CN0346

RH is the amount of water vapor in the air, expressed as a percentage of the maximum amount that the air can hold at a specific temperature. Relative humidity is an important metric because it takes into consideration the effects of temperature and pressure.

A hygrometer is the traditional device used to measure RH and has taken many forms over time, including metal paper coil, human hair, and dual thermometer implementations. Modern day electronic implementations use a capacitive element that is robust against aging effects, condensation, and rapid temperature swings.

Capacitive sensors experience a change in their dielectric constant when a polymer or metal oxide layer is subject to varying amounts of moisture. Most capacitive sensors require several seconds to respond to a change in humidity.

Humidity Sensor Characteristics

The circuit shown in Figure 1 uses the Innovative Sensor Technology P14-W series of capacitive sensors. Bulk capacitance, sensitivity, temperature, linearity, and hysteresis are the important specifications of the sensor.

The typical bulk capacitance of the sensor is 150 pF ± 50 pF at 30% RH. This common-mode capacitance does not influence the relative humidity reading but requires a special circuit to interface to the capacitance-to-digital converter.

The sensitivity of the capacitive element determines the relative humidity reading. Sensitivity is the change in capacitance for a 1% change in relative humidity and is calculated by measuring the capacitance at two unique relative humidity points and dividing by the change in percent RH.

The P14-W has a typical sensitivity of 0.25 pF/% RH.

Calculate the temperature dependence of the sensor for a particular relative humidity condition using the following equation and coefficients (taken from the Innovative Sensor Technology P14-W data sheet):

where:

B1 = 0.0014/°C
% RH = 42%
B2 = 0.1325%
RH/°C T = 23°C
B3 = −0.0317
B4 = −3.0876% RH
T_DEPEND = −0.0191% RH.

A temperature of 23°C causes a change in a 42% RH calculation of −0.0191% RH. Adding this value to the calculated % RH corrects for the temperature dependence of the sensor.

The linearity and hysteresis of the Innovative Sensor Technology P14-W series are ±1.5% RH.

Calculating Relative Humidity

Relative humidity is calculated from the capacitance, C, and temperature, T, readings as follows:

1. Subtract the bulk capacitance from the capacitance reading.
2. Divide by the sensitivity.
3. Add the reference humidity to the calculation.
4. Calculate the temperature dependence, T_DEPEND.
5. Add T_DEPEND to the result in Step 3.

As an example, assume a capacitive sensor reading of C = 153 pF at a temperature of T = 23°C, with the following ideal characteristics:

• Bulk capacitance = 150 pF at 30% RH
• T_DEPEND = −0.0191% RH
• Sensitivity = 0.25 pF/% RH
• Reference point = 30% RH, 23°C

Calculate the relative humidity according to the instructions given and the following equation:

The method for calculating the temperature dependence of the relative humidity measurement is dependent upon the particular humidity sensor selected; therefore, the data sheet must always be consulted to determine the correct formula.

Capacitance-to-Digital Converter (CDC)

The 24-bit AD7745 CDC measures capacitance by using a switched capacitor charge balancing circuit, as shown in Figure 2. The throughput rate is 10 Hz to 90 Hz.

Charge is proportional to the product of voltage and capacitance, Q = V × C, and the conversion result represents the ratio of the input sensor capacitance, C_SENS, to the internal reference capacitance, C_REF. The excitation voltage (EXC) and the internal reference voltage (V_REF) have fixed known values.

The C_SENS to be measured connects between the excitation source and the Σ-Δ modulator input. A square-wave excitation signal of 32 kHz is applied to C_SENS during the conversion, and the modulator continuously samples the charge going through C_SENS. The digital filter processes the modulator output, which is a stream of ones and zeros. The conversion value is contained in the ones density of the bit stream. The data from the digital filter is scaled, calibration coefficients are applied, and the result is read through the serial interface.

Input Range Scaling

The AD7745 has two limitations in measuring input capacitance. First, the dynamic range is ±4.096 pF, but many capacitive based humidity sensors have a larger dynamic range. Second, the maximum common-mode capacitance of the CDC is 21 pF. Many humidity sensors have a larger bulk capacitance.

The AD7745 has the ability to offset the input common-mode range by programming the internal, 7-bit, capacitor DAC (CAPDAC) registers. The CAPDAC acts as a negative capacitance connected internally to the CIN1± pin. This allows a common-mode capacitance of up to a typical value of 21 pF.

The range extension circuit shown in Figure 1 is added to ensure that the charge transfer within C_SENS remains within the input range of the AD7745. To achieve this, the excitation voltage is decreased by a factor of F, allowing the sensor capacitance to be increased by a factor of F.

Calculating Range Extension Factor

To calculate the range extension factor, the two independent excitation sources (EXCA and EXCB) of the AD7745 must be programmed such that EXCB is the inverse of EXCA. With Resistors R1 and R2 connected as shown in Figure 1, the resulting range extension factor F is the ratio of the AD7745 differential excitation voltage between EXCA and EXCB (V_EXCA/V_EXCB) and the attenuated excitation signal (V_EXCS) at the positive input of the AD8515 op amp. Calculate the range extension factor as follows:

The average voltage of the attenuated excitation voltage, V_EXCS, is VDD/2. The AD8515 op amp functions as a low impedance buffer to ensure that CSENS is fully charged when the AD7745 starts sampling.

The sensor bulk capacitance can be as high as 200 pF, and the minimum value of the AD7745 common-mode capacitance is 17 pF, resulting in a required range extension factor (F_CM) of

Calculate the sensor dynamic range as follows:

Calculate the range extension factor required for the dynamic range (F_DYN) as follows:

These calculations show that the bulk capacitance of the sensor is the parameter that determines the range extension factor; therefore, F = 11.76 is used for further calculations.

Choosing the Resistor Values

Select values for R1 and R2 to implement the desired range extension factor. A value of 100 kΩ was chosen for R1. The resistor value for R2 is calculated and rounded down to the next value in the standard E96 series.

where:

R1 = 100 kΩ
F = 11.76
R2 = 118.58 kΩ.

Use resistors with tolerances of 1% or less. A small change in the value of either resistor (R1 or R2) can significantly change the range extension factor. The resistor values of 100 kΩ for R1 and 118 kΩ for R2 result in a range extension factor of

Using the CAPDAC to Remove the Common-Mode Capacitance

The AD7745 capacitive input is factory calibrated so that the input range is 0 pF to 4.096 pF in the single-ended mode, and ±4.096 pF in the differential mode. The AD7745 contains an internal CAPDAC that allows adjustment of the input common-mode capacitance.

The CAPDAC acts as a negative capacitance connected internally to the CIN1± pin. There are two independent CAPDACs, one connected to CIN1(+) and the second connected to CIN1(−).

The CAPDACs have 7-bit resolution and a full-scale value of 21 pF ± 20%.

Calculate the required CAPDAC setting for the single-ended humidity sensing element example shown in Figure 1 by setting the CAPDAC for a common-mode capacitance of 17 pF corresponding to the decimal code value of

Test Setup

Gathering test data cannot begin until the CN-0346 system is properly set up and calibrated. First, place the EVAL-CN0346-PMDZ printed circuit board (PCB) into a humidity controlled chamber with access to a precision inductance capacitance resistance (LCR) meter (HP4284A). The LCR meter correlates any capacitance calculation with the actual capacitance value of the sensor. Two sets of wires protrude from the container for each PCB. The first set of wires is specific to I²C digital communication. The second set of wires allows direct measurement of the sensor capacitance using the LCR meter, which can only occur when there is no power connected to the EVAL-CN0346-PMDZ PCB.

Figure 3 shows the block diagram used for data collection in the bench test setup.

Second, for two specific humidity levels (5% RH and 95% RH), measure the temperature of the enclosure using the AD7745 and measure the capacitance of the sensor using the LCR meter.

Calculate the sensitivity of the sensor using these two calibration points.

Enter the sensitivity into the appropriate Relative Humidity Calculation field under the Calculations tab (see Figure 4). Use the 10% RH calibration point to fill in the C_BULK field and the RH_REF (%) field.

Lastly, calculate and input the desired CAPDAC common-mode value into the CAPDAC field, as shown in Figure 5.

The CN-0346 system is prepared and calculated. Click to Sample displays the sensor capacitance as C_CALC in the Capacitance Calculation window. Vary the humidity while collecting samples and observe the change in the relative humidity calculation.

Test Results

All test data was collected by placing Boveda packs (Boveda, Inc.) into a sealed container with three EVAL-CN0346-PMDZ PCBs, as shown in Figure 6. Boveda packs contain a specially prepared solution of pure water and salt, designed to control the humidity inside of a sealed container to a specific, predetermined relative humidity of ±2.5%.

Figure 7 shows the relative humidity error over the full range of relative humidity.

PCB Layout Considerations

In any circuit where accuracy is crucial, consider the power supply and ground return layout on the board. The PCB isolates the digital and analog sections as much as possible. The PCB for this system is constructed in a 4-layer stack up with large area ground plane layers and power plane polygons. See the MT-031 Tutorial for more information on layout and grounding, and see the MT-101 Tutorial for information on decoupling techniques.

Decouple the power supply to all ICs with 1 μF and 0.1 μF capacitors to properly suppress noise and reduce ripple. Place the capacitors as close to the device as possible. Ceramic capacitors are recommended for all high frequency decoupling.

Power supply lines must have as large a trace width as possible to provide low impedance paths and to reduce glitch effects on the supply line. Shield clocks and other fast switching digital signals from other parts of the board by connecting them to the digital ground. The PCB is shown in Figure 8.

A complete design support package for this circuit note is available at www.analog.com/CN0346-DesignSupport.