[SI-LIST] Re: Measuring Characteristic Impedance of a PCB trace
- From: Bill Wurst <billw@xxxxxxxxxxx>
- To: si-list@xxxxxxxxxxxxx
- Date: Sat, 08 Sep 2007 14:25:55 -0500
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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