Circuit Note

CN-0359

analog.com

Rev. C | 6 of 10

The peak-to-peak cell voltage can be derived from the differential

outputs of the analog front end, as shown in Equation 9 and

Equation 10:

V1P‐P=VOUT1G1×α

(9)

V2P‐P=VOUT2G2×α

(10)

where:

G1 is the AD8253 gain setting in the cell voltage measurement

circuit.

G2 is the AD8253 gain setting in the cell current measurement

circuit.

α is the attenuation from the ADA4528-2 stage.

By combining Equation 8 and Equation 10, an expression can be

obtained for IP-P:

IP‐P=VOUT2G2×α×1Rf

(11)

Finally, by substituting Equation 9 and Equation 11 back into Equa-

tion 7, the general formula for conductance as a factor of the

differential ADC measurements can be written as:

Y=G1×VOUT2

G2×VOUT1

×1Rf

(12)

In this reference design, the ADA4627-1 feedback resistor has a

value of 1 kΩ resulting in Equation 13:

Y=G1×VOUT2

G2×VOUT1

×1 mS

(13)

From the cell conductance, the ADuCM360 can then calculate the

conductivity of the liquid based on the cell constant of the sensor as

shown in Equation 14:

YX=Y×K

(14)

where:

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

Y is the measured cell conductance.

K is the cell constant in cm-1.

SYSTEM ACCURACY MEASUREMENTS

Equation 9 through Equation 13 are all based on the assumption

that the four individual ADA4528-2 op amps provide the same

attenuation value of 0.16; any deviation would introduce an error in

the final measurements. Since the attenuation of an ADA4528-2 op

amp is dependent on its feedback resistance and input resistance,

the resistors used for these should be matched as closely as

possible with their counterparts in each channel to maintain the

system accuracy.

Equation 13 also shows that the conductivity measurement de-

pends on G1, G2, and Rf, and the ratio of VOUT2 to VOUT1.

Therefore, a precision reference is not required for the ADCs within

the ADuCM360.

Additionally, the conductance calculation performed by the

ADuCM360 assumes an exact 1 kΩ value for the ADA4627-1

feedback resistance, as shown in Equation 13. The farther the

actual resistance is from this ideal value, the greater the error

introduced into the calculation; therefore, it is imperative that a high

precision resistor be used for the ADA4627-1 feedback.

Assuming that all nine resistors have 0.1% tolerance, and including

the 0.04% (max) gain error of the AD8253, a worst-case error

analysis yields approximately 0.6%.

In practice, the resistors are more likely to combine in an RSS

manner, and the RSS error due to the resistor tolerances in the

positive or negative signal chain is √5 × 0.1% = 0.22%.

Accuracy measurements were taken using precision resistors from

1 Ω to 1 MΩ (1 S to 1 μS) to simulate the conductivity cell. Figure 6

shows the results, and the maximum error is less than 0.1%.

Figure 6. System Error (%) vs. Conductivity of 1 μS to 1 S

In order to maintain accuracy over a wide input range with a

high signal-to-noise ratio, a given measurement must use a large

fraction of the ADC's input range without exceeding full-scale.

The CN0359's software implements a simple autoranging scheme,

adjusting the AD8253's gain to maintain the ADC's input between

10% and 90% of full-scale.

PREVENTING ELECTROLYSIS AND

POLARIZATION

For proper conductivity measurements, it is critical to prevent

electrolysis of the sample solution and polarization of the cell

electrodes. Electrolysis is a chemical reaction caused by applying

an excessively large voltage level to the conductivity cell, and

changes the conductivity of the sample solution over time. Polariza-

tion of the conductivity cell occurs when current is allowed to flow

across the electrodes in one direction for a sufficiently long time.

In this scenario, ions accumulate on the surfaces of the electrodes,

resulting in the formation of a space charge region, and thereby

restricting the flow of current. Both electrolysis and polarization