I also am not a great fan of fractional dB hand-wringing. Sometimes
academia needs to leave their towers and live in the streets.
Bob Heller
St. Paul, MN 55107-1208
Tel: 651- 778-6336
Fax: 651-778-6252
=========================
"ce-test,
qualified testing
bv - Gert To
Gremmen" "Price, Edward"
<g.gremmen@cetest <[email protected]>
.nl> <[email protected]>
Sent by: cc
[email protected]
Subject
RE: Measurement Accuracy and
06/08/2009 02:17 antenna factors
PM
Hi Ed, (and group)
Great, this is something we can work with.
Now prove us that the error caused by interpolation
is less then 0.5 dB, that means make a math model
(not too complex for linear interpolation)
Then we should draw conclusions from that….
First:
The calibration graph should well extend the working frequency
range
Second:
I believe it should be mandatory that each max and min point
of the graph should be a calibration point (ie dAF/df = 0).
(differentiate AF versus frequency: when variation per step is 0, we have a
flat area, a top or a bottom in the graph)
Third:
Each inflexion point should be a calibration point ( d2AF/df= 0)
(The second order differentiate = 0)
Fourth:
Each calibration point AF should not differ more than plus 1 or minus 1
>from the previous and next point.
Linear Interpolation is maybe not the best way of interpolation.
Are there any math savvy users on this list that can create
an error approximation for several interpolation methods ??
Linear
Cubic
Cubic Spline
Cosine
Hermite
See http://local.wasp.uwa.edu.au/~pbourke/miscellaneous/interpolation/
And
http://en.wikipedia.org/wiki/Interpolation
Applet showing how it works:
http://www.dr-mikes-maths.com/DotPlacer.html
(just try it using 4 point only, just as software does)
Gert Gremmen
Ce-test, qualified testing bv
Van: [email protected] [mailto:[email protected]] Namens Price, Edward
Verzonden: maandag 8 juni 2009 16:56
Aan: [email protected]
Onderwerp: RE: Measurement Accuracy and antenna factors
My antenna cal lab gives me gain and antenna factor data at 57 points, from
20 MHz through 300 MHz, using 5 MHz intervals, for my Raven biconical
antenna. I normally use this antenna only between 30 MHz and 200 MHz, but
it's nice to see how the antenna performs beyond its normal use range.
Over the 30 MHz to 200 MHz range, the AF change from one data point to the
next rarely varies by more than 1 dB, and often varies only 1/4 dB. I enter
all 57 data points into my acquisition system antenna factor file, and the
HP-85869PC software does a linear interpolation between data points.
I feel that this gives me less than a 1/2 dB uncertainty in all cases, and
likely better than 1/4 dB over most of the frequency range.
Ed Price
[email protected] WB6WSN
NARTE Certified EMC Engineer
Electromagnetic Compatibility Lab
Cubic Defense Applications
San Diego, CA USA
858-505-2780
Military & Avionics EMC Is Our Specialty
From: [email protected] [mailto:[email protected]] On Behalf Of Cortland
Richmond
Sent: Sunday, June 07, 2009 11:19 PM
To: [email protected]
Subject: RE: Measurement Accuracy and antenna factors
I favor scanning somewhat past the prescribed scan edge (and either
including calibration points, or if not provided, extrapolating straight
line in the transducer tables) because often, automated systems fail to
display an emission right on the edge of the scan and extending it makes
sure these are caught.
Many of us may also have noticed that automated systems can produce
misleading printouts unless scan segments are kept short enough to insure
all data is properly represented on paper. That is properly another
discussion.
It's already been mentioned that where large excursions are present, more
data points should be entered in transducer tables. Data points far
enough apart to introduce an additional 1 dB of error are in my opinion
too far apart.
I suspect that in-band computational errors due to reliance on missing
out-of-band data points may be satisfactorily contained by short straight
line extrapolations as above.
Cortland Richmond, KA5S
GE Aviation
Opinions my own, not my employers'!
----- Original Message -----
From: ce-test, qualified testing bv - Gert Gremmen
To: [email protected]
Sent: 6/7/2009 12:49:05 PM
Subject: Measurement Accuracy and antenna factors
A lot of effort has been put into specification of
measurement accuracies in radiated emissions.
CISPR 16-4-2 has a number of uncertainty budgets listed.
One factor that I have not seen in any budget is the
error introduced by interpolation between
antenna factor calibration points by the measuring receiver.
In general the characteristics of a calibrated antenna
are entered into the measuring receiver as a number of
F/AF pairs, more or less randomly selected from
the calibration graph. Then the AF values for frequencies
in between those pairs a quadratic spline function is used
to interpolate. The function requires 4 calibration pairs to operate
correctly
of which 2 must be lower and 2 must be higher then the
interpolated frequency. Especially near 30 MHz, where modern
antennas have steep AF graphs, a calibration point
below 30 MHz is not always available and I assume
the software duplicates the 30 MHz pair to
say 25 MHz to complete the function’s requirements.
This must introduce interpolation errors near 30 MHz.
I do now know the error that might be introduced by this
Type of function. I know that Taylor series have alternating sign
In their expansion, and that the values diminish each term,
so the error of approximation remain smaller as the last term
used to interpolate. But Taylor does not suit itself
for approximation of non computable data (such as AF).
My questions for the group are:
What requirements are to be met for the F/AF pairs to
minimize errors?
What are the errors introduced by interpolation?
How do YOU handle this additional uncertainty…?
Gert Gremmen
Ce-test qualified testing bv
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