[SI-LIST] Re: Measuring Characteristic Impedance of a PCB trace
- From: "spamtrap1@xxxxxxxx" <spamtrap1@xxxxxxxx>
- To: si-list@xxxxxxxxxxxxx
- Date: Sat, 8 Sep 2007 21:19:39 GMT
Unless some really tight accuracy is required for the impedance measurem=
ent, which I doubt, just use a TDR and be done with it. Is all this fre=
quency domain tap dancing driven by only having a VNA to work with? My =
condolences if that is the case.
Sal
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| =3D 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 =3D {g(el)*[Go(w) + jwCo]}^-1
Similarly, for a shorted load, the impedance is:
Zshort =3D 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 /
************************************
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D
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 formul=
a
> (vektor multiplication) |Zo| =3Dsqrt(|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 hav=
e
> 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| =3D3D sqrt(|Zopen|*|Zshort|)
>>>
>>>The method seems to work except I get some resonance at different
>>>frequencies where the impedance increases significantly. The frequenc=
ies
>>>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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