M AN737 Using Digital Potentiometers to Design Low-Pass Adjustable Filters INTRODUCTION The most common filter found in a data acquisition system signal path is a low-pass filter. This type of filter is usually used to reduce A/D Converter (ADC) aliasing errors. If there is more than one signal that is applied to the A/D converter through a multiplexer, each signal source may have its own set of filter requirements (i.e., settling time, fast transition region, etc.). Consequently, a variety of filters may be required in the circuit prior to the multiplexer. Usually these filters are implemented with operational amplifiers (op amps) in combination with fixed resistors and capacitors. An alternative filter design solution is to have one filter following the multiplexer. In this circuit, the low-pass filter would need to be programmable. The obvious advantage of having the filter serve many analog inputs is that there is a reduction in chip count. An example of this type of approach is shown in Figure 1. Temperature 2 Temperature 3 Acceleration Figure 2 shows the details of a single-supply, unity gain, second-order, programmable low-pass Sallen Key filter. This filter is implemented with two resistors and two capacitors. The two resistors in this circuit are replaced with the dual MCP42100, 100 kΩ, 8-bit, digital potentiometer. C1 R1 VIN PW0 PA0 R2 Programmable Low-Pass Filter Vibration Pressure 12-bit A/D Converter FIGURE 1: If a programmable low-pass filter is used in the application circuit, it can be placed after the analog multiplexer. The programmability of the filter allows for a wide variety of input signals. Programmable Low-Pass Filters In this application note, a programmable, secondorder, low-pass filter will be presented in four different scenarios. The first three scenarios will illustrate how a dual digital potentiometer and a single amplifier can be configured for low-pass second-order Butterworth, Bessel and Chebyshev responses with a programma- 2004 Microchip Technology Inc. Single-Supply, Rail-to-Rail Input Op Amp PW1 PB0 1/2 MCP42100 PA1 PB1 1/2 MCP42100 100 kΩ Digital Potentiometers Temperature 1 Analog Multiplexer ble corner frequency range of 1:100. An example of the digital potentiometer setting for these designs is summarized in Tables 1, 2 and 3. The fourth scenario will show the same circuit design, where all three approximation methods (Butterworth, Bessel and Chebyshev) can coexist with a programmable corner frequency range of 1:10. An example of the digital potentiometer settings for this combination of approximation methods is summarized in Table 4. C2 MCP601 MCP3201 12-bit ADC - Bonnie C. Baker Microchip Technology Inc. + Author: VOUT FIGURE 2: The combination of a dual digital potentiometer and a single-supply, rail-torail amplifier can be used to construct a programmable, second-order, Sallen-Key, low-pass filter. Digital potentiometers can be used to adjust system reference levels, gain errors and offset errors, while offering the added capability of digital adjustment control. Devices such as Microchip’s MCP41XXX and MCP42XXX digital potentiometer families have three resistive terminals for the single versions (MCP41010, MCP41050 and MCP41100) and six resistive terminals for the dual versions (MCP42010, MCP42050 and MCP42100) and are illustrated in Figure 3. The MCP41010 and MCP42010 are both 10 kΩ potentiometers. The MCP41050 and MCP42050 are both 50 kΩ potentiometers, while the MCP41100 and 42100 are both 100 kΩ potentiometers. DS00737C-page 1 AN737 PA0 PW0 PB0 PA PW PB RDAC2 RDAC1 Data Register 1 Data Register 0 D7 PW1 PB1 PA1 D7 D0 Digital Potentiometer Model D0 RS Decode Logic CS D7 D0 PA PW PB 16-bit Shift Register SI SCK SO Mechanical Potentiometer Model SHDN Dual Digital Potentiometer FIGURE 3: The operation of the digital potentiometer as compared to the mechanical potentiometer is functionally the same. The adjustment of the digital potentiometer is done with a serial code to the device. Although the mechanical potentiometer provides simplicity, the digital potentiometer provides flexibility and reliability. The potentiometer can be configured for two modes: the Rheostat mode and Voltage Divider mode. In the Rheostat mode, the wiper (terminal PW) is shorted to either the PA or PB terminal of the device. This configuration is shown in Figure 4. When used in the Voltage Divider mode (Figure 4.b), all three terminals are connected to differing nodes in the circuit. For the analog filter example in this application note, the digital potentiometer will be configured in the Rheostat mode. By adjusting the two digital potentiometers in Figure 2, the frequency cutoff and the filter approximation method of this second-order low-pass filter can be changed. The design equation configuration is: for this low-pass filter V K/ ( R R C C ) OUT 1 2 1 2 ----------------- = --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------V 2 IN s + s ( 1/R 1 C 1 + 1/R 2 /C 1 + 1/ R 2 C 2 – K/R 2 C 2 ) + 1/R 1 R 2 C 1 C 2 Where: K = 1 PW PW PA PB PA (a) Rheostat Mode RX = ±30% accurate 500 ppm/°C PA PB PB PW (b) Voltage Divider Mode RA/RB = ±3% accurate 15 ppm/°C FIGURE 4: A digital potentiometer can be configured in the (a) Rheostat mode or (b) Voltage Divider mode. The operational amplifier used in this application circuit is a single-supply, rail-to-rail out device. The MCP601 is a single amplifier that belongs to the MCP601/2/3/4 family of operational amplifiers. The MCP603 is also a single amplifier with a Chip Select feature. The dual version is the MCP602, while the quad version is the MCP604. These amplifiers are optimized for high speed, low offset voltage and single-supply operation. DS00737C-page 2 With this formula, the appropriate resistance and capacitance can be calculated. An alternative to this tedious design exercise is to determine the capacitor and resistor values using the FilterLab® software, a filter design program that can be downloaded from Microchip’s web site at www.microchip.com. The Circuit screen in this program allows the user to adjust the capacitors to desired values (C 1 and C2 per Figure 2). When these capacitors are set, the software changes the resistors in the circuit to appropriate values for the circuit implementation. There may be a corner frequency and stability error with low-pass filters that are designed at frequencies higher than 100 kHz. This error is introduced by the parasitic capacitance of the digital potentiometer. As a general guideline, C1 and C2 should be larger than 10 nF. For more detailed information concerning anti-aliasing filters, please refer to Microchip’s Application Note 699, entitled “Anti-Aliasing, Analog Filters for Data Acquisition Systems” (DS00699). 2004 Microchip Technology Inc. AN737 TABLE 1: A BUTTERWORTH FILTER DESIGN ADJUSTING THE RESISTORS THROUGH A DIGITAL POTENTIOMETER Specifications: Programmable cutoff frequency range of 100 Hz to 10 kHz by using capacitors of C1 = 0.047 µF, C2 = 0.018 µF and adjusting the resistors through a digital potentiometer. Closest FilterLab FilterLab Nominal Closest Calculated 1% Digital Pot. R1 Digital Pot. R1 Calculated 1% Digital Pot. R2 Digital Pot. R2 Cutoff Frequency, Hz R1 Value, kΩ Value, kΩ Code, decimal R2 Value, kΩ Value, kΩ Code, decimal 100 32.2 32.031 82 92.8 92.969 238 200 16.1 16.016 41 46.4 46.484 119 300 10.7 10.156 26 30.9 30.859 79 1000 3.22 3.125 8 9.28 9.375 24 2000 1.61 1.563 4 4.64 4.688 12 3000 1.07 1.172 3 3.09 3.125 8 10000 322 0.391 1 928 0.781 2 Butterworth Second-Order Low-Pass Filters When a Butterworth filter is required, the Sallen Key configuration shown in Figure 2 can have an adjustable frequency range of 1:100. The frequency behavior of the Butterworth filter is maximally flat in the magnitude response in pass band. The rate of attenuation in transition band is better than the Bessel filter, though not as good as the Chebyshev filter. There is no ringing in the stop band. The step response of the Butterworth filter has some overshoot and ringing in the time domain, though this is less than the Chebyshev filter. The capacitor values in this circuit are kept constant while the resistive elements are adjusted. The two capacitors should be carefully selected to be constants in the FilterLab software so that the digital potentiometer resistances are the only values that are changing. These capacitive values can easily be found in the FilterLab software through experimentation. Verification of the performance of the Butterworth filters that use 1% discrete resistors can be performed with the SPICE listing that is provided as an output from the FilterLab software. The SPICE simulations for the 100 Hz, 200 Hz, 300 Hz and 1,000 Hz filters using the values calculated by the FilterLab software are shown in Figure 5. To validate the digital potentiometer design, SPICE simulations can be performed on the Butterworth filters using the digital potentiometer values. The 100 Hz, 200 Hz, 300 Hz and 1,000 Hz filters using the calculated nominal resistance values of the digital potentiometers, per Table 2, are shown in Figure 6. From these two SPICE simulations, it is easy to see that the filters from Figure 5 behave fundamentally the same over frequency as compared to Figure 6. As an example, a programmable second-order, lowpass Butterworth filter with a corner frequency that ranges from 100 Hz to 10 kHz can be designed by setting C1 = 0.047 µF and C2 = 0.018 µF. The values calculated by the FilterLab software for this filter design are summarized in Table 1. Table 1 also includes the closest values for R1 and R 2 from the digital potentiometer, along with the digital program code for the MCP42100. 2004 Microchip Technology Inc. DS00737C-page 3 AN737 FIGURE 5: SPICE simulation of four Butterworth, second-order low-pass filters with corner frequencies of 100 Hz, 200 Hz, 300 Hz and 1,000 Hz. In this simulation, 1% resistor values were used. FIGURE 6: SPICE simulation of four Butterworth, second-order low-pass filters with corner frequencies of 100 Hz, 200 Hz, 300 Hz and 1,000 Hz. In this simulation, nominal digital potentiometer resistor values, per Table 1, were used. TABLE 2: A PROGRAMMABLE BESSEL FILTER DESIGN USING A DUAL 100 KΩ DIGITAL POTENTIOMETER. Specifications: A programmable Bessel filter with a cutoff frequency range of 100 Hz to 10 kHz can be implemented with C1 = 0.033 µF, C2 = 0.018 µF and a dual 100 kΩ digital potentiometer. Closest FilterLab FilterLab Nominal Closest Calculated 1% Digital Pot. R 1 Digital Pot. R1 Calculated 1% Digital Pot. R2 Digital Pot. R2 Cutoff Value, kΩ Code, decimal R2 Value, kΩ Value, kΩ Code, decimal Frequency, Hz R1 Value, kΩ 100 28.7 28.516 73 91.5 91.406 234 200 14.3 14.453 37 45.7 43.75 117 300 9.57 9.375 24 30.5 30.469 78 1000 2.87 2.734 7 9.15 8.984 23 2000 1.43 1.563 4 4.57 4.688 12 3000 0.957 0.781 2 3.05 3.125 8 10000 0.287 0.391 1 0.915 0.781 2 DS00737C-page 4 2004 Microchip Technology Inc. AN737 Bessel Second-Order Low-Pass Filters Chebyshev 2nd Order Low-Pass Filters When a Bessel filter is desired, the Sallen Key configuration, shown in Figure 2, can have an adjustable frequency range of 1:100. As with the Butterworth filter, the frequency response of the Bessel filter has a flat magnitude response in the pass band. Following the pass band, the rate of attenuation in the transition band is slower than the Butterworth or Chebyshev. Finally, there is no ringing in the stop band. This filter has the best step response of all of the filters mentioned in this application note, with very little overshoot or ringing. The filter in Figure 2 can also be designed in the Chebyshev approximation for an adjustable range of 1:100. With the Chebyshev filter, the frequency behavior exhibits a ripple in the pass-band that is determined by the specific placement of the poles in the circuit design. With the design discussed in this application note, the ripple is 3 dB. In general, an increase in ripple magnitude will lessen the width of the transition band. The rate of attenuation in the transition band is steeper than Butterworth and Bessel filters. Although there is ringing in the pass-band region with this filter, the stop band is devoid of ringing. The step response has a fair degree of overshoot and ringing. In Table 3, a programmable Bessel filter is designed with a corner frequency range of 100 Hz to 10 kHz, by setting C1 = 0.033 µF and C2 = 0.018 µF. Once again, in the FilterLab software, the capacitor values are kept constant, while the resistive elements are adjusted. TABLE 3: An example of the digital potentiometer settings for a 2nd order, low-pass Chebyshev filter is given in Table 3. CHEBYSHEV FILTER DESIGN Specification: Chebyshev, 3 dB Ripple, 100 to 10 kHz cutoff, C1 = 0.15 µF, C 2 = 0.015 µF Cutoff Frequency, Hz FilterLab Calculated 1% R1 Value, kΩ Closest Nominal Digital Pot. R1 Value, kΩ Digital Pot. R1 Code, decimal FilterLab Calculated 1% R2 Value, kΩ Closest Digital Pot. R 2 Value, kΩ Digital Pot. R 2 Code, decimal 100 21.0 21.094 54 75.6 75.781 194 200 10.5 10.547 27 37.8 37.891 97 300 7.01 7.031 18 25.2 25.391 65 1000 2.10 1.953 5 7.56 16.016 41 10 2000 1.05 1.563 4 3.78 3.9063 3000 0.701 0.781 2 2.52 2.344 6 10000 0.210 0.391 1 0.756 0.781 2 TABLE 4: THE BUTTERWORTH, BESSEL AND CHEBYSHEV APPROXIMATION METHODS Specifications: The Butterworth, Bessel and Chebyshev approximation methods can be designed into the circuit in Figure 2 by using a dual potentiometer and capacitive values of C1 = 0.015 µF, C2 = 0.0022 µF. The adjustable cutoff frequency range of these filters is 1,000 Hz to 10 kHz. Cutoff Frequency, Hz Filter Approximation Method Closest Digital Pot. R1 Value, Ω Digital Pot. R1 Code, decimal Closest Digital Pot. R 2 Value, Ω Digital Pot. R2 Code, decimal 1,000 Butterworth 8.203 21 94.141 241 Bessel 5.078 13 93.359 239 Chebyshev (3 dB Ripple) 3.516 9 33.984 87 Butterworth 3.906 10 47.266 121 Bessel 2.344 6 46.484 119 Chebyshev (3 dB Ripple) 15.625 40 17.188 44 Butterworth 2.734 7 31.250 80 Bessel 1.563 4 31.250 80 Chebyshev (3 dB Ripple) 10.547 27 11.328 29 Butterworth 0.781 2 9.375 24 2,000 3,000 10,000 Bessel 0.391 1 9.375 24 Chebyshev (3 dB Ripple) 3.125 8 3.516 9 2004 Microchip Technology Inc. DS00737C-page 5 AN737 Combining Butterworth, Bessel and Chebyshev Second-Order Low-Pass Filters All three approximation methods can be combined, with some limitations, in this circuit. Since there is a large variety of pole locations, the cutoff frequency range is 1:10. An example of a programmable filter with a cutoff frequency range of 1,000 Hz to 10 kHz is shown in Table 4. CONCLUSION It is possible to design second-order, low-pass, programmable filters with one dual digital potentiometer, one amplifier and two capacitors. REFERENCES AN699, “Anti-Aliasing, Analog Filters for Data Acquisition Systems”, Bonnie C. Baker, Microchip Technology Inc., DS00699, 1999. ERROR ANALYSIS OF PROGRAMMABLE FILTERS AN219, “Comparing Digital Potentiometers to Mechanical Potentiometers”, Bonnie C. Baker, Microchip Technology Inc., DS00219, 2000. Absolute Accuracy of Circuit Elements AN691, “Optimizing Digital Potentiometer Circuits to Reduce Absolute and Temperature Variations”, Bonnie C. Baker, Microchip Technology Inc., DS00691, 2001. The nominal resistance of a 100 kΩ digital potentiometer (MCP42100), per data sheet specifications, varies approximately ±30%. If the 10 kΩ digital potentiometer (MCP42010) is substituted for the MCP42100, the nominal resistance variance from part-to-part is specified at ±20% for the MCP42010. When the 10 kΩ potentiometer is substituted, the capacitive values should be increased by 10X. For instance, in the Butterworth example of Table 1, C1 should be changed to 0.47 µF and C2 changed to 0.18 µF. When this is done, the codes to the potentiometer that can stay the same, remain unchanged. The change of the potentiometer from the MPC42100 (100 kΩ) to the MCP42010 (10 kΩ) will, in fact, decrease the values, as stated in Table 1, by 10X. In this application circuit, it is suggested that the dual version of the digital potentiometer be used because there can be part-to-part variation of the nominal resistance (±30% for the MCP42100 and ±20% for the MCP42010). With the dual potentiometer, resistor-toresistor variation on chip is specified to a typical value of 0.2%. The resistance variation of these digital potentiometers is primarily dependent on the process variation of the sheet-rho of a diffused p-silicon layer and the on-resistance of the internal switches. If 20% accurate capacitors are used, the variability of this filter in a manufacturing environment is dominated by the capacitors. Wiper resistance The wiper resistance of the MCP42100 digital potentiometer is approximately 125Ω (typ) when VDD = 5.5V. This wiper resistance appears as an error in the resistance value of the digital potentiometer only at lower programmed settings. For instance, with the MCP42100, the nominal resistance step for each code is equal to 100 kΩ/256, or 390.625Ω. With a digital code setting of ‘1’, the ideal nominal resistance is 390.625Ω. However, with the added wiper resistance, this resistance is nominally 515.625Ω. DS00737C-page 6 2004 Microchip Technology Inc. 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