EIS Measurement of Small Impedances – What is Mutual Inductance?
82
An illustration of two-terminal measurements versus four-terminal measurements is provided in Figure 11-1.
Both schematic diagrams show a resistance measurement made by passing a known current through an
unknown resistance,
R
test
. The wires in the circuit have a resistance
R
wire
. A voltmeter with high input-impedance
reads a voltage that is divided by the current value to calculate the value of
R
test
.
In the two-terminal case, the voltage measurement is made using the same wires that carry the current. The
voltmeter measures:
V
=
I
test
× ( 2 ×
R
wire
+
R
test
)
The calculated
R
test
is too high, since the resistance of the wires is added to the unknown resistance.
In the four-terminal case, the voltmeter uses two additional wires to measure the voltage close to
R
test
. The
current is carried through the original pair of wires. There is no current through the voltmeter wires, so the wire
resistance does not create voltage drop. The voltmeter measures:
V
=
I
test
×
R
test
The addition of two wires to the circuit eliminates the error caused by the resistance of the wires.
Figure 11-1
Two and Four Terminal Measurements
Four-terminal measurements are also useful in AC measurements, although there is a factor called mutual
inductance (discussed below) that makes the AC case more complicated. Ignoring this complication for a
moment, a simple extension of the discussion above shows that four-terminal measurements can also eliminate
the effects of wire inductance.
In the real world, true four-terminal measurements are rarely possible. There is almost always some metallic
conductor shared by both current-carrying leads and the voltage sensing leads. The metal volume shared
between the current-carrying function and the sensing function can be minimized, but never eliminated.
What is Mutual Inductance?
Before we can define mutual inductance, we must define some terms. As discussed above, four leads connect
to the cell in an electrochemical system used to test small impedances. We group them into two pairs.
One pair is the counter and working leads (red and green). They carry the cell current, so we call them the
current-carrying leads
.
The reference and working sense leads (white and blue) form the second pair. They measure the voltage across
two points in the cell. These leads are called the
sense leads
.
