[SI-LIST] Re: How frequency effects L, C & Z
- From: Geoff Stokes <gstokes@xxxxxxxxx>
- To: si-list@xxxxxxxxxxxxx
- Date: Mon, 1 Dec 2003 15:21:21 -0000
Rich
You seem to be changing dimensions while you make comparisons. Better to
keep the structure *fixed* then see what happens. Please forgive me if I
missed your point. If you stay physically fixed, L versus freq is s-shaped,
due to internal inductance. This might help:
http://www.ansoft.com/thewave/Doing_Good_While_Playing.pdf
I think C will vary with freq if the dielectric constant does so, but
otherwise will be constant.
In the interesting paper by Karnezos et al., which you quote, Figure 6 shows
inductance increasing greatly with frequency. I expect this is the usual
practical result of measuring an inductor, i.e. the physical capacitance
shows the skirt of a parallel resonance. So you're not looking at pure
inductance. I don't actually know, but the Zeland software might be just
dividing the imaginary part of Z by f and calling it inductance. You need a
circuit model extractor to get inductance and capacitance elements alone,
which is not easy. In the paper, the interest is in showing how the
performance can be improved (inductance reduced) by changing the package
design.
Cheers
Geoff
> -----Original Message-----
> From: Rich Peyton [mailto:p2rich@xxxxxxxxxxxxx]
> Sent: 01 December 2003 14:38
> To: steven.corey@xxxxxxxxxxxxxx; si-list@xxxxxxxxxxxxx
> Subject: [SI-LIST] How frequency effects L, C & Z
>
>
> 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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