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~
TYPE 1608-A IMPEDANCE BRIDGE
~ - - - - - - - _ - - - - - . _ - -
50
c
R
L
Figure 2-4 Resistor equivalent circuit.
,resistance range, so that both R s and G p would differ
appreciably from the dc values.
However, it is highly
unlikely that a component designed as a resistor would
have the required inductance and capacitance (although
a large air-cored inductor could).
A I-kilohm re sistor
would have to have a 5000-pf shunt capacitance to pro-
duce a 0.1% error from the Qc 2 term in equation (1) and a
5-mh series inductance to produce a 0.1% error from the
Qr..
2 term in equation (2). The product QcQL
IS
equal to
(:0~2
where f0 2 is the resonant frequency (27TtC)'
To
produce a 0.1% error at 1 kc from the 2QcQL term, the
resonant frequency would have to be less than 45 kc.
b. Distributed Capacitance, "Boella Effect". For
very high-value resistors an equivalent circuit consist-
ing of a resistor and a single parallel lumped capacitor
is not good enough. Actually, there is capacitance from
every part of the surface of the resistor to every other
part.
As a result of this distributed capacitance, the
real parr of the admittance, or parallel conductance, G p ,
is frequency-dependent.
A rule of thumb for film-type
resistors is that the equivalent parallel resistance will
be reduced by approximately 10% when the product of the
re!>istance in megohms and the frequency in megacycles
is unity. Composition resistors have a somewhat larger
change. At 1 kc this would mean a 10% change at 1000
MD or, since the error is roughly proportional to R 1, the
error would be approximately 0.1% at 10 MD.
The Type
160B-A has 0:15% accuracy at 100 mJ-lU(lOMD) and re-
duces to 5% at 1 mj.LU(lOOO MD). Therefore, this effect
is just barely noticeable at the extreme of the G p range
for most resistors.
.
c.
Distributed Capacitance to Bridge Case.
If
there is distributed capacitance from the body of the re-
sistor to a third (guarded) terminal, such as the cabinet
of the Type 1608-A Bridge, the effective measured paral-
lel 'conductance, G p , will decrease with frequency. The
expression;
1
1
:Gp
=""R
u;2R2C2 gives the first error term. At 1 ke,
1
+
1
1
Gp~
-R- 1 + R2 C?- x 10
6
where R is in MD and C is in
18
pf. This gives a 1% error when R
=
100 MD and C
=
1 pf.
This effect is just noticeable if a large resistor is spaced
very close to the bridge panel, and causes no measurable
error if the unknown is_spaced away from the panel and
other grounded conductors.
d. MagnetIc Coupling - Iron Loss. If the resistor
is wire-wound and is placed near a conductor, currents
may be induced in the inductor, and the resulting eddy
current losses (and hysteresis loss if iron) will be equiv-
alent to a resistor shunting the unknown. This effect is
completely negligible in resistors, but is the main reason
why the ac and dc resistances of transformers differ.
The effect is hardly noticeable on higlr-frequency ferrite-
cored chokes measured at 1 kc.
e.
Skin Effect.
This is completely negligible at
1 kc.
The error would be worse for heavy wire and at
1 kc the error would be less than 10 ppm for 50 mil
(No.
16) wire.
L -
I
Ide
Figure 2-5. Resistance of nonlinear
resistor.
2.4.6.3 Level
Effects.
a.
Power Dissipation.
The measured ac and dc
resistance of a resistor could differ if the power level for
the two measurements were different, resulting in differ-
ent resistor temperatures. Generally, ac bridges are more
sensitive than dc bridges and therefore require less ap-
plied power for equal precision. Therefore, the ac meas-
urement would usually give a more accurate measurement
of
low-level resistance.
If the thermal time constant of the resistor being
measured is not very long compared with the period of
the ac signal, the resistance could change during the ac
cycle, giving an ac value that is frequency-dependent.
This effect would rarely be noticeable at 1 kc.
b. Nonlinear Resistors. If a resistor is nonlinear,
as is the resistance curve of Figure 2-5, there are sever-
al different ways of specifying resistance. Line A is th.e
low-level resistance which could be more easily meas-
ured using ac because of the higher sensitivity of ac
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