In article , Paul Burridge
writes:
On Tue, 7 Dec 2004 07:31:08 +0000, "Ian White, G3SEK"
wrote:
To home in on the inductance of the resistor body itself, I'd have to
build a jig that allows the wire lengths to be reduced almost to zero.
Harold W4ZCB sent a picture of something he uses, which is just a brass
plate soldered to the back of an SMA connector. The Device Under Test is
then soldered directly between the centre pin and somewhere on the
plate.
How about cutting the resistor's leads off completely and just
clamping it between say two 1" cube copper blocks? But then I guess
you would still have the problem of connecting it to the VNA. :-(
That is more trouble to set up than is needed.
In order to measure any inductance component, the only
requirement is to find the DIFFERENTIAL between a direct
short across the bridge/RLC-meter connections and the
device itself (in this case a resistor).
Neil Hecht's excellent little LC Meter II does this automatically
by the zeroing button that subtracts the shorting inductance
from the device measurement, done arithmetically in the internal
microcontroller's registers.
The inductance of a standard gauge round wire is fairly well
known and has been around for years in texts. One can compute
that inductance fairly accurately without using a bridge/meter and
then compare that to the leads of the device under test. The
difference between the shorting lead and the device leads would
then be the inductance of the device-under-test's body.
If a few nanoHenries are involved and affect the circuit the device
is to be used in, the frequency would be high enough that skin
effect would be operative. Skin effect is the curious phenomenon
where current flows in thinner and thinner volume spaces near the
surface of a conductor. The thickness of the bridge/meter
connections would only be advantageous at DC (no skin effect at
all, only "straight" volumetric conductor bulk resistance) or lower
frequencies (where the "skin" is quite deep in the conductor). An
approximation of the RF resistance in Ohms/Inch-length is:
R_rf = (2.61 x 10^-7 x Sqrt( frequency in Hz)) / (2 x (w + h))
for PCB foil and where w = trace width in inches, h = thickness
of the PCB foil in inches (about 0.002 times "ounce" rating of
foil thickness, give or take some).
Reference: Nicholas Gray, Staff Applications Engineer,
National Semiconductor, "Design Idea" insert in electronics
trades for December, 2004. See also
http://edge.national.com
However, when push comes to shove on measuring things, a
built-in inductance might be as much as 10 nanoHenries. At
100 MHz that inductance is equal to +j 6.283 Ohms. A precision
resistor of 50 Ohms at DC would have an equivalent series
magnitude of 50.39 Ohms, an increase over DC of only 0.79%.
The end result to a circuit using that device wouldn't amount to
very much change.
If that inductance were (somehow) ten times higher to 100 nHy,
then it would have +j 62.83 Ohms and the series magnitude would
(of that 50 Ohm resistor at DC) be 80.30 Ohms. That WILL have
some noticeable effect on a circuit at 100 MHz.
The upshot of all this is that one considers the frequency(s) of
operation first, then measures a part second to find out if the
resulting part inductance will have any effect on things. In order
to measure the part, the characteristics of the measuring instrument
ought to be known so as to get a reasonably accurate measurement.
Comparing the part to a wide conductor across the instrument
connections as the reference inductance, the part is then measured
with the wide conductor inductance subtracted from the mesaured
series inductance.
Some LC bridges measure admittance rather than impedance. If
that's the case, then the complex admittance (an equivalent R &
C in parallel) must be inverted to find the complex impedance
which is a series R and L. A grid-dipper sort of measurement
just won't yield any meaningful result for either Z or Y.