Circuit Note

CN-0411

Rev. 0 | Page 3 of 12

CIRCUIT DESCRIPTION

Conductivity and Total Dissolved Solids Theory

The TDS in a solution is largely composed of inorganic salts

that separate into ions in the presence of a polar solvent like

water. When a potential is applied to the solution via two

electrodes, the movement of the ions constitutes a current that,

when there is negligible electrolysis, obeys Ohm’s law. The

resistance, R, of the solution can then be calculated by

Equation 1.

VL

R

IA

ρ

=

=

(1)

where:

V is the potential difference applied to the two electrodes.

I is the measured current across the two electrodes.

ρ is the resistivity of the material in Ω cm.

L is the distance between the two electrodes.

A is the area of the electrodes.

The conductance, G, is the reciprocal of resistance and

measured in Siemens (S), and conductivity, Y, is the reciprocal

of resistivity and measured in S/cm, mS/cm, or µS/cm.

Rearranging Equation 1, the conductance can be obtained from

the potential across the two electrodes and the current through

them. Conductivity is the conductance multiplied by a factor

related to the geometry of the electrodes (see Equation 2).

,  

LI

Y

GG

AV

=

×=

(2)

Typically, conductivity is measured using a 2-electrode sensor

called a conductivity probe or conductivity cell. An excitation

voltage is applied to the conductivity cell while it is immersed in

the solution as shown in Figure 2.

Figure 2. Conductivity Cell in Solution Setup

The conductivity cell constant or simply cell constant, KCELL, is

the ratio of the gap between its two electrodes and the area of

each electrode, which shortens Equation 2 to Equation 3. The

cell constant has a unit of cm−1 but the unit may be omitted by

manufacturers of conductivity probes.

Y = KCELL × G

(3)

The typical measurement system computes conductance from

the current and voltage readings. Since the conductivity range

of values is very large, measuring conductance at the extremes

(values less than 1 µS and greater than 0.1 S) can be difficult for

ordinary instruments. By choosing a conductivity cell with an

appropriate cell constant, the range of conductivity measurement

can be extended. Conductivities less than 0.1 µS/cm can be

measured at a lower conductance by using a conductivity cell

with a lower cell constant. Conversely, conductivities greater

than 0.1 S/cm can be measured at a higher conductance by

using a conductivity cell with a higher cell constant. Typical

values of the cell constant used for a corresponding range of

conductivity measurement is shown in Table 1.

Table 1. Conductivity Cell Constants and the Range of

Conductivity

Cell Constant

Range of Measured Conductivity

0.01

< 0.1 µS/cm

0.1

0.1 µS/cm to 100 µS/cm

1

100 µS/cm to 10 mS/cm

10

10 mS/cm to 1 S/cm

Each conductivity cell has a rated excitation voltage, which

must not be exceeded so as not to damage the electrodes. Do

not apply a dc voltage to any of the electrodes.

Dielectric Properties

Polarization and the dielectric properties of the solution

primarily affect the accuracy of the measured voltage signal

across and the current through the conductivity cell.

Polarization arises from the accumulation of ions and the

chemical reactions that occur near the electrode surface. The

dielectric properties of the solution contribute to a frequency-

dependent impedance and interelectrode capacitance. A

technique used to maximize the accuracy of the conductance

measurement uses a bipolar pulse excitation. An excitation

voltage +VEXC is applied for time t1 then the opposite excitation

voltage −VEXC is applied for time t2. Also, t1and t2, and +VEXC

and −VEXC must be equal with no greater than 1% difference in

duration and magnitude, respectively. The frequency of the

signal (t1 + t2)−1 must be adjusted to the range of conductance

measurement. Typically, this is 94 Hz in the µS range and

2.4 kHz in the mS range. These frequencies are compromises

that minimize the effect of interelectrode capacitance, while

preventing the accumulation of ions on the electrode surface.

Conductivity Measurement

The front-end of the conductivity measurement can be

simplified to a voltage divider network as shown in Figure 3.

Figure 3. Simplified Conductivity Schematic as Two Series Resistors

RGAIN sets the magnitude of the voltage across and current

through the conductivity cell and solution simplified as RCOND.

A

L

V

I

A

A

B

C

RGAIN

VEXC

RCOND