Chapter 10 – EIS Measurement of Small Impedances--What is Mutual Inductance?
10 - 3
Four-terminal measurements are also useful in AC measurements, although there is a factor called mutual
inductance (discussed below) makes the AC case more complicated. Ignoring this complication for a moment,
a simple extension of the discussion above will show 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 not 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 will group them into two pairs.
One pair is the counter and working leads (red and green). They carry the cell current so we will 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 will be called the sense leads.
A “mutual inductive” effect limits the ability of any system to measure small impedances at higher frequencies.
The term mutual inductance describes the influence of the magnetic field generated by the current carrying
leads on the sense leads.
In essence, the current carrying leads are the primary of a transformer and the sense leads are the secondary.
The AC current in the primary creates a magnetic field that then couples to the secondary, where it creates an
AC voltage.
You can minimize the unwanted effect in a number of ways:
• Avoid higher frequencies
• Minimize the net field generated by the current carrying leads.
• Separate the current carrying leads from the sense leads.
• Minimize pickup of the field in the sense leads.
Each of these ways will be discussed below.
Avoid high frequencies
Mutual inductance is an inductive effect. The voltage error is given by:
Vs = M di/dt
where Vs is the induced voltage on the secondary, M is the coupling constant (with units of Henries), and di/dt
is the rate of change in the primary current. M depends on the closeness of the coupling and can range from
zero up to the value of the primary inductance (the inductance in the current carrying leads).
Assuming a constant amplitude waveform in the primary, di/dt is proportional to frequency. There is always a
frequency below which the effect of mutual inductance errors is unimportant. Unfortunately, many
electrochemical systems need information at frequencies above this limit.
Minimize the Net Magnetic Field
A current passing through a wire creates a magnetic field. The field strength is proportional to the current.
Fortunately, passing the same current in opposite directions through adjacent wires tends to cancel the external
field. This also minimizes the net inductance in the wires. In all Gamry Instruments Reference 3000
Counter/Working cable, the current carrying leads are bound together.
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