in the range of 100MHz to 1GHz, and perhaps 0.1 ohms=20
from
> 1GHz to 5GHz. However, I think it is disingenuous, because skin=20
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 =3D
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 =3D sqrt[R/jwC+L/C] >> >>Now it is clear =
that Zc
is larger than Zc_inf (=3Dsqrt(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.=20
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=20
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.=20
However, the
>>>>>losses will need to be quite substantial for the upward "creep" to =
be
>>>>>clearly visible. In other words; your transmission trace (TDT)=20
will show
>>>>>even fairly small losses through rise time amplitude degradation;=20
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=20
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=20
varying the
>>>>>skin effect and dielectric loss parameters independently, and=20
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=20
I expect
>>>>>>the impedance profile to gradually creep up to a higher value=20
(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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>>>>-- Binary/unsupported file stripped by Ecartis --
>>>>-- Type: application/pdf
>>>>-- File: tdr_study.pdf
>>>>
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