On 23 April 2013 20:56, Bill Turner <dezrat1242@yahoo.com> wrote:
> According to theory, pure inductance does not vary with frequency,
Using accurate theories, that is not true, although it is a very good
approximation to several GHz, so totally irrelevant in this context,
but I thought I would bring to peoples attention that to say the
inductance of something is fixed with frequency is not true.
There are of course there are lots of theories in electrical
engineering, which make assumptions which are not 100% true. One
example being the capacitance of a parallel plate capacitor, which
ignores the fringing capacitance and the finite loss of the
conductors. A more advanced theory will take into account the
fringing capacitance and assume this is constant. A more advanced
theory will take into account that the fringing capacitance is not
constant.
If you look at a vector network analyzer calibration kit such as the
Agilent 85032F (9 GHz) or the expensive 85054B you will see the
fringing capacitance of the open standard is not fixed wth frequency.
The fringing capacitance is approximated by a 3rd order polynomial,
and might typically change by a few percent over the range of DC-6
GHz.
C=C0 + C1 f + C2 f^2 + C3 f^3
This theory comes up from the result of truncating a coaxial line.
Sine the line is circularly symmetric, anyone who has studied
electrical engineering to a high level would not be surprised this
variation involved Bessel functions.
However, you will also see the inductance of the short circuit, is
frequency dependant. The effect of this is small, and even in my 20
GHz VNA, one can't enter the inductance of a coaxial short - it is
assumed to be zero. BUT on higher specification VNAs, the inductance
of the short can be approximated bya polynomial or the form
L=0 + L1 f + L2 f^2 + L3 f^3
You can find the contants in the data sheets of the standards.
http://na.tm.agilent.com/pna/caldefs/stddefs.html
e.g.for the 85054B calibration kit, which I'd like to purchase funds
permitting, the inductance of the shorts on the male and female N
connectors are different, and both frequency dependant. Here are the
constants for one of them.
L=0.7563 10^-12 + 459.8799 10^-24 f -52.429 10^-33 f^2 + 1.5846 10^-42 f^3
where f is in Hz, and L in Henrys.
So in essence to say fringing capacitance or inductance are
independent of frequency is not true, although for frequencies under a
few GHz the variation of capacitance is insignificant and the
variation of inductance can be ignored to many GHz.
> Probably the most useful way is with an accurate grid dip meter and a
> precision capacitor so the combination is resonant near the operating
> frequency. Done carefully, you should get within about 1% of the effective
> measurement. Any closer than that will probably be thrown off by unavoidable
> stray capacitance.
It sounds good to me.
Another technique I have used is a small (3 mm or so) loop on the end
of a bit of thin coax connected to a VNA. A dip in |S11| is seen
whenever the coil absorbs power. It is essentially the same, just a
more expensive way of doing it!!!
> Bill, W6WRT
Dave, G8WRB
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