HP 4262A Operating And Service Manual page 36

Section HI Model 4262A
Figure 3-4
Measurement Parameter Conversions
Parameter values for a component measured in a
parallel equivalent circuit and that measured in
series equivalent circuit are different from each
other. For example, the parallel capacitance of a
given component is not equal to the series capa¬
citance of that component. Figure A shows the
relationships between parallel and series para¬
meters for various values of D. Applicable dia¬
grams 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) value of 1250pF at
1kHz. As shown in Figure A, inductance or capa¬
citance values for parallel and series equivalents
are almost identical when the dissipation factor
is less than 0.01. The letter D in Figure A re¬
presents dissipation factor and is calculated by
the equations presented in Table A for each cir¬
cuit mode. The dissipation factor of a com¬
ponent always has the same dissipation factor at
Table A. Dissipation Factor Equations.
c rcuit Mode
Dissipation Factor
Conversion to other modes
Cp mode
o:
0 ' 2»fCpRp Q !
Cs » ft - D2)Cp, Rs *
■ Rp
Cs mode
Cs R
$
HHWr- D = 2*fCsRs (= -i-)
T~d2 Cs' Rp =
HP1*5
Lp mode
-&L
u = T^d2 Lp- Rs = T?l>2• Rp
Ls mode
Ls
Bn
D-iSb
h~Q-'
Lp«(l +D*)U, Rp «
'f: Test signal frequency.
Where n stands for a free integer.
FigureA. Relationships between Parallel and Series Parameters.
Figure 3-5. Conversion Between Parallel and Series Equivalents.
a given frequency for both parallel equivalent
and series equivalent circuits.
Note
Dissipation factors displayed when
CIRCUIT MODE is switched between
PRL and SER may exhibit slight dif¬
ferences due to the measurement ac¬
curacy of the 4262A.
The reciprocal of the dissipation factor (D) is
quality factor (Q) and D is often represented as
tan
<5
which is the tangent of the dissipation
angle (5). Figure 3-6 is a graphical presentation
of the equations in Table A. For example, a
series inductance of lOOOqH which has a dissipa¬
tion factor of 0.5 at 1kHz has a series resistance
of 3.14 ohms.