EIS Measurement of Small Impedances – What is Mutual Inductance?
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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 windings of a transformer, and the sense leads are the
secondary windings. 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 are discussed below.
Avoid high frequencies
Mutual inductance is an inductive effect. The voltage error is given by:
V
s
=
M
d
i
/d
t
where
V
s
is the induced voltage on the secondary,
M
is the coupling constant (with units of Henries), and d
i
/d
t
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, d
i
/d
t
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 cables, the current-carrying leads are bound together.
From basic physics, the
E
B
cross-product relationship for current through a wire obeys the Right-Hand-Rule:
if your right thumb points in the direction of the current flow in a wire, when you curl your fingers around the
wire, the magnetic field curves around the wire in the same direction as your fingers. The current in the
primary wires is flowing in opposite directions in the two wires of the cable, so your thumb points in opposite
directions for each wire, causing some cancellation of the fields. If the wires were superimposed, in exactly the
same place, the cancellation would be perfect.
Because the wires cannot be in identically the same location, the cancellation is imperfect, and some net
magnetic field is always present. The more the wires are separated, the larger the net field.
The most common arrangement for inductance and field minimization is the twisted pair. Two insulated wires
are simply twisted together. A coaxial-wire arrangement with current flowing in opposite directions in the
center conductor and the outer conductor is also effective.
Separate the pairs
If you place a magnetic-field probe near a wire passing current, you measure a field inversely proportional to
the square of the distance between the probe and the wire.
In an electrochemical system, the probe is our sense wiring. Separating the sense wires from the current-
carrying wires can dramatically reduce the magnetic coupling, reducing errors in the EIS measurement
