Hioki IM3536 - Page 244

Appx.2
Measurement Parameters and Calculation Formula
From the voltage
V
which is applied between the terminals of the sample under test, the current
I
which ows through the test sample at this time, the phase angle
θ
between this voltage V and this
current I, and the angular velocity
ω
which corresponds to the measurement frequency.
The phase angle
θ
is shown based on the impedance
Z
. When measuring based on the admittance
Y
, the
sign of the phase angle
θ
must be reversed.
Item Series equivalent circuit mode Parallel equivalent circuit mode
Z
(
)
22
XR
I
V
Z +==
(
)
22
BG
Z
1
Y +==
θ
cosZESRR
S
==






==
G
1
cosY
1
R
P
φ
θ
sinZX =
φ
cosYG =
φ
sinYB =
ω
X
L
S
=
B
1
L
P
ω
−=
X
1
C
S
ω
−=
ω
B
C
P
=
θ
θ
sin
cos
D =






==
D
1
cos
sin
Q
θ
θ
Y
(
)
22
XR
I
V
Z +==
(
)
22
BG
Z
1
Y +==
θ
cosZESRR
S
==






==
G
1
cosY
1
R
P
φ
θ
sinZX =
φ
cosYG =
φ
sinYB =
ω
X
L
S
=
B
1
L
P
ω
−=
X
1
C
S
ω
−=
ω
B
C
P
=
θ
θ
sin
cos
D =






==
D
1
cos
sin
Q
θ
θ
R
(
)
22
XR
I
V
Z +==
(
)
22
BG
Z
1
Y +==
θ
cosZESRR
S
==






==
G
1
cosY
1
R
P
φ
θ
sinZX =
φ
cosYG =
φ
sinYB =
ω
X
L
S
=
B
1
L
P
ω
−=
X
1
C
S
ω
−=
ω
B
C
P
=
θ
θ
sin
cos
D =






==
D
1
cos
sin
Q
θ
θ
(
)
22
XR
I
V
Z +==
(
)
22
BG
Z
1
Y +==
θ
cosZESRR
S
==






==
G
1
cosY
1
R
P
φ
θ
sinZX =
φ
cosYG =
φ
sinYB =
ω
X
L
S
=
B
1
L
P
ω
−=
X
1
C
S
ω
−=
ω
B
C
P
=
θ
θ
sin
cos
D =






==
D
1
cos
sin
Q
θ
θ
*
X
(
)
22
XR
I
V
Z +==
(
)
22
BG
Z
1
Y +==
θ
cosZESRR
S
==






==
G
1
cosY
1
R
P
φ
θ
sinZX =
φ
cosYG =
φ
sinYB =
ω
X
L
S
=
B
1
L
P
ω
−=
X
1
C
S
ω
−=
ω
B
C
P
=
θ
θ
sin
cos
D =






==
D
1
cos
sin
Q
θ
θ
G
(
)
22
XR
I
V
Z +==
(
)
22
BG
Z
1
Y +==
θ
cosZESRR
S
==






==
G
1
cosY
1
R
P
φ
θ
sinZX =
φ
cosYG =
φ
sinYB =
ω
X
L
S
=
B
1
L
P
ω
−=
X
1
C
S
ω
−=
ω
B
C
P
=
θ
θ
sin
cos
D =






==
D
1
cos
sin
Q
θ
θ
*
B
(
)
22
XR
I
V
Z +==
(
)
22
BG
Z
1
Y +==
θ
cosZESRR
S
==






==
G
1
cosY
1
R
P
φ
θ
sinZX =
φ
cosYG =
φ
sinYB =
ω
X
L
S
=
B
1
L
P
ω
−=
X
1
C
S
ω
−=
ω
B
C
P
=
θ
θ
sin
cos
D =






==
D
1
cos
sin
Q
θ
θ
*
L
(
)
22
XR
I
V
Z +==
(
)
22
BG
Z
1
Y +==
θ
cosZESRR
S
==






==
G
1
cosY
1
R
P
φ
θ
sinZX =
φ
cosYG =
φ
sinYB =
ω
X
L
S
=
B
1
L
P
ω
−=
X
1
C
S
ω
−=
ω
B
C
P
=
θ
θ
sin
cos
D =






==
D
1
cos
sin
Q
θ
θ
(
)
22
XR
I
V
Z +==
(
)
22
BG
Z
1
Y +==
θ
cosZESRR
S
==






==
G
1
cosY
1
R
P
φ
θ
sinZX =
φ
cosYG =
φ
sinYB =
ω
X
L
S
=
B
1
L
P
ω
−=
X
1
C
S
ω
−=
ω
B
C
P
=
θ
θ
sin
cos
D =






==
D
1
cos
sin
Q
θ
θ
C
(
)
22
XR
I
V
Z +==
(
)
22
BG
Z
1
Y +==
θ
cosZESRR
S
==






==
G
1
cosY
1
R
P
φ
θ
sinZX =
φ
cosYG =
φ
sinYB =
ω
X
L
S
=
B
1
L
P
ω
−=
X
1
C
S
ω
−=
ω
B
C
P
=
θ
θ
sin
cos
D =






==
D
1
cos
sin
Q
θ
θ
(
)
22
XR
I
V
Z +==
(
)
22
BG
Z
1
Y +==
θ
cosZESRR
S
==






==
G
1
cosY
1
R
P
φ
θ
sinZX =
φ
cosYG =
φ
sinYB =
ω
X
L
S
=
B
1
L
P
ω
−=
X
1
C
S
ω
−=
ω
B
C
P
=
θ
θ
sin
cos
D =






==
D
1
cos
sin
Q
θ
θ
D
(
)
22
XR
I
V
Z +==
(
)
22
BG
Z
1
Y +==
θ
cosZESRR
S
==






==
G
1
cosY
1
R
P
φ
θ
sinZX =
φ
cosYG =
φ
sinYB =
ω
X
L
S
=
B
1
L
P
ω
−=
X
1
C
S
ω
−=
ω
B
C
P
=
θ
θ
sin
cos
D =






==
D
1
cos
sin
Q
θ
θ
Q
(
)
22
XR
I
V
Z +==
(
)
22
BG
Z
1
Y +==
θ
cosZESRR
S
==






==
G
1
cosY
1
R
P
φ
θ
sinZX =
φ
cosYG =
φ
sinYB =
ω
X
L
S
=
B
1
L
P
ω
−=
X
1
C
S
ω
−=
ω
B
C
P
=
θ
θ
sin
cos
D =






==
D
1
cos
sin
Q
θ
θ
*
ϕ
: phase angle of admittance
Y
(
ϕ
=-
θ
)
Ls
,
Cs
,
Rs
: The measured values of
L
,
C
, and
R
in series equivalent circuit mode.
Lp
,
Cp
,
Rp
: The measured values of
L
,
C
, and
R
in parallel equivalent circuit mode.