[SI-LIST] Re: TDR and line losses
- From: "Kyung Suk (Dan) Oh" <doh@xxxxxxxxxx>
- To: Paul Levin <levinpa@xxxxxxxxxxxxx>
- Date: Wed, 26 Nov 2003 13:21:14 -0800
Paul, it is a very good point but I have implicitly included
the imaginary part by making the inductance as function of
frequency, L(f).
The reason I have not explicitly written as R(f)(1+j)+jwL
is that this leads to the internal inductance of
R(f)/(2*Pi*sqrt(f)), as you pointed out.
This is a good approximation only at high frequencies and
it makes the internal inductance contribution to be infinite
near dc which is not true in practice. Although the internal
inductance still increases as the frequency decreases,
I do not think it would be that large.
Thanks,
________________________________________
Kyung Suk (Dan) Oh, Ph.D.
Pricipal Signal Integrity Engineer
Rambus Inc.
doh@xxxxxxxxxx
650-947-5363
>
Paul Levin wrote:
> Dear All,
>
> Also, in Doh's equation recall that the term he called R(f)
> needs to be multiplied by (1+j). That the additional reactive
> impedance has the same magnitude as the resistive impedance
> is shown in Ramo, Whinnery and VanDuzer, "Fields and Waves in
> Electronic Communications," among other references.
>
> The fact that the jR(f) term is increasing only proportional
> to the SQRT of frequency, means that the effective "internal
> inductance" (= R(f)/w) is *decreasing* in proportion to the
> SQRT of frequency, hence tending towards zero. This leads to
> noticeably higher inductance (hence Zc) at lower frequencies.
>
> Regards,
>
> Paul
> ___________________
>
> doh wrote:
>
>> Hi Mike,
>>
>> I am glad you have asked this question.
>> My original mail does not clearly explain about the physics.
>>
>> Let me fist describe what happened at the reflection stage and
>> discuss the propagation stage next.
>>
>> When the initial signal hits the transmission line interface,
>> as you mentioned, the fast frequency component sees the
>> lower characteristic impedance and low frequency component
>> sees the high characteristic impedance as it can be shown
>> in the following equation for the characteristic impedance:
>>
>> Zc(f) = sqrt[(R(f)+jwL(f))/(G(f)+jwC)]
>>
>> (assuming G(f) at the low frequency is relative smaller than R(f))
>> So the upward creep happens due to the frequency-dependent nature
>> of the characteristic impedance.
>>
>> Once the signal is transmitted to the transmission line side,
>> it would not reflect at all regardless of the frequency content
>> of the signal or frequency variation of the transmission line
>> (assuming the uniform transmission line).
>> What happened is that different frequency components travel at
>> different attenuations and possibly at different velocities
>> but no reflection would occur since the characteristic impedance
>> does not change for a particular frequency component along the
>> propagation.
>>
>> Yes, we will observe the slowing down of the signal edge due to
>> the frequency dependent loss but it would not see any reflection
>> until the signal reflects back from the other end.
>> Another words, the power transmitted can be reduced to the far end
>> but the reduced amount of power is dissipated rather than reflected
>> along the propagation.
>>
>> It is interesting to note that some of the most commonly used transient
>> simulation techniques for lossy uniform transmission lines are based
>> on the delay extraction technique and cannot model any reflection during
>> the propagation.
>>
>> Regards,
>>
>> -Dan
>>
>>
>> Mcmaster, Michael wrote:
>>
>>> I'm curious if there's also another factor involved here. As the test
>>> signal propagates down the transmission line, won't the fastest
>>> portions of
>>> the signal be reflected back at the minor changes in impedance,
>>> slowing down
>>> the rise time? For a material like FR4 with a frequency dependent
>>> dielectric constant, you would expect the "apparent" impedance to
>>> drop, not
>>> increase. Since this doesn't happen, it's apparent this is not as
>>> significant as those described by others. But does anybody have an
>>> idea how
>>> significant this is? Mike McMaster
>>> RF Product Engineer
>>> Merix Corporation
>>> 503-992-4263
>>>
>>>
>>>
>>>
>>>
>>>> ----------
>>>> From: Eric Bogatin[SMTP:eric@xxxxxxxxxxxx]
>>>> Reply To: eric@xxxxxxxxxxxx
>>>> Sent: Wednesday, November 26, 2003 6:18 AM
>>>> To: Si-List
>>>> Cc: eric bogatin
>>>> Subject: [SI-LIST] TDR and line losses
>>>>
>>>> While the explanations below for increasing slope of the TDR trace due
>>>> to series resistive losses are perfectly correct, there is another,
>>>> subtle explanation, which is more commonly the case.
>>>>
>>>> When we look at the front screen of the TDR instrument and interpret
>>>> the results, we are assuming that the signal going into the
>>>> transmission line under test is an ideal step increase in voltage. In
>>>> fact, the skin depth losses in the cables from the front of the TDR to
>>>> the device under test will cause the signal going into the device to
>>>> have a long rising tail.
>>>>
>>>> When you look at the reflected signal from the T line, you see the
>>>> initial voltage reflected back to be slightly lower than expected,
>>>> creeping up as time proceeds. This produces an artifact of seemingly
>>>> increasing impedance down the trace.
>>>>
>>>> One interpretation is resistive losses in the line. One interpretation
>>>> is actual increasing characteristic impedance down the line due to
>>>> geometry variation. Another explanation is non ideal rise time
>>>> waveform.
>>>>
>>>> The most efficient way of distinguishing these effects is to simulate
>>>> the measured response using the initial, measured incident waveform as
>>>> the stimulus. TDA Systems IConnect software is a perfect tool that
>>>> facilities this analysis. You record the measured step wave with the
>>>> cable end disconnected from the source, then record the TDR response.
>>>>
>>>> If you have a simple interconnect you are measuring, you might be able
>>>> to model it as a uniform transmission line. If you are able to get
>>>> excellent agreement between the measured TDR response and the behavior
>>>> expected based on the ideal T line and the real waveform from the TDR,
>>>> you know you are seeing an artifact of the TDR.
>>>>
>>>> If you still see the creeping up, try using a lossy line model in
>>>> IConnect. This will help identify the problem as a real lossy line
>>>> effect.
>>>>
>>>> In my experience, I clearly see lossy line effects in the shape of the
>>>> transmitted signal, but I find the creeping up of the reflected signal
>>>> is more often due to the non ideal incident step.
>>>>
>>>> --eric
>>>>
>>>>
>>>> ********************************************************************
>>>> Recently published by Prentice Hall, www.phptr.com
>>>> Signal Integrity-Simplified, by Eric Bogatin
>>>>
>>>> Attend the GTL Signal Integrity University in Sunnyvale, CA - Nov
>>>> 6-13
>>>>
>>>> GTL 122 - Fundamental Principles of Signal Integrity
>>>> GTL 250 - High Speed Board Design
>>>> GTL 260 - Interconnect Models from Measurement
>>>> ----------------------------------------------------------------------
>>>> ---------------
>>>> Dr. Eric Bogatin
>>>> CTO, GigaTest Labs
>>>> 26235 w 110th Terr
>>>> Olathe, KS 66061
>>>> v: 913-393-1305, f: 913-393-1306
>>>> e: eric@xxxxxxxxxxxx
>>>> www.GigaTest.com
>>>> ********************************************************************
>>>>
>>>>
>>>> Msg: #6 in digest
>>>> Date: Mon, 24 Nov 2003 09:34:16 -0800
>>>> From: "Kyung Suk (Dan) Oh" <doh@xxxxxxxxxx>
>>>> Subject: [SI-LIST] Re: TDR and line losses
>>>>
>>>> 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
>>>>
>>>>
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>>>
>>>
>>>
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