Specifications

The auto-balancing bridge instruments for low frequency impedance measurement (below 100 kHz)
usually employ a simple I-V converter circuit (an operational amplifier with a negative feedback
loop) in place of the ammeter as shown in Figure 2-2 (b). The bridge section works to measure
impedance as follows:
The test signal current (Ix) flows through the DUT and also flows into the I-V converter. The opera-
tional amplifier of the I-V converter makes the same current as Ix flow through the resistor (Rr) on the
negative feedback loop. Since the feedback current (Ir) is equal to the input current (Ix) flows through
the Rr and the potential at the Low terminal is automatically driven to zero volts. Thus, it is called vir-
tual ground. The I-V converter output voltage (Vr) is represented by the following equation:
Vr = Ir x Rr = Ix x Rr (2-1)
Ix is determined by the impedance (Zx) of the DUT and the voltage Vx across the DUT as follows:
Ix =
Vx
(2-2)
Zx
From the equations 2-1 and 2-2, the equation for impedance (Zx) of the DUT is derived as follows:
Zx =
Vx
= Rr
Vx
(2-3)
Ix Vr
The vector voltages Vx and Vr are measured with the vector voltmeters as shown in Figure 2-2 (b).
Since the value of Rr is known, the complex impedance Zx of the DUT can be calculated by using
equation 2-3. The Rr is called the range resistor and is the key circuit element, which determines the
impedance measurement range. The Rr value is selected from several range resistors depending on
the Zx of the DUT as described in Section 2.4.3.
In order to avoid tracking errors between the two voltmeters, most of the impedance measuring
instruments measure the Vx and Vr with a single vector voltmeter by alternately selecting them as
shown in Figure 2-3. The circuit block, including the input channel selector and the vector volt-
meter, is called the vector ratio detector, whose name comes from the function of measuring the
vector ratio of Vx and Vr.
Figure 2-3. Impedance measurement using a single vector voltmeter
DUT
V
High Low
R
r
R
s
V
x
V
r
Auto-balancing bridge section
Signal source section
Vector ratio detector section
2-5