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[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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Follow-Ups:

[SI-LIST] Re: How frequency effects L, C & Z
From: Steve Corey
[SI-LIST] How frequency effects L, C & Z

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