Specifications

2.3.3 Vector ratio detector section
The vector ratio detector (VRD) section measures the ratio of vector voltages across the DUT, V
x
,
and across the range resistor (Vr) series circuit, as shown in Figure 2-6 (b). The VRD consists of an
input selector switch (S), a phase detector, and an A-D converter, also shown in this diagram.) The
measured vector voltages, Vx and Vr, are used to calculate the complex impedance (Zx) in accor-
dance with equation 2-3.
Figure 2-6. Vector ratio detector section block diagram
In order to measure the Vx and Vr, these vector signals are resolved into real and imaginary compo-
nents, Vx = a + jb and Vr = c + jd, as shown in Figure 2-6 (a). The vector voltage ratio of Vx/Vr is
represented by using the vector components a, b, c, and d as follows:
Vx
=
a + jb
=
ac + bd
+ j
bc - ad
(2-4)
Vr c + jd c
2
+ d
2
c
2
+ d
2
The VRD circuit is operated as follows. First, the input selector switch (S) is set to the Vx position.
The phase detector is driven with 0° and 90° reference phase signals to extracts the real and imagi-
nary components (a and jb) of the Vx signal. The A-D converter next to the phase detector outputs
digital data for the magnitudes of a and jb. Next, S is set to the Vr position. The phase detector and
the A-D converter perform the same for the Vr signal to extract the real and imaginary components
(c and jd) of the Vr signal.
From the equations 2-3 and 2-4, the equation that represents the complex impedance Zx of the DUT
is derived as follows (equation 2-5):
Zx = Rx + jXx = Rr
Vx
= Rr
[
ac + bd
+ j
bc - ad
]
(2-5)
Vr c
2
+ d
2
c
2
+ d
2
The resistance and the reactance of the DUT are thus calculated as:
Rx = Rr
ac + bd
, Xx = Rr
bc - ad
(2-6)
c
2
+ d
2
c
2
+ d
2
Various impedance parameters (Cp, Cs, Lp, Ls, D, Q, etc) are calculated from the measured Rx and
Xx values by using parameter conversion equations which are described in Section 1.
V
X
= a + jb
90º
V
r
= c + jd
b
ac
d
(a) Vector diagram of V
x
and V
r
(b) Block diagram
DU T
R
r
H
c
L
c
L
p
H
p
V
X
V
r
ATT A/D
Buffer
Buffer
Phase
detector
To digital
section
S
0º
0º, 90º
2-8