Section III
Model 4342A
Paragraphs 3-51 to 3-54
Measurements Requiring Corrections
Figure 3-10 is a graphical solution to equa-
tion 3-11. The corrected Q value Qt may be
deemed the quality factor calculated
as
wLo/Ro from inductance Lo, equivalent series
resistance Ro,
and the measurement frequency
(refer to paragraph 3-43).
However, Qt is
not identical to "effective Q".
The correct-
ed Q is also a "circuit Q" which includes the
additional losses of the measuring circuit.
3-51. By substituting equation 3-6 in equa-
tion 3-11, the correction factor in equation
3-11 can be converted into a relationship of
measurement frequency and self resonant fre-
quency of sample. And the corrected quality
factor may be expressed as follows:
Qt = Qi
+
fl 2”“““’
(eq. 3-13)
fo
Where, fl:
measurement frequency.
fo: self resonant frequency of
sample.
A graphic expression of the above equation is
shown in Figure 3-9.
When fl is greater than
fo ,
equation 3-13 produces a negative Qt.
However, this negative Q has no meaning and
should not be used.
A negative Q is obtained
when the reactance of the sample becomes
capacitive (effect of distributed capacitance)
instead of inductive at frequencies above fo.
3-52.
CORRECTION FOR INDUCTANCE.
3-53. The residual inductance of the meas-
uring circuit is included in the measured
inductance of sample.
When the sample value
is in the vicinity of 0.5~H or less, the
measured inductance should be compensated for
such residual inductance.
This compensation
can be made simply by subtraction as follows:
Lm = Li - Lres . . . . . . . . . . . . (eq. 3-14)
Where, Lm:
measured value excluding re-
sidual inductance.
Li: measured inductance.
Lres: residual inductance of meas-
uring circuit.
The Lres in the 4342A is approximately
O.OlpH.
3-54. Correction of the measured inductance
to arrive at a true model of the equivalent
circuit of the sample also requires a correc-
tion for the distributed capacitance (similar
to the correction in para. 3-50 for indicated
9)
.
The corrected inductance value is given
by the following equation:
Lt =
Li
Where, Lt:
Li:
c:
Cd:
C
C + Cd
. . . . . . . . . .
(eq. 3-15)
corrected inductance value.
indicated inductance value.
sum of C and AC dial readings.
distributed capacitance of
sample.
Equation 3-15 may be converted into a fre-
quency form as follows:
Lt = Li {l - [%I21 . . . . . . (eq. 3-16)
Where, fi:
measurement frequency
fo: self resonant frequency
of
sample.
Graphic solutions of equations 3-15 and
3-16 are shown in Figures 3-10 and 3-9,
respectively.
3-16
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