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Model 4342A
Section
III
Paragraphs
3-49 to 3-44
3-39.
Inductance
Measurement
(at
a desired
frequency).
3-40.
Occasionally
it
may
be necessary
to
measure
inductance
at frequencies
other
than
the
specific
"L"
frequencies.
The frequency
characteristic
measurements
of an inductor
or of an inductor
core
are representative
examples.
In such instances,
the
inductance
may
be measured
as follows:
a.
Connect
unknown inductor
and resonate
it
using
the procedure
same
as
des-
cribed
in Q Measurement
(para.
3-34)
steps
a through
e.
b.
Note FREQUENCY dial,
L/C dial
C scale
and AC dial
readings.
Substitute
these
values
in the following
equation:
L = l/w2C "N0.0253/f2C
. . . . . (eq.
3-5)
Where,
L:
inductance
value
(indicated
L)
of
sample
in henries.
f:
measurement
frequency
in
hertz.
W:
2~r times
the measurement
frequency.
c:
sum of C and AC dial
readings
in farads.
Cd
,4,,A;,i~,
I
r
Cd
3-41. MEASUREMENTS REQUIRING CORRECTIONS.
3-42.
Effects
of
Distributed
Capacitance.
3-43.
The presence
of distributed
capaci-
tances
in a sample influences
Q meter
indi-
cations
with
a factor
that
is related
to both
its
capacity
and the measurement
frequency.
Considerations
for
the distributed
capaci-
tances
in an inductor
may be equivalently
expressed
as shown in Figure
3-8.
In the
low frequency
region,
the
impedance
of the
distributed
capacitance
Cd is extremely
high
and has negligible
effect
on the resonating
circuit.
Thus,
the sample measured
has
an inductance
of Lo, an equivalent
series
resistance
of Ro, and a Q value
of wLo/Ro
(where,
w is 2~ times
the measurement
frequency).
In the high
frequency
region,
the inductor
develops
a parallel
resonance
with
the distributed
capacitance
and the
im-
pedance
of the
sample increases
at frequen-
cies near
the resonant
frequency.
Therefore,
readings
for measured
inductances
will
be
higher
as the measurement
frequency
gets
closer
to the self-resonant
frequency.
Additionally,
at parallel
resonance,
the
equivalent
series
resistance
is substantially
increased
(this
is because,
at resonance,
the
impedance
of the sample changes
from re-
active
to resistive
because
of the phase
shift
in the measurement
current)
and the
measured
Q value
reading
is lower
than that
determined
by wLo/Ro.
Typical
variations
of Q and inductance
values
under
these
condi-
tions
are given
in Figure
3-9.
3-44.
Ratio
of the measurement
frequency
and
the self-resonant
frequency
can be converted
to a distributed
capacitance
and tuning
capa-
citance
relationship
with
the
following
equa-
tion:
fl/fo
= kd/(C
+ Cd) . . . . . . . (eq.
3-6)
Where,
fi:
measurement
frequency.
fo:
self-resonant
frequency
of
sample.
Cd:
distributed
capacitance
of
sample.
c:
tuning
capacitance
of Q
meter.
Figure
3-10 graphically
shows the variation
of measured
Q and inductance
as capacitance
is taken
for
the parameter.
The ideal
inductance
and Q values
in the presence
of
no distributed
capacitance
(or when it
is
negligible)
are correlated
with
the actually
measured
values
by correction
factors
which
correspond
to readings
along
the vertical
Figure
3-8.
Distributed
Capacitance
Circuit
Model.
axis
scales
in Figures
3-9 and 3-10.
3-13
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