Instructions

9
Measurement Principles
Circuit models
Resistors, capacitors and inductors can all be represented at a given frequency by a simple
series or parallel equivalent circuit. It must be stressed that this is a simple equivalent circuit and
as such will only be representative over a limited frequency range. The effects of a wide
frequency range are discussed later.
The Models used by the LCR400 are as follows:
Lpj
Rp
LpRpj
Zp
Lsj
RsZs
ω
ω
ω
+
=
+
=
Rs
Ls
Lp
Rp
Q
ω
ω
=
=
Lp
Q
Q
Ls
2
2
1+
=
Q
L
Rs
s
ω
=
LpQRp
ω =
Cs
jRsZs
ω
1
−=
RpCpj
Rp
Zp
ω +
=
1
RpCp
RsCsD
ω
ω
1
==
Q
D
1
=
(D is also known as tan δ )
CpDCs
)1
(
2
+
=
Rp
D
D
Rs
2
2
1+
=
where ω = 2πf
Resistors
All resistors have parasitic impedances, both inductance and capacitance and distributed effects
of both. Fortunately, however, in normal use these parasitic effects are usually very small
compared with the resistance.
The LCR 400 provides the opportunity to evaluate the series and parallel components of resistors
at 100Hz and 1kHz and 10kHz.
Some types of resistor have more prominent parasitic effects than others. Wire wound resistors,
unless they are specially wound, have more inductance than their carbon and metal film
equivalents. Even carbon film resistors have inductance due to the inductance of the leads and
the spiral cut used to trim the resistance. There is also always capacitance between the end cap
connections - on metal film resistors it is typically around 0.25pF. This usually only becomes
significant on high value resistors or/and at high frequencies. Bifilar wound resistors may have
low inductance but the close proximity of the windings can introduce significant capacitance –
distributed along the resistance. To predict the performance of such a component at high