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Model 4277A
SECTION III
Expanding the above equation, we have
G + joiCp
1
u)Cs
1
Oi^Cs'
where, Cs (= - -^) J equivalent series circuit
capacitance
B
Cp C= —)
: equivalent parallel
circuit capacitance
Obviously, if no series resistance (R) or parallel
conductance (G) are
present,
the
equivalent
series circuit capacitance (Cs) and equivalent
parallel circuit capacitance (Cp) are identical.
Likewise, if R and G are not present, the
equivalent series circuit inductance (Ls) and
equivalent parallel circuit inductance (Lp) are
identical.
However, a sample value measured in a parallel
measurement circuit can be correlated with that
of
a series
circuit by a simple
conversion
formula which considers the effect of dissipation
factor.
See Table 3-9.
Figure 3-7 graphically
shows the relationships of parallel and series
parameters for various dissipation factor values.
Applicable diagrams and equations are given in
the chart.
For example, a parallel capacitance
(Cp) of lOOOpF with a dissipation factor of 0.5 is
equivalent to a series capacitance (Cs) of 1250pF
with an identical dissipation factor. As shown in
Figure 3-7, inductance or capacitance values for
parallel and series equivalents are nearly equal
when the dissipation factor is less than 0.03.
The dissipation factor of a component always has
the same value at a given frequency for both
parallel and series equivalents.
In ordinary
LCR measuring instruments, the
measurement circuit is set (automatically or
manually) to a predetermined equivalent circuit
with respect to either the selected range or to
the dissipation factor value of the sample. The
wider circuit mode selection capability of the
4277A, which is free from these restrictions,
permits taking
measurements
in
the desired
circuit mode and of comparing such measured
values directly with those obtained by another
instrument. This obviates the inconvenience and
necessity of employing instruments capable of
taking measurements with the same equivalent
circuit
to
assure
measurement
result
correspondence.
Figure 3-7.
Parallel
and
Series
Parameter
Relationship.
Table 3-9.
Dissipation Factor Equations and Equivalent Circuit
Conversion Formulas
Circuit Mode
Dissipation Factor
Conversion to Other Modes
C
Cp
G
D =
i
wCp
Q
Cs = (-1 t D") Cp, R' =
i
C8 R
D = wCsR =
^
...
1
1
Cp - X +
C . 1 +
R
L
LP
G
D
=
ojLpG
= ^
LS
=
1
i
d2 Lp. R
=
1
■ G
LS R
HZlWirM)
p ™
= i_
wLs
Q
Lp
=
(1
^
0==) Ls, G
=
• i
3-35
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