Circuit Note CN-0129 Devices Connected/Referenced Circuit Designs Using Analog Devices Products Apply these product pairings quickly and with confidence. For more information and/or support call 1-800-AnalogD (1-800-262-5643) or visit www.analog.com/circuit. AD7745/ AD7746 24-Bit Capacitance-to-Digital Converter AD8515 1.8 V Low Power CMOS Rail-to-Rail Op Amp Extending the Capacitive Input Range of the AD7745/AD7746 Capacitance-to-Digital Converter excitation voltage needs to be decreased by a factor of F, so that the sensing capacitance connected to the input can be increased by a factor F. CIRCUIT FUNCTION AND BENEFITS This circuit provides a method to extend the capacitive input range of the AD7745/AD7746. How to use the on-chip CapDAC sufficiently in order to minimize the range extension factor and, therefore, optimize the circuit to achieve the best possible performance is also explained. The AD7745 has one capacitance input channel, while the AD7746 has two channels. Each channel can be configured as single-ended or differential. The AD7745/AD7746 have two independent excitation sources EXCA and EXCB. For the range extension, the excitation sources have to be set up in a way that EXCB is the inverse of EXCA. With resistor R1 and R2 connected as shown in Figure 1, the resulting range extension factor F is the ratio of the AD7746 excitation voltage between EXCA and EXCB (VEXC(A−B)) and the attenuated excitation signal (VEXCS) at the positive input of the AD8515 op amp. The range extension factor F can be calculated as follows: CIRCUIT DESCRIPTION The AD7745/AD7746 capacitance-to-digital converters measure capacitance by using switching capacitor technology to build up a charge balancing circuit. As charge is proportional to the product of voltage and capacitance, Q = V × C, the conversion result represents the ratio between the input capacitance, CSENS, and the internal reference capacitance, CREF, as the excitation voltages EXCx and the internal reference voltage VREF have fixed known values. F= V EXC ( A– B ) V EXCS = R1 + R2 R1 – R2 By using both excitation sources, the mean voltage of the attenuated excitation voltage EXCS remains around VDD/2. The AD8515 operational amplifier in the circuit functions as a low impedance source to ensure the sensing capacitance CSENS is fully charged when the AD7745/AD7746 starts sampling. The range extension circuit has to ensure that the charge transfer within the sensing capacitance CSENS remains within the input range of the AD7745/AD7746. To achieve this, the U1 C1 0.1µF 5 1 U2 2 3 4 R1 100kΩ R2 118kΩ CSENS AD8515 1 SCL SDA 16 SCL SDA 2 RDY NC 15 3 EXCA R4 10kΩ VDD EXCB 5 REFIN(+) VIN(–) 12 6 REFIN(–) VIN(+) 11 7 CIN1(–) NC 10 8 CIN1(+) NC GND 13 HOST SYSTEM VDD VDD 14 4 NOTES 1. VDD = 2.7V TO 3.6V, OR 4.75V TO 5.25V R3 10kΩ C2 1µF GND 9 08598-001 VDD RDY AD7745 RANGE EXTENSION CIRCUIT Figure 1. AD7745 Capacitive Input Range Extension Circuit (Simplified Schematic: Decoupling and All Connections Not Shown) Rev.0 “Circuits from the Lab” from Analog Devices have been designed and built by Analog Devices engineers. Standard engineering practices have been employed in the design and construction of each circuit, and their function and performance have been tested and verified in a lab environment at room temperature. However, you are solely responsible for testing the circuit and determining its suitability and applicability for your use and application. Accordingly, in no event shall Analog Devices be liable for direct, indirect, special, incidental, consequential or punitive damages due to any cause whatsoever connected to the use of any“Circuit from the Lab”. (Continued on last page) One Technology Way, P.O. Box 9106, Norwood, MA 02062-9106, U.S.A. Tel: 781.329.4700 www.analog.com Fax: 781.461.3113 ©2009 Analog Devices, Inc. All rights reserved. CN-0129 Circuit Note Characteristics of Capacitive Humidity Sensor The example of a common capacitive polymer humidity sensor element is used to explain the required calculation and considerations for the input range extension of the AD7745/AD7746. Typical technical data of such a capacitive sensor element are shown in Table 1. Table 1. Typical Technical Data for Capacitive Sensor Element Humidity Range Capacitance Rate of Rise 0% to 100% Relative Humidity (RH) 150 pF ± 50 pF (at 23°C and 30% RH) 0.25 pF/%RH The AD7745/AD7746 capacitive input is factory calibrated. This calibration factor is stored in the Cap Gain Register. The calibration factor stored in the Cap Gain Register is calculated as follows: FGAIN _ CAL = Calculating the Required Range Extension Factor, F The first task is to find out which of the sensor’s parameters is the main contributor for the required range extension. The sensor’s bulk capacitance can be as high as 200 pF, resulting in a required range extension factor of 200 pF FFIX = = 11.76 17 pF The sensor’s dynamic range is calculated Hence, the internal reference capacitance CREF can be defined as the product of the AD7745/AD7746’s allowed full range input capacitance and the gain calibration factor. C REF = 4.096 pF × FGAIN _ CAL The AD7745/AD7746 are designed so that the ratio between full-range CapDAC capacitance and internal reference capacitance CREF is 3.2. Therefore, the CapDAC full range can be calculated as follows: CREF = 4.096 pF × 1.4 = 5.7344 pF CCAPDAC = CREF × 3.2 = 18.3501 pF The calculations show that the sensors bulk capacitance is the parameter that determines the range extension factor; therefore, F = 11.76 is used for further calculations. Choosing the Resistor Values R1 and R2 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. R1× (F + 1) (F – 1) C LSB CAPDAC = (11.76 – 1) = 118.587 kΩ 100 kΩ – 118 kΩ = 0.1445 pF Calculating the Required CapDAC Setting The resistor values of 100 kΩ for R1 and 118 kΩ for R2 result in a range extension factor of 100 kΩ + 118 kΩ 127 CDAC EFF = CLSB CAPDAC × F CDAC EFF = 0.1445 pF × 12.111 = 1.7499 pF R2 = 118 kΩ (from E96 resistor table) F= 18.3501 pF The range extension circuit ensures that the charge transfer within the sensing capacitance CSENS remains within the input range of the AD7745/AD7746. Taking charge from the sensing capacitance at the CIN input, by the CapDAC, results in a decrease in measured capacitance. This is used to compensate for a sensor’s bulk capacitance. One LSB of the CapDAC capacitance represents compensation on the sensing capacitance of where F = 11.76 100 kΩ × (11.76 + 1) 216 If the gain calibration factor is 1.4, the resulting CREF and CCAPDAC values are as follows: The range extension factor required for the dynamic range is calculated as follows: 25 pF FDYN = = 3.05 8.192 pF R2 = (216 + GAIN _ CAL) C CAPDAC = C REF × 3.2 C DYN = (0.25 pF/%RH ) × 100% RH = 25 pF R2 = The reason for this is that the AD7745/AD7746 on-chip capacitances can vary with the production process from batch to batch. However, the ratio variation between the on-chip capacitances is very small. = 12.111 Using the CapDAC The AD7745/AD7746 have CapDACs that can be used to compensate for the bulk capacitance of a sensor element. For the AD7745/AD7746, the CapDACs have a full-scale value of 17 pF minimum and 21 pF typical. Therefore, for a given CapDAC setting, the capacitances can vary significantly from part to part. The CapDAC has some dynamic nonlinearity (DNL). It is recommended to setup the CapDAC to have the intended calibration point of the application at zero-scale of the capacitive input range. The remaining offset can then be easily calibrated by using the available system offset calibration function. The required CapDAC setting for our humidity sensing element example is calculated as follows: Rev. 0 | Page 2 of 4 DAC SET = DAC SET = C SENSOR C DAC EFF 150 pF 1.7499 pF = 85.72 → 86 (0x56) Circuit Note CN-0129 Resulting CapDAC values and settings are CCAPDAC = 4.096 pF × 1.373978 × 3.2 = 18.009 pF 18.009 pF C LSB CAPDAC = = 0.141803 pF 127 CDAC EFF = 0.1418 pF × 12.07709 = 1.71257 pF Measurement Using the Range Extension Circuit The variable capacitance was set to a defined value using a precision LCR meter. This capacitance was then connected to the range extension board, where the CapDAC was set to the calculated value of this defined bulk capacitance CBULK. A system offset calibration was performed to have the zero point at CBULK. For each measurement taken, the capacitance was set to the desired value using the LCR meter, then connected to the range extension board measuring the capacitance seen by the AD7746. Finally, the extended capacitance value was calculated using the factor resulting from the measured resistor values. The following bulk capacitance values were used: CBULK = 100 pF, 150 pF, and 200 pF. Calculations for the Range Extension Circuit DAC SET100 = DAC SET150 = DAC SET200 = C DYN = 12.07709 × (±4.096 pF) = ± 49.4678 pF The resulting range for the measurement is ±45 pF in steps of 15 pF. Calculating the gain calibration factor value read out: 0x5FBD = 24509 FGAIN _ CAL 216 + 24509 = = 1.373978 216 1.71257 pF = 87.59 → 88 (0x58) = 116.78 → 117 (0x75) 0.8 ERROR (100pF ± 45pF) ERROR (150pF ± 45pF) ERROR (200pF ± 45pF) 0.6 0.4 0.2 0 –0.2 –0.4 –0.6 –0.8 –1.0 –50 –40 –30 –20 –10 0 10 20 30 40 50 MEASURED CAPACITANCE (pF) 100.004 kΩ + 118.060 kΩ Calculating the dynamic capacitive input range, 1.71257 pF 200 pF = 58.39 → 58 (0x3A) 1.0 The resulting range extension factor F is calculated 100.004 kΩ – 118.060 kΩ F = 12.07709 1.71257 pF 150 pF From Figure 2, the measurement shows that the error caused by the range extension circuit is not dependent on the bulk capacitance value measured but on the range extension circuit itself. All three measurements show similar behavior and are linear; therefore, the error caused by the range extension circuit can be easily compensated for in software. From the previous calculations, we know the required resistor values are 100 kΩ and 118 kΩ. The resistors used were measured and had the following values: R1 = 100.004 kΩ; R2 = 118.060 kΩ. F= 100 pF Measurement Errors ERROR (pF) An AD7746 demo board with a range extension circuit was used to perform the measurements. A variable capacitance was used during the measurement. The board was connected to a standard AD7746 evaluation board; the standard evaluation board software was used to configure the device and to read the conversion results. Circuits such as these must be constructed on a multilayer PC board with a large area ground plane. Proper layout, grounding, and decoupling techniques must be used to achieve optimum performance (see Tutorial MT-031, Grounding Data Converters and Solving the Mystery of "AGND" and "DGND" and Tutorial MT-101, Decoupling Techniques). 08598-002 A system offset calibration will compensate for the small remaining offset. Figure 2. Gain Error vs. Measured Capacitance LEARN MORE Webinar: Leveraging Advanced Converter Architectures for Impedance and Capacitance Sensors. Analog Devices. MT-031 Tutorial, Grounding Data Converters and Solving the Mystery of AGND and DGND. Analog Devices. MT-101 Tutorial, Decoupling Techniques. Analog Devices. Data Sheets and Evaluation Boards AD7745/AD7746 Data Sheet AD7745/AD7746 Evaluation Board AD8515 Data Sheet Rev. 0 | Page 3 of 4 CN-0129 Circuit Note (Continued from first page) "Circuits from the Lab" are intended only for use with Analog Devices products and are the intellectual property of Analog Devices or its licensors. While you may use the "Circuits from the Lab" in the design of your product, no other license is granted by implication or otherwise under any patents or other intellectual property by application or use of the "Circuits from the Lab". Information furnished by Analog Devices is believed to be accurate and reliable. However, "Circuits from the Lab" are supplied "as is" and without warranties of any kind, express, implied, or statutory including, but not limited to, any implied warranty of merchantability, noninfringement or fitness for a particular purpose and no responsibility is assumed by Analog Devices for their use, nor for any infringements of patents or other rights of third parties that may result from their use. Analog Devices reserves the right to change any "Circuits from the Lab" at any time without notice, but is under no obligation to do so. Trademarks and registered trademarks are the property of their respective owners. ©2009 Analog Devices, Inc. All rights reserved. Trademarks and registered trademarks are the property of their respective owners. CN08598-0-10/09(0) Rev. 0 | Page 4 of 4