CN0326

Fundamentals of pH Measurements

The pH value is a measure of the relative amount of hydrogen and hydroxide ions in an aqueous solution. In terms of molar concentrations, water at 25°C contains 1 × 10⁻⁷ moles/liter of hydrogen ions and the same concentration of hydroxide ions. A neutral solution is one in which the hydrogen ion concentration exactly equals the hydroxide ion concentration. pH is another way of expressing the hydrogen ion concentration and is defined as follows:

Therefore, if the hydrogen ion concentration is 1.0 × 10⁻² moles/liter, the pH is 2.00.

The pH electrodes are electrochemical sensors used by many industries but are of particular importance to the water and wastewater industry. The pH probe consists of a glass measuring electrode and a reference electrode, which is analogous to a battery. When the probe is place in a solution, the measuring electrode generates a voltage depending on the hydrogen activity of the solution, which is compared to the potential of the reference electrode. As the solution becomes more acidic (lower pH) the potential of the glass electrode becomes more positive (+mV) in comparison to the reference electrode; and as the solution becomes more alkaline (higher pH) the potential of the glass electrode becomes more negative (−mV) in comparison to the reference electrode. The difference between these two electrodes is the measured potential. A typical pH probe ideally produces 59.154 mV/pH units at 25^oC. This is expressed in the Nernst equation as follows

The equation shows that the voltage generated is dependent on the acidity or alkalinity of the solution and varies with the hydrogen ion activity in a known manner. The change in temperature of the solution changes the activity of its hydrogen ions. When the solution is heated, the hydrogen ions move faster which result in an increase in potential difference across the two electrodes. In addition, when the solution is cooled, the hydrogen activity decreases causing a decrease in the potential difference. Electrodes are designed ideally to produce a zero volt potential when placed in a buffer solution with a pH of 7.

A good reference on the theory of pH is pH Theory and Practice, Radiometer Analytical SAS, Villeurbanne Cedex, France.

Circuit Details

The design provides a complete solution for pH sensor with temperature compensation. The circuit has three critical stages: the pH probe buffer, the ADC, and the digital and power isolator as shown in Figure 1.

The AD8603, a precision micro power (50 μA maximum) and low noise (22 nV/√Hz) CMOS operational amplifier configured as a buffer to the input of one of the channels of the AD7793.The AD8603 has a typical input bias current of 200 fA that provides an effective solution to the pH probe that has high internal resistance.

The pH sensing and temperature compensation system is based on the AD7793, 24-bit sigma-delta (Σ-Δ) with. It has three differential analog inputs and has an on-chip, low noise, programmable gain amplifier (PGA) that ranges from unity gain to 128. The AD7793 consumes only a maximum of 500 μA making it suitable for any low power applications. It has a low noise, low drift internal band gap reference and can accept external differential reference. The output data rate from the part is software programmable and can be varied from 4.17 Hz to 470 Hz.

The ADuM5401, quad-channel digital isolator with an integrated dc-to-dc converter provides the digital signal and power isolation between the microcontroller and the AD7793 digital lines. The iCoupler chip-scale transformer technology is used to isolate the logic signals and the power feedback path in the dc-to-dc converter.

Buffer for pH Sensor Interface

The electrode of a typical pH probe is made up of glass that creates an extremely high resistance that can range from 1 MΩ to 1 GΩ and acts as a resistance in series with the pH voltage source as shown in Figure 2.

The buffer amplifier bias current flowing through this series resistance introduces an offset error in the system. To isolate the circuit from this high source resistance, a buffer amplifier with high input impedance and very low input bias current is needed for this application. The AD8603 is used as a buffer amplifier for this application as shown in Figure 2. The low input current of the AD8603 minimizes the voltage error produced by the bias current flowing through the electrode resistance.

For 200 fA typical input bias current, the offset error is 0.2 mV (0.0037 pH) for a pH probe that has 1 GΩ series resistance at 25^oC. Even at the maximum input bias current of 1 pA, the error is only 1 mV.

The cut-off frequency of the 10 kΩ/1 μF low pass noise filter for the buffer amplifier output is given by f= 1/2πRC, or 16 Hz.

Guarding, shielding, high insulation resistance standoffs, and other such standard picoamp methods must be used to minimize leakage at the high impedance input of the AD8603 buffer.

ADC Channel 1 Configuration, pH sensor

This stage involves measuring the small voltage generated by the pH electrode. Table 1 shows the specifications of a typical pH probe. Based on the Nernst equation, the full range voltage from the probe can range from ±414 mV (±59.14 mV/pH) at 25°C to ±490 mV (±70 mV/pH) at 80°C.

When reading the pH probe output voltage, the ADC uses the external 1.05 V reference and is configured with a gain of 1. The full-scale input range is ±V _REF/G = ±1.05 V, and the maximum signal from the pH probe is ±490 mV at 80°C.

Because the output of the sensor is bipolar, and the AD7793 operates from a single power supply, the signal generated by the pH probe should be biased above ground so that it is within the acceptable common-mode range of the ADC. This bias voltage is generated by injecting the 210 μA IOUT2 current into the 5 kΩ, 0.1% resistor as shown in Figure 2. This generates the 1.05 V common-mode bias voltage that also serves as the ADC reference voltage.

ADC Channel 2 Configuration, RTD

The second channel of the ADC monitors the voltage generated across an RTD being driven by the IOUT2 current output pins of the AD7793. The 210 μA excitation current drives the series combination of the RTD and precision resistor (5 kΩ, 0.1%). (See Figure 1).

The temperature coefficient for pure platinum is 0.003926 Ω/Ω/°C. The normal coefficient for industrial RTDs is 0.00385 Ω/Ω/°C per the DIN Std. 43760-1980 and IEC 751-1983. The accuracy of an RTD is usually stated at 0°C. The DIN 43760 standard recognizes two classes as shown in Table 2, and ASTM E–1137 recognizes two grades as shown in Table 3.

The RTD resistance value can be computed as

The RTD resistance varies from 0°C (1000 Ω) to 100°C (1385 Ω), producing a voltage signal range of 210 mV to 290 mV with 210 μA excitation current.

The precision 5 kΩ resistor generates the 1.05 V used as an external reference. With a gain of one, the analog input range is ±1.05 V (±V_REF/G). This architecture gives a ratiometric configuration. Changes in the value of the excitation current do not affect the accuracy of the system.

Although 100 Ω Pt RTDs are popular, other resistances (200 Ω, 500 Ω, 1000 Ω, etc.) and materials (Nickel, Copper, Nickel Iron) can be specified. This application uses a 1 kΩ DIN 43760 Class A RTD for temperature compensation of the pH sensor. A 1000 Ω RTD is less sensitive to wiring resistance errors than a 100 Ω RTD.

A 2-wire connection is made as shown in Figure 3. A constant current is applied through the leads of the RTD, and the voltage across the RTD itself is measured. The measuring device is the AD7793 that exhibits high input impedance and low input bias current. The sources of errors in this scheme are lead resistance, the stability of the constant current source produced by AD7793, and the input impedance and/or bias current in the input amplifier, and the associated drift.

Another possibility for eliminating wiring resistance errors is the 3-wire RTD configuration that is described in detail in Circuit Note CN-0287.

Output Coding

The EVAL-SDP-CB1Z system demonstration platform board and the PC processes the data output from the AD7793.

Digital and Power Isolation

The ADuM5401 isolates the ADC digital signals and also supplies isolated regulated 3.3 V power to the circuit. The input to the ADuM5401 (V_DD1) should be between 3.0 V and 3.6 V. Take care with the layout of the ADuM5401 to minimize EMI/RFI problems. For more details, please refer to Application Note AN-1109, Recommendations for Control of Radiated Emissions with iCoupler Devices.

System Calibration

In order to accurately measure the RTD resistance, the ±5% variation in the IOUT2 current must be taken into account. The AIN3(+) input to the AD7793 is used to measure the voltage dropped across the precision 5 kΩ 0.1% resistor. The exact IOUT2 current is then determined by dividing this voltage by 5 kΩ. The RTD resistance is calculated by dividing the voltage across the RTD by the exact IOUT2 current.

A two-point calibration procedure shown in Figure 4 is used to calibrate the pH meter in the EVAL-CN0326-PMDZ evaluation software.

The user is required to use a minimum of two buffer solutions, where a neutral pH buffer with a value of pH-7 should be used to remove the offset introduced by the pH probe and by the system. The neutral buffer solution can be used to set the first point for calibration. The pH of the second buffer solution depends on the pH of the solution to be measured. A pH-10 buffer solution can be used when measuring alkaline base solutions, and a pH-4 buffer can be used when measuring acidic solutions. For more precise measurement, a three point calibration can be performed. This can be done by using two different sets of buffer solutions in Step 2 and in Step 3 as shown in Figure 4, where the pH-7 solution is used to remove the offset.

The software includes a list of buffer solution recommended by the NIST. Each buffer solution described in the list has its own temperature coefficient from 0°C to 95°C, which can be found in “pH Theory and Practice” by Radiometer Analytical. The software uses this table to correlate the mV input from the pH probe to the correct pH value that correspond to the temperature read from the RTD sensor using linear interpolation to fill in the gaps in the table. The user is given an option to enable/disable the option for continuous temperature compensation by clicking the green button as shown in Figure 4.

Buffer solutions are commonly found in the market for pH sensor calibration. Other NIST-certified pH reference can also be used for calibration. Because of the variety of buffer solutions available, the software also provides the user an option to use their desired NIST-certified pH reference for calibration as shown in Figure 4.

The software also provides the user an option to use other RTD resistance values, but by default it is set to 1000 Ω.

System Noise Considerations

For an output data rate of 16.7 Hz and a gain of 1, the rms noise of the AD7793 equals 1.96 μV (noise is referred to input, taken from AD7793 data sheet). The peak-to-peak noise is

6.6 × RMS Noise = 6.6 × 1.96 μV = 12.936 μV

If the pH meter has a sensitivity of 59 mV/pH, the pH meter should measure the pH level to a noise-free resolution of

12.936 μV / (59 mV/pH) = 0.000219 pH

This includes only the noise contribution of the AD7793. The actual system results are presented in the next section.

Test Data and Results

All data capture was performed using the CN0326 LabVIEW evaluation software. A Yokogawa GS200 precision voltage source was used to simulate the input of a pH sensor.

By sweeping the precision voltage from −420 mV to +420 mV in 1 mV increments, the EVAL-CN0326-PMDZ was able to capture the data according to the user defined calibration option.

The peak-to-peak noise of the AD8603 buffer and the AD7793 in the actual system was determined by shorting the input pH probe BNC connector and acquiring 1000 samples. As seen by the histogram in Figure 5, the code spread is approximately 500 codes, which translates to a peak-to-peak noise of 31.3 μV, with an equivalent pH reading spread of 0.00053 pH peak-to-peak.

The system was tested with three different resistors in series with the ADC input to simulate the different impedances of the high impedance glass electrode. The system was also calibrated to give 60 mV/pH. According to Figure 6, the linearity error increases with the increase of simulated glass electrode impedance. Figure 6 also shows that over the entire simulated pH output voltage range, the linearity error is less than 0.5% with for a 200 MΩ pH probe impedance.

The test data was taken using the board shown in Figure 7. Complete documentation for the system can be found in the CN-0326 Design Support package.