FreeLists / si-list / [SI-LIST] Re: Measuring Characteristic Impedance of a PCB trace

[steve weir <weirsi@xxxxxxxxxx>]

Gustavo, VNAs are really good at characterizing discontinuities in Tx 
lines.  But as Sal points out, for digital transmission lines a TDR/TDT 
provides a: quick, accurate, and simple picture of Zchar for a trace 
section.  The advantage that the TDR has is that it only excites the 
line intermittently and so does not have to contend with the wave modes 
that can bedevil interpretation of VNA measurements.  The wave modes can 
be particularly nasty with low Dk and low tanloss dielectrics.  The 
modal resonance issue with test traces has come up a number of times 
before.  For anyone who does not have access or the time to do careful 
design with a 3D solver, I would advise using a TDR/TDT to save grief, 
at least for initial characterization.  The limiting issue then becomes 
that of the launch design.

Regards,


Steve.

Gustavo Blando wrote:
> Hi Cody, we've also struggle with the same issue.
> Even though we do not have a definitive bullet-proof method to extract the
> frequency dependent characteristic impedance of a trace, we've tried a
> couple of different methods.
>
> All the methods bellow assumes you have a VNA measurement of a transmission
> line from end to end, and that you have calibrated out or de-embedded your
> probes and connections from the DUT.
>
> 1. There are formulas that using the telegrapher equations will convert
> S_parameters to frequency dependent RLGC parameters. Do a web search and
> you'll find some references. 
> >From the RLGC you get the Zc(f)= sqrt( ( R(f) + jwL(f) ) / (G(f) + jwC(f) ).
> To use this method directly, you'll need very good VNA measurement and even
> then I have found that small amount of noise will tend to make your results
> oscillate, but "in theory" assuming a quasi-TEM propagation this should
> work.
>
> 2. If more information is known about your system, for example (line-width,
> Dk(f), tand(f) <-- can be measured etc, and having a good transmission line
> causal model you can fit the S-parameters to this model and get the RLGC and
> from there Zc(f). I understand this might require a lot of work particularly
> if you are only interested in a quick impedance measurement, but it has the
> added advantage that you end up with a fitted model of your transmission
> line as well.
>
> 3. The last method is very simple and probably the one that addresses your
> question more directly.
> After you take your VNA measurement, you can simply renormalize the S
> parameters to different impedances and monitor the change of magnitude of
> S11[dB]. 
> The impedance that makes your S11 the smallest is basically the one better
> matched to your transmission line, and hence equal to your Zc at that freq. 
> After having applied this method for many measurements I have found that in
> general there is one impedance value that will give the smallest S-parameter
> for a rather wide frequency range (several GHz).
>
> Depending what you want or need you can even go to the extreme in method (3)
> changing the renormalization impedance and monitoring the magnitude of S11
> at each frequency point. Although I've never tried this particular case yet
> I think for the most part it'll give you how the impedance is changing with
> frequency.
>
> Regards
> Gus
>
> From: si-list-bounce@xxxxxxxxxxxxx [mailto:si-list-bounce@xxxxxxxxxxxxx] On
> Behalf Of Bill Wurst
> Sent: Saturday, September 08, 2007 3:26 PM
> To: si-list@xxxxxxxxxxxxx
> Subject: [SI-LIST] Re: Measuring Characteristic Impedance of a PCB trace
>
> Hi Cody,
>
> I don't think your fundamental question, "Can anyone recommend a 
> different method for measuring characteristic impedance over frequency?" 
> was ever answered, but first I think it would be instructive to 
> understand the limitations of the method you are using.
>
> The basis for the equation:
>       |Zo| = sqrt(|Zopen|*|Zshort|)
> is that for the special case of an open load, the impedance at the 
> source or generator end of the transmission line is:
>       Zopen = {g(el)*[Go(w) + jwCo]}^-1
> Similarly, for a shorted load, the impedance is:
>       Zshort = g(el)*[Ro(w) + jwLo]
> where j is the sqrt(-1), w is radian frequency, Ro(w) represents ohmic 
> losses (both dc and ac) in the conductor, Go(w) represents dielectric 
> losses, Lo & Co are respectively the intrinsic inductance of the 
> transmission line in units of H/m and the intrinsic capacitance in F/m, 
> and g(el) is a function, the argument of which is the electrical length 
> (el) of the line.  Note that el is itself a function of w, as well as 
> the relative permittivity of the transmission dielectric.  The above 
> assumes the absence of parasitics that often result with a short or 
> open, and an el less than a quarter wavelength.  It also ignores the 
> interconnect between the VNA and the line under test.
>
> The most severe limitation of this method comes about from the fact that 
> as el increases and approaches a quarter wavelength, g(el) approaches 
> infinity.  This happens for all odd multiples of 1/4 lamda with 
> increasing el.  At 1/4 lamda, g(el) has a discontinuity as it changes 
> sign.  With el increasing and approaching an even multiple of 1/4 lamda, 
> g(el) becomes less negative and approaches zero.  Mathematically, in the 
> limit, the above equation for Zo still holds, but achieving accurate 
> measurements and accurately computing the product of a very small number 
> and a very large number when el is near a 1/4 lamda becomes difficult. 
> This leads to the "resonances" you observed.  The above method will 
> yield accurate results as long as measurements are restricted to the 
> frequency ranges that are sufficiently removed from 1/4 lamda 
> ("sufficiently" will depend on the measurement system and the line under 
> test).  Obviously, this shortcoming can be avoided if the electrical 
> length of the line is such that it is sufficiently shorter than 1/4 
> lamda at the highest measured frequency, but this may not be an option 
> for you.
>
> For those skilled in the use of the Smith Chart, the above is fairly 
> intuitive.  For anyone who would like to learn about the Smith Chart, 
> there is an upcoming free webinar given by Les Besser.  You can find out 
> more about and sign up for the webinar at:
>       http://www.besserassociates.com/webSpecials.htm
> Click on the "FREE tutorial webinars" link at the top of the page.
>
> As for measurement alternatives for the characteristic impedance over 
> frequency, it is possible to use a TDR and software like Tektronix 
> iConnect to derive S11 as a function of frequency from time domain 
> measurements.  However, this method can also have limitations in that 
> sometimes the s-parameters the FFT algorithm produces are not causal or 
> yield passive gain.
>
> Best regards,
>      -Bill
>
>        /************************************
>       /      William C. Wurst, PE         /
>      /        billw@xxxxxxxxxxx          /
>     / Advanced Electronic Concepts, LLC /
>    /           www.aec-lab.com         /
>    ************************************
> =================================================================
> Peter J wrote:
>   
>> Hi Cody,
>> It is normal to get those resonaces when you measure an open stub like
>>     
> that.
>   
>> If you calibrate and do the measurement accurately and take the formula
>> (vektor multiplication) |Zo| =sqrt(|Zopen|*|Zshort|)  you get the Z0 over
>> the frequency VNA frequency range. When you calibrate be sure that you
>> de-embedded fixture, koax/board transition, or what ever means you have
>> connected your test object.
>>
>> BR
>> Homer
>>
>> 2007/9/5, tao xu <helen.tao.xu@xxxxxxxxx>:
>>
>>     
>>> Hi, Cody
>>> my first thought is that you can make the trace short to avoide the
>>> resonance appearing in your intrested frequency range. But please make
>>> sure
>>> length is till much bigger than width.
>>>
>>> thanks and regards
>>> Helen
>>>
>>>
>>> On 9/5/07, codymiller@xxxxxxxxxx <codymiller@xxxxxxxxxx> wrote:
>>>
>>>       
>>>> All,
>>>>
>>>> I am trying to measure the characteristic impedance of a strip line
>>>> trace, using a VNA. I would like to determine the frequency at which the
>>>> trace becomes very lossey. I am using a formula found in the Agilent
>>>> Impedance Measurement Handbook page 5-23.
>>>> http://cp.literature.agilent.com/litweb/pdf/5950-3000.pdf
>>>>
>>>> The method requires S11 of the transmission line open as well as S11
>>>> with it shorted.
>>>>
>>>> |Zo| =3D sqrt(|Zopen|*|Zshort|)
>>>>
>>>> The method seems to work except I get some resonance at different
>>>> frequencies where the impedance increases significantly. The frequencies
>>>> of these resonants changes with different lengths of PCB trace.
>>>>
>>>> Can anyone recommend a different method for measuring characteristic
>>>> impedance over frequency?
>>>>
>>>> Thanks,
>>>> Cody Miller
>>>> codymiller@xxxxxxxxxx
>>>> ------------------------------------------------------------------
>>>>         
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