Circuit Note

CN-0359

analog.com

Rev. C | 3 of 10

CIRCUIT DESCRIPTION

CONDUCTIVITY THEORY

The resistivity of a material or liquid is defined as the resistance of a

cube of the material with perfectly conductive contacts on opposite

faces. The resistance can be calculated using Equation 1:

R=ρLA

(1)

where:

R is the resistance.

ρ is the resistivity of the material.

L is the distance between the contacts.

A is the area of the contacts.

Resistivity is measured in units of Ω cm. A 1 Ω cm material has a

resistance of 1 Ω when contacted on opposite faces of a 1 cm × 1

cm × 1 cm cube.

Conductance is the reciprocal of resistance, and conductivity is the

reciprocal of resistivity. The unit of measurement of conductance is

Siemens (S), and the unit of measurement of conductivity is S/cm,

mS/cm, or μS/cm.

All aqueous solutions conduct electricity to some degree. Adding

electrolytes such as salts, acids, or bases to pure water increases

the conductivity (and decreases resistivity).

For the purposes of this circuit note, Y is the general symbol for

conductivity measured in S/cm, mS/cm, or μS/cm. However, in

many cases, the distance term is dropped for convenience, and the

conductivity is simply expressed as S, mS, or μS.

A conductivity system measures conductivity by means of electron-

ics connected to a sensor called a conductivity cell immersed in a

solution, as shown in Figure 2.

Figure 2. Conductivity Cell Geometry and Electrical Connections

The electronic circuitry applies an alternating voltage on the sensor

and measures the resulting current, which is related to the conduc-

tivity. Because conductivity has a large temperature coefficient (up

to 4%/°C), a temperature sensor is incorporated into the circuitry

to adjust the reading to a standard temperature, usually 25°C

(77°F). When measuring solutions, the temperature coefficient of

the conductivity of the water itself must be considered.

A basic conductivity sensor typically consists of two electrodes that

are insulated from one another. The electrodes, typically Type 316

stainless steel, titanium palladium alloy, or graphite, are specifically

sized and spaced to provide a known cell constant. Theoretically, a

cell constant of 1.0/cm describes two electrodes, each sized 1 cm2

in area, and spaced 1 cm apart. Cell constants must be matched to

the measurement system for a given range of operation.

For instance, if a sensor with a cell constant of 1.0/cm is used in

pure water with a conductivity of 1 μS/cm, the cell has a resistance

of 1 MΩ. Conversely, the same cell in seawater has a resistance

of 30 Ω. Because the resistance ratio is so large, it is difficult for

ordinary instruments to accurately measure such extremes with

only one cell constant.

When measuring the 1 μS/cm solution, the cell is configured with

large area electrodes spaced a small distance apart. For example,

a cell with a cell constant of 0.01/cm results in a measured cell re-

sistance of approximately 10,000 Ω rather than 1 MΩ. It is easier to

accurately measure 10,000 Ω than 1 MΩ; therefore, the measuring

instrument can operate over the same range of cell resistance for

both ultrapure water and high conductivity seawater by using cells

with different cell constants.

The cell constant is defined as the ratio of the distance between the

electrodes to the area of the electrodes, which can be calculated

using Equation 2:

K=LA

(2)

where:

K is the cell constant in cm-1.

L is the distance between electrodes in cm.

A is the area of electrode surface in cm2.

The instrumentation then measures the cell conductance using

Equation 3:

Y=IV

(3)

Y is the measured cell conductance in S.

I is the cell current.

V is the excitation voltage.

The conductivity of the liquid is then calculated using Equation 4:

Yx=K×Y

(4)

Yx is the conductivity of the liquid in S/cm.

K is the cell constant in cm-1.

Y is measured conductance in S.

There are two types of conductivity cells: those with two electrodes,

and those with four electrodes, as shown in Figure 3. The electro-

des are often referred to as poles.